TSTP Solution File: ITP279^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP279^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 03:30:48 EDT 2023
% Result : Timeout 299.35s 300.13s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.41/2.42 % Problem : ITP279^1 : TPTP v8.1.2. Released v8.1.0.
% 2.41/2.43 % Command : do_cvc5 %s %d
% 2.44/2.64 % Computer : n012.cluster.edu
% 2.44/2.64 % Model : x86_64 x86_64
% 2.44/2.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.44/2.64 % Memory : 8042.1875MB
% 2.44/2.64 % OS : Linux 3.10.0-693.el7.x86_64
% 2.44/2.64 % CPULimit : 300
% 2.44/2.64 % WCLimit : 300
% 2.44/2.64 % DateTime : Sun Aug 27 16:52:12 EDT 2023
% 2.44/2.64 % CPUTime :
% 4.97/5.15 %----Proving TH0
% 4.97/5.15 %------------------------------------------------------------------------------
% 4.97/5.15 % File : ITP279^1 : TPTP v8.1.2. Released v8.1.0.
% 4.97/5.15 % Domain : Interactive Theorem Proving
% 4.97/5.15 % Problem : Sledgehammer problem VEBT_Space 00164_007689
% 4.97/5.15 % Version : [Des22] axioms.
% 4.97/5.15 % English :
% 4.97/5.15
% 4.97/5.15 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 4.97/5.15 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 4.97/5.15 % Source : [Des22]
% 4.97/5.15 % Names : 0076_VEBT_Space_00164_007689 [Des22]
% 4.97/5.15
% 4.97/5.15 % Status : Theorem
% 4.97/5.15 % Rating : 0.92 v8.1.0
% 4.97/5.15 % Syntax : Number of formulae : 11111 (6427 unt; 864 typ; 0 def)
% 4.97/5.15 % Number of atoms : 24896 (11740 equ; 0 cnn)
% 4.97/5.15 % Maximal formula atoms : 71 ( 2 avg)
% 4.97/5.15 % Number of connectives : 96809 (2254 ~; 489 |;1283 &;84973 @)
% 4.97/5.15 % ( 0 <=>;7810 =>; 0 <=; 0 <~>)
% 4.97/5.15 % Maximal formula depth : 39 ( 5 avg)
% 4.97/5.15 % Number of types : 93 ( 92 usr)
% 4.97/5.15 % Number of type conns : 2422 (2422 >; 0 *; 0 +; 0 <<)
% 4.97/5.15 % Number of symbols : 775 ( 772 usr; 56 con; 0-8 aty)
% 4.97/5.15 % Number of variables : 22187 (1489 ^;20162 !; 536 ?;22187 :)
% 4.97/5.15 % SPC : TH0_THM_EQU_NAR
% 4.97/5.15
% 4.97/5.15 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.97/5.15 % from the van Emde Boas Trees session in the Archive of Formal
% 4.97/5.15 % proofs -
% 4.97/5.15 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 4.97/5.15 % 2022-02-18 16:54:12.966
% 4.97/5.15 %------------------------------------------------------------------------------
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__List__Olist_It__Complex__Ocomplex_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__List__Olist_I_Eo_J_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Filter__Ofilter_It__Real__Oreal_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Filter__Ofilter_It__Int__Oint_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__VEBT____Definitions__OVEBT,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 4.97/5.16 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 4.97/5.16 thf(ty_n_t__Code____Numeral__Ointeger,type,
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% 4.97/5.16 thf(ty_n_t__Extended____Nat__Oenat,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__List__Olist_I_Eo_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Complex__Ocomplex,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Set__Oset_I_Eo_J,type,
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% 4.97/5.16
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Real__Oreal,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Rat__Orat,type,
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% 4.97/5.16 thf(ty_n_t__Num__Onum,type,
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% 4.97/5.16
% 4.97/5.16 thf(ty_n_t__Nat__Onat,type,
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% 4.97/5.16 thf(ty_n_t__Int__Oint,type,
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% 4.97/5.16 % Explicit typings (772)
% 4.97/5.16 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
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% 4.97/5.16 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Oand__int__rel,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Oand__not__num,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Oconcat__bit,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
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% 4.97/5.16 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
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% 4.97/5.16 has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Oadjust__div,type,
% 4.97/5.16 adjust_div: product_prod_int_int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Oadjust__mod,type,
% 4.97/5.16 adjust_mod: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Odivmod__nat,type,
% 4.97/5.16 divmod_nat: nat > nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Oeucl__rel__int,type,
% 4.97/5.16 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 4.97/5.16 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 4.97/5.16 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 4.97/5.16 unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 4.97/5.16 unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 4.97/5.16 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 4.97/5.16 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Complex__Ocomplex,type,
% 4.97/5.16 comm_s2602460028002588243omplex: complex > nat > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 4.97/5.16 comm_s4660882817536571857er_int: int > nat > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 4.97/5.16 comm_s4663373288045622133er_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 4.97/5.16 comm_s4028243227959126397er_rat: rat > nat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Real__Oreal,type,
% 4.97/5.16 comm_s7457072308508201937r_real: real > nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 semiri3624122377584611663nteger: nat > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 4.97/5.16 semiri5044797733671781792omplex: nat > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 4.97/5.16 semiri1406184849735516958ct_int: nat > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 4.97/5.16 semiri1408675320244567234ct_nat: nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 4.97/5.16 semiri773545260158071498ct_rat: nat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 4.97/5.16 semiri2265585572941072030t_real: nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 4.97/5.16 invers8013647133539491842omplex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 4.97/5.16 inverse_inverse_rat: rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 4.97/5.16 inverse_inverse_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 4.97/5.16 at_bot_real: filter_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oat__top_001t__Int__Oint,type,
% 4.97/5.16 at_top_int: filter_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 4.97/5.16 at_top_nat: filter_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 4.97/5.16 at_top_real: filter_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 4.97/5.16 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 4.97/5.16 eventually_real: ( real > $o ) > filter_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Int__Oint,type,
% 4.97/5.16 filterlim_nat_int: ( nat > int ) > filter_int > filter_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 4.97/5.16 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 4.97/5.16 finite_card_o: set_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 4.97/5.16 finite_card_complex: set_complex > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 4.97/5.16 finite_card_int: set_int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 finite_card_list_nat: set_list_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 4.97/5.16 finite_card_nat: set_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 4.97/5.16 finite410649719033368117t_unit: set_Product_unit > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 finite_card_set_nat: set_set_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 4.97/5.16 finite_card_char: set_char > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 4.97/5.16 finite3207457112153483333omplex: set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 4.97/5.16 finite_finite_int: set_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 4.97/5.16 finite_finite_nat: set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.97/5.16 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 4.97/5.16 bij_be8532844293280997160at_nat: ( list_nat > nat ) > set_list_nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 4.97/5.16 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Obij__betw_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 4.97/5.16 bij_be5333170631980326235at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Nat__Onat,type,
% 4.97/5.16 comp_C2179886998970519596um_nat: ( code_integer > num ) > ( nat > code_integer ) > nat > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 4.97/5.16 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 4.97/5.16 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 comp_int_real_real: ( int > real ) > ( real > int ) > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 4.97/5.16 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 4.97/5.16 gcd_Gcd_int: set_int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 4.97/5.16 gcd_Gcd_nat: set_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Obezw,type,
% 4.97/5.16 bezw: nat > nat > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Obezw__rel,type,
% 4.97/5.16 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 4.97/5.16 gcd_gcd_int: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 4.97/5.16 gcd_gcd_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 4.97/5.16 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 abs_abs_Code_integer: code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 4.97/5.16 abs_abs_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 4.97/5.16 abs_abs_int: int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 4.97/5.16 abs_abs_rat: rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 4.97/5.16 abs_abs_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 4.97/5.16 minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 4.97/5.16 minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 4.97/5.16 minus_1139252259498527702_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
% 4.97/5.16 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
% 4.97/5.16 minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 4.97/5.16 minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 4.97/5.16 minus_minus_complex: complex > complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 4.97/5.16 minus_minus_int: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 4.97/5.16 minus_minus_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 4.97/5.16 minus_minus_rat: rat > rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 4.97/5.16 minus_minus_real: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.97/5.16 minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
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% 4.97/5.16
% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
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% 4.97/5.16 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 4.97/5.16 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
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% 4.97/5.16
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% 4.97/5.16 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
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% 4.97/5.16 thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
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% 4.97/5.16
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% 4.97/5.16
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% 4.97/5.16
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% 4.97/5.16
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% 4.97/5.16
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% 4.97/5.16
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% 4.97/5.16 append_int: list_int > list_int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 4.97/5.16 append_nat: list_nat > list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001_Eo,type,
% 4.97/5.16 concat_o: list_list_o > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 4.97/5.16 concat_int: list_list_int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 4.97/5.16 concat_nat: list_list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.97/5.16 concat5449216342283422845nteger: list_l1551831396326329630nteger > list_P5311841565141990158nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.97/5.16 concat3620511419746071180nt_int: list_l5644688499257182253nt_int > list_P8915022641806594461nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.97/5.16 concat1359917873574114197nteger: list_l7035113777618258358nteger > list_P7828571989066258726nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.97/5.16 concat27718206033014914nt_int: list_l6845168789323398563nt_int > list_P651320350408439699nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 concat4512918505337516154nt_int: list_l1670014477004246597nt_int > list_P5707943133018811711nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__Real__Oreal,type,
% 4.97/5.16 concat_real: list_list_real > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 4.97/5.16 distinct_int: list_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 4.97/5.16 distinct_nat: list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Ofoldr_001_Eo_001t__Int__Oint,type,
% 4.97/5.16 foldr_o_int: ( $o > int > int ) > list_o > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 4.97/5.16 linord2614967742042102400et_nat: set_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 4.97/5.16 cons_int: int > list_int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 4.97/5.16 cons_nat: nat > list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 4.97/5.16 nil_int: list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 4.97/5.16 nil_nat: list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 4.97/5.16 hd_nat: list_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 4.97/5.16 map_Co3516991824712006758nteger: ( ( code_integer > option6357759511663192854e_term ) > list_P5311841565141990158nteger ) > list_C878401137130745250e_term > list_l1551831396326329630nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 4.97/5.16 map_in2673801078721063236nt_int: ( ( int > option6357759511663192854e_term ) > list_P8915022641806594461nt_int ) > list_i8448526496819171953e_term > list_l5644688499257182253nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 4.97/5.16 map_Pr1383036205076807398nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > list_P7828571989066258726nteger ) > list_P1316552470764441098e_term > list_l7035113777618258358nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__List__Olist_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 4.97/5.16 map_Pr6227401909088194244nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > list_P651320350408439699nt_int ) > list_P1743416141875011707e_term > list_l6845168789323398563nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_Eo_001_Eo,type,
% 4.97/5.16 map_o_o: ( $o > $o ) > list_o > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_Eo_001t__Int__Oint,type,
% 4.97/5.16 map_o_int: ( $o > int ) > list_o > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_Eo_001t__Nat__Onat,type,
% 4.97/5.16 map_o_nat: ( $o > nat ) > list_o > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_Eo_001t__Real__Oreal,type,
% 4.97/5.16 map_o_real: ( $o > real ) > list_o > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 map_o_VEBT_VEBT: ( $o > vEBT_VEBT ) > list_o > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.97/5.16 map_complex_complex: ( complex > complex ) > list_complex > list_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001_Eo,type,
% 4.97/5.16 map_int_o: ( int > $o ) > list_int > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 map_int_int: ( int > int ) > list_int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.97/5.16 map_in7266296235447420877nt_int: ( int > list_P5707943133018811711nt_int ) > list_int > list_l1670014477004246597nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Nat__Onat,type,
% 4.97/5.16 map_int_nat: ( int > nat ) > list_int > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 map_in7157766398909135175nt_int: ( int > product_prod_int_int ) > list_int > list_P5707943133018811711nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Real__Oreal,type,
% 4.97/5.16 map_int_real: ( int > real ) > list_int > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 map_int_VEBT_VEBT: ( int > vEBT_VEBT ) > list_int > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 map_li7225945977422193158st_nat: ( list_nat > list_nat ) > list_list_nat > list_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 map_li576258494306137302st_nat: ( list_VEBT_VEBT > list_nat ) > list_list_VEBT_VEBT > list_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__List__Olist_It__Real__Oreal_J,type,
% 4.97/5.16 map_li2470829856544091186t_real: ( list_VEBT_VEBT > list_real ) > list_list_VEBT_VEBT > list_list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001_Eo,type,
% 4.97/5.16 map_nat_o: ( nat > $o ) > list_nat > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Int__Oint,type,
% 4.97/5.16 map_nat_int: ( nat > int ) > list_nat > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Real__Oreal,type,
% 4.97/5.16 map_nat_real: ( nat > real ) > list_nat > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 map_nat_VEBT_VEBT: ( nat > vEBT_VEBT ) > list_nat > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.97/5.16 map_Pr6982716525268357333nteger: ( produc8923325533196201883nteger > produc8763457246119570046nteger ) > list_P5578671422887162913nteger > list_P5311841565141990158nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.97/5.16 map_Pr4561634935768196077nteger: ( produc8923325533196201883nteger > produc1908205239877642774nteger ) > list_P5578671422887162913nteger > list_P7828571989066258726nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.97/5.16 map_Pr1306541819098601986nt_int: ( product_prod_int_int > produc7773217078559923341nt_int ) > list_P5707943133018811711nt_int > list_P8915022641806594461nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.97/5.16 map_Pr1898935522916328184nt_int: ( product_prod_int_int > produc2285326912895808259nt_int ) > list_P5707943133018811711nt_int > list_P651320350408439699nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 map_real_real: ( real > real ) > list_real > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 map_set_nat_set_nat: ( set_nat > set_nat ) > list_set_nat > list_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 4.97/5.16 map_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.97/5.16 map_VEBT_VEBT_int: ( vEBT_VEBT > int ) > list_VEBT_VEBT > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.97/5.16 map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 4.97/5.16 map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 4.97/5.16 set_o2: list_o > set_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 4.97/5.16 set_complex2: list_complex > set_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 4.97/5.16 set_int2: list_int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 4.97/5.16 set_list_o2: list_list_o > set_list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 4.97/5.16 set_list_int2: list_list_int > set_list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 set_list_nat2: list_list_nat > set_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 4.97/5.16 set_nat2: list_nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 4.97/5.16 set_real2: list_real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 set_set_nat2: list_set_nat > set_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 4.97/5.16 tl_nat: list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001_Eo,type,
% 4.97/5.16 nth_o: list_o > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 4.97/5.16 nth_complex: list_complex > nat > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 4.97/5.16 nth_int: list_int > nat > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 4.97/5.16 nth_nat: list_nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 4.97/5.16 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 4.97/5.16 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 4.97/5.16 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 4.97/5.16 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 4.97/5.16 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 4.97/5.16 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.97/5.16 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 4.97/5.16 nth_real: list_real > nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 nth_set_nat: list_set_nat > nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 produc4846348955484107138nteger: list_C878401137130745250e_term > list_P5578671422887162913nteger > list_P5311841565141990158nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 produc5707002291657922193nt_int: list_i8448526496819171953e_term > list_P5707943133018811711nt_int > list_P8915022641806594461nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 produc2929234284598166170nteger: list_P1316552470764441098e_term > list_P5578671422887162913nteger > list_P7828571989066258726nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 produc8640348060098379399nt_int: list_P1743416141875011707e_term > list_P5707943133018811711nt_int > list_P651320350408439699nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 4.97/5.16 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 4.97/5.16 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 4.97/5.16 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 4.97/5.16 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 4.97/5.16 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.97/5.16 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.97/5.16 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 4.97/5.16 remdups_nat: list_nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001_Eo,type,
% 4.97/5.16 replicate_o: nat > $o > list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 4.97/5.16 replicate_complex: nat > complex > list_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 4.97/5.16 replicate_int: nat > int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 4.97/5.16 replicate_nat: nat > nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 4.97/5.16 replicate_real: nat > real > list_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 replicate_set_nat: nat > set_nat > list_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 4.97/5.16 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 4.97/5.16 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osubseqs_001_Eo,type,
% 4.97/5.16 subseqs_o: list_o > list_list_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 4.97/5.16 subseqs_int: list_int > list_list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 4.97/5.16 subseqs_nat: list_nat > list_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oupt,type,
% 4.97/5.16 upt: nat > nat > list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oupto,type,
% 4.97/5.16 upto: int > int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oupto__aux,type,
% 4.97/5.16 upto_aux: int > int > list_int > list_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_List_Oupto__rel,type,
% 4.97/5.16 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_OSuc,type,
% 4.97/5.16 suc: nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 4.97/5.16 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 4.97/5.16 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.97/5.16 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Onat_Opred,type,
% 4.97/5.16 pred: nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 semiri4939895301339042750nteger: nat > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 4.97/5.16 semiri8010041392384452111omplex: nat > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 4.97/5.16 semiri1314217659103216013at_int: nat > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 4.97/5.16 semiri1316708129612266289at_nat: nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 4.97/5.16 semiri681578069525770553at_rat: nat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 4.97/5.16 semiri5074537144036343181t_real: nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 4.97/5.16 size_size_list_o: list_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 4.97/5.16 size_s3451745648224563538omplex: list_complex > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 4.97/5.16 size_size_list_int: list_int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 4.97/5.16 size_s2710708370519433104list_o: list_list_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 4.97/5.16 size_s533118279054570080st_int: list_list_int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 4.97/5.16 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 4.97/5.16 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 size_size_list_nat: list_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 4.97/5.16 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 4.97/5.16 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 4.97/5.16 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 4.97/5.16 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 4.97/5.16 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 4.97/5.16 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 4.97/5.16 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 4.97/5.16 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 4.97/5.16 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 4.97/5.16 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 4.97/5.16 size_size_list_real: list_real > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.97/5.16 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 4.97/5.16 size_size_num: num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.97/5.16 size_size_option_num: option_num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.97/5.16 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 4.97/5.16 size_size_char: char > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 4.97/5.16 nat_list_encode: list_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 4.97/5.16 nat_list_encode_rel: list_nat > list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 4.97/5.16 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 4.97/5.16 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 4.97/5.16 nat_prod_encode: product_prod_nat_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 4.97/5.16 nat_set_decode: nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 4.97/5.16 nat_set_encode: set_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Nat__Bijection_Otriangle,type,
% 4.97/5.16 nat_triangle: nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_NthRoot_Oroot,type,
% 4.97/5.16 root: nat > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_NthRoot_Osqrt,type,
% 4.97/5.16 sqrt: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_OBitM,type,
% 4.97/5.16 bitM: num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oinc,type,
% 4.97/5.16 inc: num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 4.97/5.16 neg_nu7009210354673126013omplex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 4.97/5.16 neg_numeral_dbl_int: int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 4.97/5.16 neg_numeral_dbl_rat: rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 4.97/5.16 neg_numeral_dbl_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 4.97/5.16 neg_nu6511756317524482435omplex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 4.97/5.16 neg_nu3811975205180677377ec_int: int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 4.97/5.16 neg_nu3179335615603231917ec_rat: rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 4.97/5.16 neg_nu6075765906172075777c_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 4.97/5.16 neg_nu8557863876264182079omplex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 4.97/5.16 neg_nu5851722552734809277nc_int: int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 4.97/5.16 neg_nu5219082963157363817nc_rat: rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 4.97/5.16 neg_nu8295874005876285629c_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 4.97/5.16 neg_numeral_sub_int: num > num > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum_OBit0,type,
% 4.97/5.16 bit0: num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum_OBit1,type,
% 4.97/5.16 bit1: num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum_OOne,type,
% 4.97/5.16 one: num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.97/5.16 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum_Osize__num,type,
% 4.97/5.16 size_num: num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onum__of__nat,type,
% 4.97/5.16 num_of_nat: nat > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 numera6620942414471956472nteger: num > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 4.97/5.16 numera6690914467698888265omplex: num > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 numera1916890842035813515d_enat: num > extended_enat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 4.97/5.16 numeral_numeral_int: num > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 4.97/5.16 numeral_numeral_nat: num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 4.97/5.16 numeral_numeral_rat: num > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 4.97/5.16 numeral_numeral_real: num > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Opow,type,
% 4.97/5.16 pow: num > num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Opred__numeral,type,
% 4.97/5.16 pred_numeral: num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Num_Osqr,type,
% 4.97/5.16 sqr: num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 4.97/5.16 none_num: option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 4.97/5.16 some_num: num > option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 4.97/5.16 case_option_int_num: int > ( num > int ) > option_num > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 4.97/5.16 case_option_num_num: num > ( num > num ) > option_num > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 4.97/5.16 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 4.97/5.16 size_option_num: ( num > nat ) > option_num > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 bot_bo4199563552545308370d_enat: extended_enat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 4.97/5.16 bot_bot_nat: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 4.97/5.16 bot_bot_set_int: set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 bot_bot_set_nat: set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.97/5.16 bot_bot_set_real: set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 4.97/5.16 ord_less_int: int > int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 4.97/5.16 ord_less_nat: nat > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 4.97/5.16 ord_less_num: num > num > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 4.97/5.16 ord_less_rat: rat > rat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 4.97/5.16 ord_less_real: real > real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.97/5.16 ord_less_set_complex: set_complex > set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 4.97/5.16 ord_less_set_int: set_int > set_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 ord_less_set_nat: set_nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.97/5.16 ord_less_set_real: set_real > set_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.97/5.16 ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 4.97/5.16 ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_Eo_J,type,
% 4.97/5.16 ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 4.97/5.16 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 4.97/5.16 ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 4.97/5.16 ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 4.97/5.16 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Real__Oreal_J,type,
% 4.97/5.16 ord_le4104064031414453916r_real: filter_real > filter_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 4.97/5.16 ord_less_eq_int: int > int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 4.97/5.16 ord_less_eq_nat: nat > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 4.97/5.16 ord_less_eq_num: num > num > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 4.97/5.16 ord_less_eq_rat: rat > rat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 4.97/5.16 ord_less_eq_real: real > real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.97/5.16 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 4.97/5.16 ord_less_eq_set_int: set_int > set_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 4.97/5.16 ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.97/5.16 ord_less_eq_set_real: set_real > set_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.97/5.16 ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Omax_001t__Extended____Nat__Oenat,type,
% 4.97/5.16 ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 4.97/5.16 ord_max_int: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 4.97/5.16 ord_max_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 4.97/5.16 order_Greatest_nat: ( nat > $o ) > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 4.97/5.16 top_top_set_o: set_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
% 4.97/5.16 top_top_set_int: set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 4.97/5.16 top_top_set_list_nat: set_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 top_top_set_nat: set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.97/5.16 top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.97/5.16 top_to1996260823553986621t_unit: set_Product_unit ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.97/5.16 top_top_set_real: set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 4.97/5.16 top_top_set_char: set_char ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 4.97/5.16 power_power_complex: complex > nat > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 4.97/5.16 power_power_int: int > nat > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 4.97/5.16 power_power_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 4.97/5.16 power_power_rat: rat > nat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 4.97/5.16 power_power_real: real > nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 4.97/5.16 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 4.97/5.16 product_Pair_o_int: $o > int > product_prod_o_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 4.97/5.16 product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 4.97/5.16 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 product_Pair_int_int: int > int > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 4.97/5.16 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 4.97/5.16 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 4.97/5.16 product_Pair_num_num: num > num > product_prod_num_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 4.97/5.16 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.97/5.16 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.97/5.16 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 4.97/5.16 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.97/5.16 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 4.97/5.16 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 4.97/5.16 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.97/5.16 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 4.97/5.16 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 4.97/5.16 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.97/5.16 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 4.97/5.16 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.97/5.16 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 product_fst_int_int: product_prod_int_int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 product_snd_int_int: product_prod_int_int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rat_OFrct,type,
% 4.97/5.16 frct: product_prod_int_int > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rat_Onormalize,type,
% 4.97/5.16 normalize: product_prod_int_int > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rat_Oof__int,type,
% 4.97/5.16 of_int: int > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rat_Oquotient__of,type,
% 4.97/5.16 quotient_of: rat > product_prod_int_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 4.97/5.16 real_V2521375963428798218omplex: set_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 4.97/5.16 real_V3694042436643373181omplex: complex > complex > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 4.97/5.16 real_V975177566351809787t_real: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 4.97/5.16 real_V1022390504157884413omplex: complex > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 4.97/5.16 real_V7735802525324610683m_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 4.97/5.16 real_V4546457046886955230omplex: real > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 4.97/5.16 real_V1803761363581548252l_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 4.97/5.16 real_V2046097035970521341omplex: real > complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 4.97/5.16 real_V1485227260804924795R_real: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 4.97/5.16 divide1717551699836669952omplex: complex > complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 4.97/5.16 divide_divide_int: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 4.97/5.16 divide_divide_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 4.97/5.16 divide_divide_rat: rat > rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 4.97/5.16 divide_divide_real: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 4.97/5.16 dvd_dvd_complex: complex > complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 4.97/5.16 dvd_dvd_int: int > int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 4.97/5.16 dvd_dvd_nat: nat > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 4.97/5.16 dvd_dvd_rat: rat > rat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 4.97/5.16 dvd_dvd_real: real > real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 4.97/5.16 modulo_modulo_int: int > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 4.97/5.16 modulo_modulo_nat: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 zero_n356916108424825756nteger: $o > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 4.97/5.16 zero_n1201886186963655149omplex: $o > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 4.97/5.16 zero_n2684676970156552555ol_int: $o > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 4.97/5.16 zero_n2687167440665602831ol_nat: $o > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 4.97/5.16 zero_n2052037380579107095ol_rat: $o > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 4.97/5.16 zero_n3304061248610475627l_real: $o > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 4.97/5.16 suminf_complex: ( nat > complex ) > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
% 4.97/5.16 suminf_int: ( nat > int ) > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 4.97/5.16 suminf_nat: ( nat > nat ) > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 4.97/5.16 suminf_real: ( nat > real ) > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 4.97/5.16 summable_complex: ( nat > complex ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
% 4.97/5.16 summable_int: ( nat > int ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 4.97/5.16 summable_nat: ( nat > nat ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 4.97/5.16 summable_real: ( nat > real ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 4.97/5.16 sums_real: ( nat > real ) > real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 4.97/5.16 collect_complex: ( complex > $o ) > set_complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 4.97/5.16 collect_int: ( int > $o ) > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 4.97/5.16 collect_nat: ( nat > $o ) > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 4.97/5.16 collect_real: ( real > $o ) > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 4.97/5.16 pow_nat: set_nat > set_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 4.97/5.16 image_int_int: ( int > int ) > set_int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 4.97/5.16 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 4.97/5.16 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 4.97/5.16 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.97/5.16 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 4.97/5.16 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 4.97/5.16 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 4.97/5.16 image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 image_real_real: ( real > real ) > set_real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 4.97/5.16 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 4.97/5.16 insert_int: int > set_int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 4.97/5.16 insert_nat: nat > set_nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 4.97/5.16 insert_real: real > set_real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 4.97/5.16 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 4.97/5.16 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 4.97/5.16 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 4.97/5.16 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 4.97/5.16 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 4.97/5.16 set_or1266510415728281911st_int: int > int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 4.97/5.16 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 4.97/5.16 set_or1222579329274155063t_real: real > real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 4.97/5.16 set_or4662586982721622107an_int: int > int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 4.97/5.16 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 4.97/5.16 set_ord_atLeast_nat: nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 4.97/5.16 set_ord_atMost_int: int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 4.97/5.16 set_ord_atMost_nat: nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 4.97/5.16 set_or6656581121297822940st_int: int > int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 4.97/5.16 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 4.97/5.16 set_or5832277885323065728an_int: int > int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 4.97/5.16 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 4.97/5.16 set_or1633881224788618240n_real: real > real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 4.97/5.16 set_or1210151606488870762an_nat: nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 4.97/5.16 set_or5849166863359141190n_real: real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 4.97/5.16 set_ord_lessThan_int: int > set_int ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 4.97/5.16 set_ord_lessThan_nat: nat > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 4.97/5.16 set_or5984915006950818249n_real: real > set_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Oascii__of,type,
% 4.97/5.16 ascii_of: char > char ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Ochar_OChar,type,
% 4.97/5.16 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Ochar_Osize__char,type,
% 4.97/5.16 size_char: char > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 4.97/5.16 comm_s629917340098488124ar_nat: char > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Ointeger__of__char,type,
% 4.97/5.16 integer_of_char: char > code_integer ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 4.97/5.16 unique3096191561947761185of_nat: nat > char ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.97/5.16 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 4.97/5.16 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 4.97/5.16 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 4.97/5.16 topolo2815343760600316023s_real: real > filter_real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 4.97/5.16 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 4.97/5.16 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oarccos,type,
% 4.97/5.16 arccos: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 4.97/5.16 arcosh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oarcsin,type,
% 4.97/5.16 arcsin: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oarctan,type,
% 4.97/5.16 arctan: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 4.97/5.16 arsinh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 4.97/5.16 artanh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 4.97/5.16 cos_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 4.97/5.16 cos_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocos__coeff,type,
% 4.97/5.16 cos_coeff: nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 4.97/5.16 cosh_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 4.97/5.16 cosh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 4.97/5.16 cot_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 4.97/5.16 cot_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 4.97/5.16 diffs_real: ( nat > real ) > nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 4.97/5.16 exp_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 4.97/5.16 exp_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 4.97/5.16 ln_ln_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Olog,type,
% 4.97/5.16 log: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Opi,type,
% 4.97/5.16 pi: real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 4.97/5.16 powr_real: real > real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 4.97/5.16 sin_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 4.97/5.16 sin_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Osin__coeff,type,
% 4.97/5.16 sin_coeff: nat > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 4.97/5.16 sinh_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 4.97/5.16 sinh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 4.97/5.16 tan_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 4.97/5.16 tan_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 4.97/5.16 tanh_complex: complex > complex ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 4.97/5.16 tanh_real: real > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 4.97/5.16 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 4.97/5.16 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 4.97/5.16 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 4.97/5.16 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 4.97/5.16 vEBT_VEBT_high: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 4.97/5.16 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 4.97/5.16 vEBT_VEBT_low: nat > nat > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 4.97/5.16 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 4.97/5.16 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 4.97/5.16 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 4.97/5.16 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 4.97/5.16 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 4.97/5.16 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 4.97/5.16 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 4.97/5.16 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 4.97/5.16 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt,type,
% 4.97/5.16 vEBT_VEBT_cnt: vEBT_VEBT > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt__rel,type,
% 4.97/5.16 vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace,type,
% 4.97/5.16 vEBT_VEBT_space: vEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H,type,
% 4.97/5.16 vEBT_VEBT_space2: vEBT_VEBT > nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H__rel,type,
% 4.97/5.16 vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace__rel,type,
% 4.97/5.16 vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 4.97/5.16 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.97/5.16 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.97/5.16 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 4.97/5.16 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.97/5.16 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_Wellfounded_Opred__nat,type,
% 4.97/5.16 pred_nat: set_Pr1261947904930325089at_nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 4.97/5.16 fChoice_real: ( real > $o ) > real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001_Eo,type,
% 4.97/5.16 member_o: $o > set_o > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 4.97/5.16 member_Code_integer: code_integer > set_Code_integer > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 4.97/5.16 member_complex: complex > set_complex > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Int__Oint,type,
% 4.97/5.16 member_int: int > set_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 4.97/5.16 member_list_o: list_o > set_list_o > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 4.97/5.16 member_list_int: list_int > set_list_int > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 4.97/5.16 member_list_nat: list_nat > set_list_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.97/5.16 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Nat__Onat,type,
% 4.97/5.16 member_nat: nat > set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Rat__Orat,type,
% 4.97/5.16 member_rat: rat > set_rat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Real__Oreal,type,
% 4.97/5.16 member_real: real > set_real > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.97/5.16 member_set_nat: set_nat > set_set_nat > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 4.97/5.16 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_c,type,
% 4.97/5.16 c: real ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_deg____,type,
% 4.97/5.16 deg: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_m____,type,
% 4.97/5.16 m: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_ma____,type,
% 4.97/5.16 ma: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_mi____,type,
% 4.97/5.16 mi: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_na____,type,
% 4.97/5.16 na: nat ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_summary____,type,
% 4.97/5.16 summary: vEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 thf(sy_v_treeList____,type,
% 4.97/5.16 treeList: list_VEBT_VEBT ).
% 4.97/5.16
% 4.97/5.16 % Relevant facts (10208)
% 4.97/5.16 thf(fact_0__C4_Ohyps_C_I3_J,axiom,
% 4.97/5.16 m = na ).
% 4.97/5.16
% 4.97/5.16 % "4.hyps"(3)
% 4.97/5.16 thf(fact_1_c__def,axiom,
% 4.97/5.16 ( c
% 4.97/5.16 = ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % c_def
% 4.97/5.16 thf(fact_2__C4_Ohyps_C_I7_J,axiom,
% 4.97/5.16 ord_less_eq_nat @ mi @ ma ).
% 4.97/5.16
% 4.97/5.16 % "4.hyps"(7)
% 4.97/5.16 thf(fact_3__C4_OIH_C_I2_J,axiom,
% 4.97/5.16 ord_less_eq_real @ ( vEBT_VEBT_cnt @ summary ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ m ) @ c ) ) ).
% 4.97/5.16
% 4.97/5.16 % "4.IH"(2)
% 4.97/5.16 thf(fact_4__092_060open_062cnt_A_INode_ANone_Adeg_AtreeList_Asummary_J_A_092_060le_062_A2_A_K_A_I2_A_094_A_In_A_L_An_J_A_N_A15_A_P_A10_J_092_060close_062,axiom,
% 4.97/5.16 ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ deg @ treeList @ summary ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % \<open>cnt (Node None deg treeList summary) \<le> 2 * (2 ^ (n + n) - 15 / 10)\<close>
% 4.97/5.16 thf(fact_5__C4_Ohyps_C_I4_J,axiom,
% 4.97/5.16 ( deg
% 4.97/5.16 = ( plus_plus_nat @ na @ m ) ) ).
% 4.97/5.16
% 4.97/5.16 % "4.hyps"(4)
% 4.97/5.16 thf(fact_6_left__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [A: complex,B: complex,V: num] :
% 4.97/5.16 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 4.97/5.16 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % left_diff_distrib_numeral
% 4.97/5.16 thf(fact_7_left__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [A: real,B: real,V: num] :
% 4.97/5.16 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.97/5.16 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % left_diff_distrib_numeral
% 4.97/5.16 thf(fact_8_left__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [A: rat,B: rat,V: num] :
% 4.97/5.16 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.97/5.16 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % left_diff_distrib_numeral
% 4.97/5.16 thf(fact_9_left__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [A: int,B: int,V: num] :
% 4.97/5.16 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.97/5.16 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % left_diff_distrib_numeral
% 4.97/5.16 thf(fact_10_right__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [V: num,B: complex,C: complex] :
% 4.97/5.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 4.97/5.16 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % right_diff_distrib_numeral
% 4.97/5.16 thf(fact_11_right__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [V: num,B: real,C: real] :
% 4.97/5.16 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 4.97/5.16 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % right_diff_distrib_numeral
% 4.97/5.16 thf(fact_12_right__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [V: num,B: rat,C: rat] :
% 4.97/5.16 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 4.97/5.16 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % right_diff_distrib_numeral
% 4.97/5.16 thf(fact_13_right__diff__distrib__numeral,axiom,
% 4.97/5.16 ! [V: num,B: int,C: int] :
% 4.97/5.16 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 4.97/5.16 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % right_diff_distrib_numeral
% 4.97/5.16 thf(fact_14__092_060open_062_092_060forall_062t_092_060in_062set_AtreeList_O_Acnt_At_A_092_060le_062_A2_A_K_A_I2_A_094_An_A_N_Ac_J_092_060close_062,axiom,
% 4.97/5.16 ! [X: vEBT_VEBT] :
% 4.97/5.16 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 4.97/5.16 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ c ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % \<open>\<forall>t\<in>set treeList. cnt t \<le> 2 * (2 ^ n - c)\<close>
% 4.97/5.16 thf(fact_15_semiring__norm_I85_J,axiom,
% 4.97/5.16 ! [M: num] :
% 4.97/5.16 ( ( bit0 @ M )
% 4.97/5.16 != one ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(85)
% 4.97/5.16 thf(fact_16_semiring__norm_I83_J,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( one
% 4.97/5.16 != ( bit0 @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(83)
% 4.97/5.16 thf(fact_17_numeral__times__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.16 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_times_numeral
% 4.97/5.16 thf(fact_18_numeral__times__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.16 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_times_numeral
% 4.97/5.16 thf(fact_19_numeral__times__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.16 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_times_numeral
% 4.97/5.16 thf(fact_20_numeral__times__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.16 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_times_numeral
% 4.97/5.16 thf(fact_21_numeral__times__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.16 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_times_numeral
% 4.97/5.16 thf(fact_22_mult__numeral__left__semiring__numeral,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: complex] :
% 4.97/5.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 4.97/5.16 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % mult_numeral_left_semiring_numeral
% 4.97/5.16 thf(fact_23_mult__numeral__left__semiring__numeral,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: real] :
% 4.97/5.16 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 4.97/5.16 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % mult_numeral_left_semiring_numeral
% 4.97/5.16 thf(fact_24_mult__numeral__left__semiring__numeral,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: rat] :
% 4.97/5.16 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 4.97/5.16 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % mult_numeral_left_semiring_numeral
% 4.97/5.16 thf(fact_25_mult__numeral__left__semiring__numeral,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: nat] :
% 4.97/5.16 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 4.97/5.16 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % mult_numeral_left_semiring_numeral
% 4.97/5.16 thf(fact_26_mult__numeral__left__semiring__numeral,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: int] :
% 4.97/5.16 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 4.97/5.16 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % mult_numeral_left_semiring_numeral
% 4.97/5.16 thf(fact_27_numeral__le__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_le_iff
% 4.97/5.16 thf(fact_28_numeral__le__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_le_iff
% 4.97/5.16 thf(fact_29_numeral__le__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_le_iff
% 4.97/5.16 thf(fact_30_numeral__le__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_le_iff
% 4.97/5.16 thf(fact_31__092_060open_062cnt_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_A_092_060le_062_A2_A_K_A_I2_A_094_An_A_L_A1_J_A_K_A_I2_A_094_An_A_N_Ac_J_A_L_A1_092_060close_062,axiom,
% 4.97/5.16 ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) ) @ ( plus_plus_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ one_one_real ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ c ) ) @ one_one_real ) ).
% 4.97/5.16
% 4.97/5.16 % \<open>cnt (Node (Some (mi, ma)) deg treeList summary) \<le> 2 * (2 ^ n + 1) * (2 ^ n - c) + 1\<close>
% 4.97/5.16 thf(fact_32__C4_OIH_C_I1_J,axiom,
% 4.97/5.16 ! [X: vEBT_VEBT] :
% 4.97/5.16 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 4.97/5.16 => ( ( vEBT_invar_vebt @ X @ na )
% 4.97/5.16 & ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ c ) ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % "4.IH"(1)
% 4.97/5.16 thf(fact_33_power2__diff,axiom,
% 4.97/5.16 ! [X2: complex,Y: complex] :
% 4.97/5.16 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.16 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % power2_diff
% 4.97/5.16 thf(fact_34_power2__diff,axiom,
% 4.97/5.16 ! [X2: real,Y: real] :
% 4.97/5.16 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.16 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % power2_diff
% 4.97/5.16 thf(fact_35_power2__diff,axiom,
% 4.97/5.16 ! [X2: rat,Y: rat] :
% 4.97/5.16 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.16 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % power2_diff
% 4.97/5.16 thf(fact_36_power2__diff,axiom,
% 4.97/5.16 ! [X2: int,Y: int] :
% 4.97/5.16 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.16 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % power2_diff
% 4.97/5.16 thf(fact_37__C4_Ohyps_C_I1_J,axiom,
% 4.97/5.16 vEBT_invar_vebt @ summary @ m ).
% 4.97/5.16
% 4.97/5.16 % "4.hyps"(1)
% 4.97/5.16 thf(fact_38_numeral__eq__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( numera6690914467698888265omplex @ M )
% 4.97/5.16 = ( numera6690914467698888265omplex @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_iff
% 4.97/5.16 thf(fact_39_numeral__eq__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_real @ M )
% 4.97/5.16 = ( numeral_numeral_real @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_iff
% 4.97/5.16 thf(fact_40_numeral__eq__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_rat @ M )
% 4.97/5.16 = ( numeral_numeral_rat @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_iff
% 4.97/5.16 thf(fact_41_numeral__eq__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_nat @ M )
% 4.97/5.16 = ( numeral_numeral_nat @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_iff
% 4.97/5.16 thf(fact_42_numeral__eq__iff,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_int @ M )
% 4.97/5.16 = ( numeral_numeral_int @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_iff
% 4.97/5.16 thf(fact_43_semiring__norm_I6_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 4.97/5.16 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(6)
% 4.97/5.16 thf(fact_44_semiring__norm_I87_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( bit0 @ M )
% 4.97/5.16 = ( bit0 @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(87)
% 4.97/5.16 thf(fact_45_semiring__norm_I90_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ( bit1 @ M )
% 4.97/5.16 = ( bit1 @ N ) )
% 4.97/5.16 = ( M = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(90)
% 4.97/5.16 thf(fact_46_add__numeral__left,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: complex] :
% 4.97/5.16 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 4.97/5.16 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % add_numeral_left
% 4.97/5.16 thf(fact_47_add__numeral__left,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: real] :
% 4.97/5.16 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 4.97/5.16 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % add_numeral_left
% 4.97/5.16 thf(fact_48_add__numeral__left,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: rat] :
% 4.97/5.16 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 4.97/5.16 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % add_numeral_left
% 4.97/5.16 thf(fact_49_add__numeral__left,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: nat] :
% 4.97/5.16 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 4.97/5.16 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % add_numeral_left
% 4.97/5.16 thf(fact_50_add__numeral__left,axiom,
% 4.97/5.16 ! [V: num,W: num,Z: int] :
% 4.97/5.16 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 4.97/5.16 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.97/5.16
% 4.97/5.16 % add_numeral_left
% 4.97/5.16 thf(fact_51_numeral__plus__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.16 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_plus_numeral
% 4.97/5.16 thf(fact_52_numeral__plus__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.16 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_plus_numeral
% 4.97/5.16 thf(fact_53_numeral__plus__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.16 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_plus_numeral
% 4.97/5.16 thf(fact_54_numeral__plus__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.16 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_plus_numeral
% 4.97/5.16 thf(fact_55_numeral__plus__numeral,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.16 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_plus_numeral
% 4.97/5.16 thf(fact_56_semiring__norm_I2_J,axiom,
% 4.97/5.16 ( ( plus_plus_num @ one @ one )
% 4.97/5.16 = ( bit0 @ one ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(2)
% 4.97/5.16 thf(fact_57_power__one,axiom,
% 4.97/5.16 ! [N: nat] :
% 4.97/5.16 ( ( power_power_rat @ one_one_rat @ N )
% 4.97/5.16 = one_one_rat ) ).
% 4.97/5.16
% 4.97/5.16 % power_one
% 4.97/5.16 thf(fact_58_power__one,axiom,
% 4.97/5.16 ! [N: nat] :
% 4.97/5.16 ( ( power_power_real @ one_one_real @ N )
% 4.97/5.16 = one_one_real ) ).
% 4.97/5.16
% 4.97/5.16 % power_one
% 4.97/5.16 thf(fact_59_power__one,axiom,
% 4.97/5.16 ! [N: nat] :
% 4.97/5.16 ( ( power_power_nat @ one_one_nat @ N )
% 4.97/5.16 = one_one_nat ) ).
% 4.97/5.16
% 4.97/5.16 % power_one
% 4.97/5.16 thf(fact_60_power__one,axiom,
% 4.97/5.16 ! [N: nat] :
% 4.97/5.16 ( ( power_power_int @ one_one_int @ N )
% 4.97/5.16 = one_one_int ) ).
% 4.97/5.16
% 4.97/5.16 % power_one
% 4.97/5.16 thf(fact_61_power__one,axiom,
% 4.97/5.16 ! [N: nat] :
% 4.97/5.16 ( ( power_power_complex @ one_one_complex @ N )
% 4.97/5.16 = one_one_complex ) ).
% 4.97/5.16
% 4.97/5.16 % power_one
% 4.97/5.16 thf(fact_62_semiring__norm_I7_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 4.97/5.16 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(7)
% 4.97/5.16 thf(fact_63_semiring__norm_I9_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 4.97/5.16 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(9)
% 4.97/5.16 thf(fact_64_semiring__norm_I88_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( bit0 @ M )
% 4.97/5.16 != ( bit1 @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(88)
% 4.97/5.16 thf(fact_65_semiring__norm_I89_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( bit1 @ M )
% 4.97/5.16 != ( bit0 @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(89)
% 4.97/5.16 thf(fact_66_semiring__norm_I84_J,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( one
% 4.97/5.16 != ( bit1 @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(84)
% 4.97/5.16 thf(fact_67_semiring__norm_I86_J,axiom,
% 4.97/5.16 ! [M: num] :
% 4.97/5.16 ( ( bit1 @ M )
% 4.97/5.16 != one ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(86)
% 4.97/5.16 thf(fact_68_semiring__norm_I13_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 4.97/5.16 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(13)
% 4.97/5.16 thf(fact_69_semiring__norm_I11_J,axiom,
% 4.97/5.16 ! [M: num] :
% 4.97/5.16 ( ( times_times_num @ M @ one )
% 4.97/5.16 = M ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(11)
% 4.97/5.16 thf(fact_70_semiring__norm_I12_J,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( times_times_num @ one @ N )
% 4.97/5.16 = N ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(12)
% 4.97/5.16 thf(fact_71_semiring__norm_I71_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(71)
% 4.97/5.16 thf(fact_72_semiring__norm_I68_J,axiom,
% 4.97/5.16 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(68)
% 4.97/5.16 thf(fact_73_semiring__norm_I73_J,axiom,
% 4.97/5.16 ! [M: num,N: num] :
% 4.97/5.16 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 4.97/5.16 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.16
% 4.97/5.16 % semiring_norm(73)
% 4.97/5.16 thf(fact_74_distrib__right__numeral,axiom,
% 4.97/5.16 ! [A: complex,B: complex,V: num] :
% 4.97/5.16 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 4.97/5.16 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_right_numeral
% 4.97/5.16 thf(fact_75_distrib__right__numeral,axiom,
% 4.97/5.16 ! [A: real,B: real,V: num] :
% 4.97/5.16 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.97/5.16 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_right_numeral
% 4.97/5.16 thf(fact_76_distrib__right__numeral,axiom,
% 4.97/5.16 ! [A: rat,B: rat,V: num] :
% 4.97/5.16 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.97/5.16 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_right_numeral
% 4.97/5.16 thf(fact_77_distrib__right__numeral,axiom,
% 4.97/5.16 ! [A: nat,B: nat,V: num] :
% 4.97/5.16 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 4.97/5.16 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_right_numeral
% 4.97/5.16 thf(fact_78_distrib__right__numeral,axiom,
% 4.97/5.16 ! [A: int,B: int,V: num] :
% 4.97/5.16 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.97/5.16 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_right_numeral
% 4.97/5.16 thf(fact_79_distrib__left__numeral,axiom,
% 4.97/5.16 ! [V: num,B: complex,C: complex] :
% 4.97/5.16 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 4.97/5.16 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_left_numeral
% 4.97/5.16 thf(fact_80_distrib__left__numeral,axiom,
% 4.97/5.16 ! [V: num,B: real,C: real] :
% 4.97/5.16 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.16 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_left_numeral
% 4.97/5.16 thf(fact_81_distrib__left__numeral,axiom,
% 4.97/5.16 ! [V: num,B: rat,C: rat] :
% 4.97/5.16 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.16 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_left_numeral
% 4.97/5.16 thf(fact_82_distrib__left__numeral,axiom,
% 4.97/5.16 ! [V: num,B: nat,C: nat] :
% 4.97/5.16 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.16 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_left_numeral
% 4.97/5.16 thf(fact_83_distrib__left__numeral,axiom,
% 4.97/5.16 ! [V: num,B: int,C: int] :
% 4.97/5.16 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.16 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.97/5.16
% 4.97/5.16 % distrib_left_numeral
% 4.97/5.16 thf(fact_84_one__eq__numeral__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( one_one_complex
% 4.97/5.16 = ( numera6690914467698888265omplex @ N ) )
% 4.97/5.16 = ( one = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % one_eq_numeral_iff
% 4.97/5.16 thf(fact_85_one__eq__numeral__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( one_one_real
% 4.97/5.16 = ( numeral_numeral_real @ N ) )
% 4.97/5.16 = ( one = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % one_eq_numeral_iff
% 4.97/5.16 thf(fact_86_one__eq__numeral__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( one_one_rat
% 4.97/5.16 = ( numeral_numeral_rat @ N ) )
% 4.97/5.16 = ( one = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % one_eq_numeral_iff
% 4.97/5.16 thf(fact_87_one__eq__numeral__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( one_one_nat
% 4.97/5.16 = ( numeral_numeral_nat @ N ) )
% 4.97/5.16 = ( one = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % one_eq_numeral_iff
% 4.97/5.16 thf(fact_88_one__eq__numeral__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( one_one_int
% 4.97/5.16 = ( numeral_numeral_int @ N ) )
% 4.97/5.16 = ( one = N ) ) ).
% 4.97/5.16
% 4.97/5.16 % one_eq_numeral_iff
% 4.97/5.16 thf(fact_89_numeral__eq__one__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( ( numera6690914467698888265omplex @ N )
% 4.97/5.16 = one_one_complex )
% 4.97/5.16 = ( N = one ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_one_iff
% 4.97/5.16 thf(fact_90_numeral__eq__one__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_real @ N )
% 4.97/5.16 = one_one_real )
% 4.97/5.16 = ( N = one ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_one_iff
% 4.97/5.16 thf(fact_91_numeral__eq__one__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_rat @ N )
% 4.97/5.16 = one_one_rat )
% 4.97/5.16 = ( N = one ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_one_iff
% 4.97/5.16 thf(fact_92_numeral__eq__one__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_nat @ N )
% 4.97/5.16 = one_one_nat )
% 4.97/5.16 = ( N = one ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_one_iff
% 4.97/5.16 thf(fact_93_numeral__eq__one__iff,axiom,
% 4.97/5.16 ! [N: num] :
% 4.97/5.16 ( ( ( numeral_numeral_int @ N )
% 4.97/5.16 = one_one_int )
% 4.97/5.16 = ( N = one ) ) ).
% 4.97/5.16
% 4.97/5.16 % numeral_eq_one_iff
% 4.97/5.16 thf(fact_94_power__add__numeral2,axiom,
% 4.97/5.16 ! [A: real,M: num,N: num,B: real] :
% 4.97/5.16 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 4.97/5.16 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 4.97/5.16
% 4.97/5.16 % power_add_numeral2
% 4.97/5.16 thf(fact_95_power__add__numeral2,axiom,
% 4.97/5.16 ! [A: rat,M: num,N: num,B: rat] :
% 4.97/5.16 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 4.97/5.17 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral2
% 4.97/5.17 thf(fact_96_power__add__numeral2,axiom,
% 4.97/5.17 ! [A: nat,M: num,N: num,B: nat] :
% 4.97/5.17 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 4.97/5.17 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral2
% 4.97/5.17 thf(fact_97_power__add__numeral2,axiom,
% 4.97/5.17 ! [A: int,M: num,N: num,B: int] :
% 4.97/5.17 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 4.97/5.17 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral2
% 4.97/5.17 thf(fact_98_power__add__numeral2,axiom,
% 4.97/5.17 ! [A: complex,M: num,N: num,B: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 4.97/5.17 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral2
% 4.97/5.17 thf(fact_99_power__add__numeral,axiom,
% 4.97/5.17 ! [A: real,M: num,N: num] :
% 4.97/5.17 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 4.97/5.17 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral
% 4.97/5.17 thf(fact_100_power__add__numeral,axiom,
% 4.97/5.17 ! [A: rat,M: num,N: num] :
% 4.97/5.17 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 4.97/5.17 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral
% 4.97/5.17 thf(fact_101_power__add__numeral,axiom,
% 4.97/5.17 ! [A: nat,M: num,N: num] :
% 4.97/5.17 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 4.97/5.17 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral
% 4.97/5.17 thf(fact_102_power__add__numeral,axiom,
% 4.97/5.17 ! [A: int,M: num,N: num] :
% 4.97/5.17 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 4.97/5.17 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral
% 4.97/5.17 thf(fact_103_power__add__numeral,axiom,
% 4.97/5.17 ! [A: complex,M: num,N: num] :
% 4.97/5.17 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 4.97/5.17 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add_numeral
% 4.97/5.17 thf(fact_104_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: real,P: real > $o] :
% 4.97/5.17 ( ( member_real @ A @ ( collect_real @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_105_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: complex,P: complex > $o] :
% 4.97/5.17 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_106_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: list_nat,P: list_nat > $o] :
% 4.97/5.17 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_107_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: set_nat,P: set_nat > $o] :
% 4.97/5.17 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_108_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: nat,P: nat > $o] :
% 4.97/5.17 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_109_mem__Collect__eq,axiom,
% 4.97/5.17 ! [A: int,P: int > $o] :
% 4.97/5.17 ( ( member_int @ A @ ( collect_int @ P ) )
% 4.97/5.17 = ( P @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % mem_Collect_eq
% 4.97/5.17 thf(fact_110_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_real] :
% 4.97/5.17 ( ( collect_real
% 4.97/5.17 @ ^ [X3: real] : ( member_real @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_111_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_complex] :
% 4.97/5.17 ( ( collect_complex
% 4.97/5.17 @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_112_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_list_nat] :
% 4.97/5.17 ( ( collect_list_nat
% 4.97/5.17 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_113_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_set_nat] :
% 4.97/5.17 ( ( collect_set_nat
% 4.97/5.17 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_114_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_nat] :
% 4.97/5.17 ( ( collect_nat
% 4.97/5.17 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_115_Collect__mem__eq,axiom,
% 4.97/5.17 ! [A2: set_int] :
% 4.97/5.17 ( ( collect_int
% 4.97/5.17 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 4.97/5.17 = A2 ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_mem_eq
% 4.97/5.17 thf(fact_116_Collect__cong,axiom,
% 4.97/5.17 ! [P: complex > $o,Q: complex > $o] :
% 4.97/5.17 ( ! [X4: complex] :
% 4.97/5.17 ( ( P @ X4 )
% 4.97/5.17 = ( Q @ X4 ) )
% 4.97/5.17 => ( ( collect_complex @ P )
% 4.97/5.17 = ( collect_complex @ Q ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_cong
% 4.97/5.17 thf(fact_117_Collect__cong,axiom,
% 4.97/5.17 ! [P: list_nat > $o,Q: list_nat > $o] :
% 4.97/5.17 ( ! [X4: list_nat] :
% 4.97/5.17 ( ( P @ X4 )
% 4.97/5.17 = ( Q @ X4 ) )
% 4.97/5.17 => ( ( collect_list_nat @ P )
% 4.97/5.17 = ( collect_list_nat @ Q ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_cong
% 4.97/5.17 thf(fact_118_Collect__cong,axiom,
% 4.97/5.17 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.97/5.17 ( ! [X4: set_nat] :
% 4.97/5.17 ( ( P @ X4 )
% 4.97/5.17 = ( Q @ X4 ) )
% 4.97/5.17 => ( ( collect_set_nat @ P )
% 4.97/5.17 = ( collect_set_nat @ Q ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_cong
% 4.97/5.17 thf(fact_119_Collect__cong,axiom,
% 4.97/5.17 ! [P: nat > $o,Q: nat > $o] :
% 4.97/5.17 ( ! [X4: nat] :
% 4.97/5.17 ( ( P @ X4 )
% 4.97/5.17 = ( Q @ X4 ) )
% 4.97/5.17 => ( ( collect_nat @ P )
% 4.97/5.17 = ( collect_nat @ Q ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_cong
% 4.97/5.17 thf(fact_120_Collect__cong,axiom,
% 4.97/5.17 ! [P: int > $o,Q: int > $o] :
% 4.97/5.17 ( ! [X4: int] :
% 4.97/5.17 ( ( P @ X4 )
% 4.97/5.17 = ( Q @ X4 ) )
% 4.97/5.17 => ( ( collect_int @ P )
% 4.97/5.17 = ( collect_int @ Q ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Collect_cong
% 4.97/5.17 thf(fact_121_semiring__norm_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 4.97/5.17 = ( bit1 @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(3)
% 4.97/5.17 thf(fact_122_semiring__norm_I4_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 4.97/5.17 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(4)
% 4.97/5.17 thf(fact_123_semiring__norm_I5_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 4.97/5.17 = ( bit1 @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(5)
% 4.97/5.17 thf(fact_124_semiring__norm_I8_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 4.97/5.17 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(8)
% 4.97/5.17 thf(fact_125_semiring__norm_I10_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 4.97/5.17 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(10)
% 4.97/5.17 thf(fact_126_num__double,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 4.97/5.17 = ( bit0 @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % num_double
% 4.97/5.17 thf(fact_127_semiring__norm_I16_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 4.97/5.17 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(16)
% 4.97/5.17 thf(fact_128_semiring__norm_I14_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 4.97/5.17 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(14)
% 4.97/5.17 thf(fact_129_semiring__norm_I15_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 4.97/5.17 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(15)
% 4.97/5.17 thf(fact_130_power__mult__numeral,axiom,
% 4.97/5.17 ! [A: real,M: num,N: num] :
% 4.97/5.17 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_numeral
% 4.97/5.17 thf(fact_131_power__mult__numeral,axiom,
% 4.97/5.17 ! [A: nat,M: num,N: num] :
% 4.97/5.17 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_numeral
% 4.97/5.17 thf(fact_132_power__mult__numeral,axiom,
% 4.97/5.17 ! [A: int,M: num,N: num] :
% 4.97/5.17 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_numeral
% 4.97/5.17 thf(fact_133_power__mult__numeral,axiom,
% 4.97/5.17 ! [A: complex,M: num,N: num] :
% 4.97/5.17 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_numeral
% 4.97/5.17 thf(fact_134_semiring__norm_I69_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(69)
% 4.97/5.17 thf(fact_135_semiring__norm_I72_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 4.97/5.17 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(72)
% 4.97/5.17 thf(fact_136_semiring__norm_I70_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(70)
% 4.97/5.17 thf(fact_137_le__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [A: real,B: real,W: num] :
% 4.97/5.17 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.97/5.17 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_divide_eq_numeral1(1)
% 4.97/5.17 thf(fact_138_le__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [A: rat,B: rat,W: num] :
% 4.97/5.17 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.97/5.17 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_divide_eq_numeral1(1)
% 4.97/5.17 thf(fact_139_divide__le__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [B: real,W: num,A: real] :
% 4.97/5.17 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 4.97/5.17 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_le_eq_numeral1(1)
% 4.97/5.17 thf(fact_140_divide__le__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [B: rat,W: num,A: rat] :
% 4.97/5.17 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 4.97/5.17 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_le_eq_numeral1(1)
% 4.97/5.17 thf(fact_141_one__plus__numeral,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral
% 4.97/5.17 thf(fact_142_one__plus__numeral,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral
% 4.97/5.17 thf(fact_143_one__plus__numeral,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral
% 4.97/5.17 thf(fact_144_one__plus__numeral,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral
% 4.97/5.17 thf(fact_145_one__plus__numeral,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral
% 4.97/5.17 thf(fact_146_numeral__plus__one,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_plus_one
% 4.97/5.17 thf(fact_147_numeral__plus__one,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 4.97/5.17 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_plus_one
% 4.97/5.17 thf(fact_148_numeral__plus__one,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 4.97/5.17 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_plus_one
% 4.97/5.17 thf(fact_149_numeral__plus__one,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 4.97/5.17 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_plus_one
% 4.97/5.17 thf(fact_150_numeral__plus__one,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 4.97/5.17 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_plus_one
% 4.97/5.17 thf(fact_151__092_060open_0622_A_K_A_I2_A_094_A_In_A_L_An_J_A_L_A_I1_A_N_Ac_J_A_K_A2_A_094_An_A_N_Ac_A_L_A1_A_P_A2_J_A_092_060le_062_A2_A_K_A_I2_A_094_A_In_A_L_An_J_A_N_A15_A_P_A10_J_092_060close_062,axiom,
% 4.97/5.17 ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( times_times_real @ ( minus_minus_real @ one_one_real @ c ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) ) ) @ c ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % \<open>2 * (2 ^ (n + n) + (1 - c) * 2 ^ n - c + 1 / 2) \<le> 2 * (2 ^ (n + n) - 15 / 10)\<close>
% 4.97/5.17 thf(fact_152_one__add__one,axiom,
% 4.97/5.17 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_add_one
% 4.97/5.17 thf(fact_153_one__add__one,axiom,
% 4.97/5.17 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 4.97/5.17 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_add_one
% 4.97/5.17 thf(fact_154_one__add__one,axiom,
% 4.97/5.17 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 4.97/5.17 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_add_one
% 4.97/5.17 thf(fact_155_one__add__one,axiom,
% 4.97/5.17 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.97/5.17 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_add_one
% 4.97/5.17 thf(fact_156_one__add__one,axiom,
% 4.97/5.17 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 4.97/5.17 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_add_one
% 4.97/5.17 thf(fact_157_numeral__le__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 4.97/5.17 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_le_one_iff
% 4.97/5.17 thf(fact_158_numeral__le__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 4.97/5.17 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_le_one_iff
% 4.97/5.17 thf(fact_159_numeral__le__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 4.97/5.17 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_le_one_iff
% 4.97/5.17 thf(fact_160_numeral__le__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 4.97/5.17 = ( ord_less_eq_num @ N @ one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_le_one_iff
% 4.97/5.17 thf(fact_161__C4_Ohyps_C_I8_J,axiom,
% 4.97/5.17 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 4.97/5.17
% 4.97/5.17 % "4.hyps"(8)
% 4.97/5.17 thf(fact_162__092_060open_062cnt_A_INode_ANone_Adeg_AtreeList_Asummary_J_A_092_060le_062_A2_A_K_A_I2_A_094_A_In_A_L_An_J_A_L_A_I1_A_N_Ac_J_A_K_A2_A_094_An_A_N_Ac_A_L_A1_A_P_A2_J_092_060close_062,axiom,
% 4.97/5.17 ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ deg @ treeList @ summary ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( times_times_real @ ( minus_minus_real @ one_one_real @ c ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) ) ) @ c ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % \<open>cnt (Node None deg treeList summary) \<le> 2 * (2 ^ (n + n) + (1 - c) * 2 ^ n - c + 1 / 2)\<close>
% 4.97/5.17 thf(fact_163__C4_Ohyps_C_I2_J,axiom,
% 4.97/5.17 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 4.97/5.17 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 4.97/5.17
% 4.97/5.17 % "4.hyps"(2)
% 4.97/5.17 thf(fact_164__C4_Ohyps_C_I6_J,axiom,
% 4.97/5.17 ( ( mi = ma )
% 4.97/5.17 => ! [X: vEBT_VEBT] :
% 4.97/5.17 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ treeList ) )
% 4.97/5.17 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % "4.hyps"(6)
% 4.97/5.17 thf(fact_165_is__num__normalize_I1_J,axiom,
% 4.97/5.17 ! [A: real,B: real,C: real] :
% 4.97/5.17 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.17 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % is_num_normalize(1)
% 4.97/5.17 thf(fact_166_is__num__normalize_I1_J,axiom,
% 4.97/5.17 ! [A: rat,B: rat,C: rat] :
% 4.97/5.17 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.17 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % is_num_normalize(1)
% 4.97/5.17 thf(fact_167_is__num__normalize_I1_J,axiom,
% 4.97/5.17 ! [A: int,B: int,C: int] :
% 4.97/5.17 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.17 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % is_num_normalize(1)
% 4.97/5.17 thf(fact_168_numeral__Bit1,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 4.97/5.17 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit1
% 4.97/5.17 thf(fact_169_numeral__Bit1,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 4.97/5.17 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit1
% 4.97/5.17 thf(fact_170_numeral__Bit1,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 4.97/5.17 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit1
% 4.97/5.17 thf(fact_171_numeral__Bit1,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 4.97/5.17 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit1
% 4.97/5.17 thf(fact_172_numeral__Bit1,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 4.97/5.17 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit1
% 4.97/5.17 thf(fact_173_diff__le__diff__pow,axiom,
% 4.97/5.17 ! [K: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.97/5.17 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_le_diff_pow
% 4.97/5.17 thf(fact_174_nat__eq__add__iff1,axiom,
% 4.97/5.17 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ J @ I )
% 4.97/5.17 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 4.97/5.17 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 4.97/5.17 = N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_eq_add_iff1
% 4.97/5.17 thf(fact_175_nat__eq__add__iff2,axiom,
% 4.97/5.17 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.17 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 4.97/5.17 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( M
% 4.97/5.17 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_eq_add_iff2
% 4.97/5.17 thf(fact_176_nat__le__add__iff1,axiom,
% 4.97/5.17 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ J @ I )
% 4.97/5.17 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_le_add_iff1
% 4.97/5.17 thf(fact_177_nat__le__add__iff2,axiom,
% 4.97/5.17 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.17 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_le_add_iff2
% 4.97/5.17 thf(fact_178_nat__diff__add__eq1,axiom,
% 4.97/5.17 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ J @ I )
% 4.97/5.17 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_diff_add_eq1
% 4.97/5.17 thf(fact_179_nat__diff__add__eq2,axiom,
% 4.97/5.17 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.17 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.17 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % nat_diff_add_eq2
% 4.97/5.17 thf(fact_180_left__add__mult__distrib,axiom,
% 4.97/5.17 ! [I: nat,U: nat,J: nat,K: nat] :
% 4.97/5.17 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 4.97/5.17 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_mult_distrib
% 4.97/5.17 thf(fact_181_power2__nat__le__imp__le,axiom,
% 4.97/5.17 ! [M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 4.97/5.17 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_nat_le_imp_le
% 4.97/5.17 thf(fact_182_power2__nat__le__eq__le,axiom,
% 4.97/5.17 ! [M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_nat_le_eq_le
% 4.97/5.17 thf(fact_183_self__le__ge2__pow,axiom,
% 4.97/5.17 ! [K: nat,M: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.97/5.17 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % self_le_ge2_pow
% 4.97/5.17 thf(fact_184_one__plus__numeral__commute,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 4.97/5.17 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral_commute
% 4.97/5.17 thf(fact_185_one__plus__numeral__commute,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 4.97/5.17 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral_commute
% 4.97/5.17 thf(fact_186_one__plus__numeral__commute,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 4.97/5.17 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral_commute
% 4.97/5.17 thf(fact_187_one__plus__numeral__commute,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 4.97/5.17 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral_commute
% 4.97/5.17 thf(fact_188_one__plus__numeral__commute,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 4.97/5.17 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_plus_numeral_commute
% 4.97/5.17 thf(fact_189_power__one__over,axiom,
% 4.97/5.17 ! [A: complex,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 4.97/5.17 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_over
% 4.97/5.17 thf(fact_190_power__one__over,axiom,
% 4.97/5.17 ! [A: real,N: nat] :
% 4.97/5.17 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 4.97/5.17 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_over
% 4.97/5.17 thf(fact_191_power__one__over,axiom,
% 4.97/5.17 ! [A: rat,N: nat] :
% 4.97/5.17 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 4.97/5.17 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_over
% 4.97/5.17 thf(fact_192_add__One__commute,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( plus_plus_num @ one @ N )
% 4.97/5.17 = ( plus_plus_num @ N @ one ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_One_commute
% 4.97/5.17 thf(fact_193_le__num__One__iff,axiom,
% 4.97/5.17 ! [X2: num] :
% 4.97/5.17 ( ( ord_less_eq_num @ X2 @ one )
% 4.97/5.17 = ( X2 = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_num_One_iff
% 4.97/5.17 thf(fact_194_le__numeral__extra_I4_J,axiom,
% 4.97/5.17 ord_less_eq_real @ one_one_real @ one_one_real ).
% 4.97/5.17
% 4.97/5.17 % le_numeral_extra(4)
% 4.97/5.17 thf(fact_195_le__numeral__extra_I4_J,axiom,
% 4.97/5.17 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 4.97/5.17
% 4.97/5.17 % le_numeral_extra(4)
% 4.97/5.17 thf(fact_196_le__numeral__extra_I4_J,axiom,
% 4.97/5.17 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 4.97/5.17
% 4.97/5.17 % le_numeral_extra(4)
% 4.97/5.17 thf(fact_197_le__numeral__extra_I4_J,axiom,
% 4.97/5.17 ord_less_eq_int @ one_one_int @ one_one_int ).
% 4.97/5.17
% 4.97/5.17 % le_numeral_extra(4)
% 4.97/5.17 thf(fact_198_power__mult,axiom,
% 4.97/5.17 ! [A: real,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 4.97/5.17 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult
% 4.97/5.17 thf(fact_199_power__mult,axiom,
% 4.97/5.17 ! [A: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 4.97/5.17 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult
% 4.97/5.17 thf(fact_200_power__mult,axiom,
% 4.97/5.17 ! [A: int,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 4.97/5.17 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult
% 4.97/5.17 thf(fact_201_power__mult,axiom,
% 4.97/5.17 ! [A: complex,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 4.97/5.17 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult
% 4.97/5.17 thf(fact_202_power__even__eq,axiom,
% 4.97/5.17 ! [A: real,N: nat] :
% 4.97/5.17 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_even_eq
% 4.97/5.17 thf(fact_203_power__even__eq,axiom,
% 4.97/5.17 ! [A: nat,N: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_even_eq
% 4.97/5.17 thf(fact_204_power__even__eq,axiom,
% 4.97/5.17 ! [A: int,N: nat] :
% 4.97/5.17 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_even_eq
% 4.97/5.17 thf(fact_205_power__even__eq,axiom,
% 4.97/5.17 ! [A: complex,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_even_eq
% 4.97/5.17 thf(fact_206_one__power2,axiom,
% 4.97/5.17 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = one_one_rat ) ).
% 4.97/5.17
% 4.97/5.17 % one_power2
% 4.97/5.17 thf(fact_207_one__power2,axiom,
% 4.97/5.17 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = one_one_real ) ).
% 4.97/5.17
% 4.97/5.17 % one_power2
% 4.97/5.17 thf(fact_208_one__power2,axiom,
% 4.97/5.17 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = one_one_nat ) ).
% 4.97/5.17
% 4.97/5.17 % one_power2
% 4.97/5.17 thf(fact_209_one__power2,axiom,
% 4.97/5.17 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = one_one_int ) ).
% 4.97/5.17
% 4.97/5.17 % one_power2
% 4.97/5.17 thf(fact_210_one__power2,axiom,
% 4.97/5.17 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = one_one_complex ) ).
% 4.97/5.17
% 4.97/5.17 % one_power2
% 4.97/5.17 thf(fact_211_one__le__numeral,axiom,
% 4.97/5.17 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_numeral
% 4.97/5.17 thf(fact_212_one__le__numeral,axiom,
% 4.97/5.17 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_numeral
% 4.97/5.17 thf(fact_213_one__le__numeral,axiom,
% 4.97/5.17 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_numeral
% 4.97/5.17 thf(fact_214_one__le__numeral,axiom,
% 4.97/5.17 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_numeral
% 4.97/5.17 thf(fact_215_numeral__One,axiom,
% 4.97/5.17 ( ( numera6690914467698888265omplex @ one )
% 4.97/5.17 = one_one_complex ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_One
% 4.97/5.17 thf(fact_216_numeral__One,axiom,
% 4.97/5.17 ( ( numeral_numeral_real @ one )
% 4.97/5.17 = one_one_real ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_One
% 4.97/5.17 thf(fact_217_numeral__One,axiom,
% 4.97/5.17 ( ( numeral_numeral_rat @ one )
% 4.97/5.17 = one_one_rat ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_One
% 4.97/5.17 thf(fact_218_numeral__One,axiom,
% 4.97/5.17 ( ( numeral_numeral_nat @ one )
% 4.97/5.17 = one_one_nat ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_One
% 4.97/5.17 thf(fact_219_numeral__One,axiom,
% 4.97/5.17 ( ( numeral_numeral_int @ one )
% 4.97/5.17 = one_one_int ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_One
% 4.97/5.17 thf(fact_220_power__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: real] :
% 4.97/5.17 ( ( ord_less_eq_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_eq_real @ one_one_real @ A )
% 4.97/5.17 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing
% 4.97/5.17 thf(fact_221_power__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: rat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.97/5.17 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing
% 4.97/5.17 thf(fact_222_power__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.97/5.17 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing
% 4.97/5.17 thf(fact_223_power__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: int] :
% 4.97/5.17 ( ( ord_less_eq_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_eq_int @ one_one_int @ A )
% 4.97/5.17 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing
% 4.97/5.17 thf(fact_224_one__le__power,axiom,
% 4.97/5.17 ! [A: real,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_real @ one_one_real @ A )
% 4.97/5.17 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_power
% 4.97/5.17 thf(fact_225_one__le__power,axiom,
% 4.97/5.17 ! [A: rat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.97/5.17 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_power
% 4.97/5.17 thf(fact_226_one__le__power,axiom,
% 4.97/5.17 ! [A: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.97/5.17 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_power
% 4.97/5.17 thf(fact_227_one__le__power,axiom,
% 4.97/5.17 ! [A: int,N: nat] :
% 4.97/5.17 ( ( ord_less_eq_int @ one_one_int @ A )
% 4.97/5.17 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_le_power
% 4.97/5.17 thf(fact_228_left__right__inverse__power,axiom,
% 4.97/5.17 ! [X2: real,Y: real,N: nat] :
% 4.97/5.17 ( ( ( times_times_real @ X2 @ Y )
% 4.97/5.17 = one_one_real )
% 4.97/5.17 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y @ N ) )
% 4.97/5.17 = one_one_real ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_right_inverse_power
% 4.97/5.17 thf(fact_229_left__right__inverse__power,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat,N: nat] :
% 4.97/5.17 ( ( ( times_times_rat @ X2 @ Y )
% 4.97/5.17 = one_one_rat )
% 4.97/5.17 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y @ N ) )
% 4.97/5.17 = one_one_rat ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_right_inverse_power
% 4.97/5.17 thf(fact_230_left__right__inverse__power,axiom,
% 4.97/5.17 ! [X2: nat,Y: nat,N: nat] :
% 4.97/5.17 ( ( ( times_times_nat @ X2 @ Y )
% 4.97/5.17 = one_one_nat )
% 4.97/5.17 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y @ N ) )
% 4.97/5.17 = one_one_nat ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_right_inverse_power
% 4.97/5.17 thf(fact_231_left__right__inverse__power,axiom,
% 4.97/5.17 ! [X2: int,Y: int,N: nat] :
% 4.97/5.17 ( ( ( times_times_int @ X2 @ Y )
% 4.97/5.17 = one_one_int )
% 4.97/5.17 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y @ N ) )
% 4.97/5.17 = one_one_int ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_right_inverse_power
% 4.97/5.17 thf(fact_232_left__right__inverse__power,axiom,
% 4.97/5.17 ! [X2: complex,Y: complex,N: nat] :
% 4.97/5.17 ( ( ( times_times_complex @ X2 @ Y )
% 4.97/5.17 = one_one_complex )
% 4.97/5.17 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y @ N ) )
% 4.97/5.17 = one_one_complex ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_right_inverse_power
% 4.97/5.17 thf(fact_233_power__divide,axiom,
% 4.97/5.17 ! [A: complex,B: complex,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 4.97/5.17 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_divide
% 4.97/5.17 thf(fact_234_power__divide,axiom,
% 4.97/5.17 ! [A: real,B: real,N: nat] :
% 4.97/5.17 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 4.97/5.17 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_divide
% 4.97/5.17 thf(fact_235_power__divide,axiom,
% 4.97/5.17 ! [A: rat,B: rat,N: nat] :
% 4.97/5.17 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 4.97/5.17 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_divide
% 4.97/5.17 thf(fact_236_power3__eq__cube,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.97/5.17 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power3_eq_cube
% 4.97/5.17 thf(fact_237_power3__eq__cube,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.97/5.17 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power3_eq_cube
% 4.97/5.17 thf(fact_238_power3__eq__cube,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.97/5.17 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power3_eq_cube
% 4.97/5.17 thf(fact_239_power3__eq__cube,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.97/5.17 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power3_eq_cube
% 4.97/5.17 thf(fact_240_power3__eq__cube,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 4.97/5.17 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power3_eq_cube
% 4.97/5.17 thf(fact_241_power2__eq__square,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( times_times_real @ A @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_eq_square
% 4.97/5.17 thf(fact_242_power2__eq__square,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( times_times_rat @ A @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_eq_square
% 4.97/5.17 thf(fact_243_power2__eq__square,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( times_times_nat @ A @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_eq_square
% 4.97/5.17 thf(fact_244_power2__eq__square,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( times_times_int @ A @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_eq_square
% 4.97/5.17 thf(fact_245_power2__eq__square,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( times_times_complex @ A @ A ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_eq_square
% 4.97/5.17 thf(fact_246_power4__eq__xxxx,axiom,
% 4.97/5.17 ! [X2: real] :
% 4.97/5.17 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.97/5.17
% 4.97/5.17 % power4_eq_xxxx
% 4.97/5.17 thf(fact_247_power4__eq__xxxx,axiom,
% 4.97/5.17 ! [X2: rat] :
% 4.97/5.17 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.97/5.17
% 4.97/5.17 % power4_eq_xxxx
% 4.97/5.17 thf(fact_248_power4__eq__xxxx,axiom,
% 4.97/5.17 ! [X2: nat] :
% 4.97/5.17 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.97/5.17
% 4.97/5.17 % power4_eq_xxxx
% 4.97/5.17 thf(fact_249_power4__eq__xxxx,axiom,
% 4.97/5.17 ! [X2: int] :
% 4.97/5.17 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.97/5.17
% 4.97/5.17 % power4_eq_xxxx
% 4.97/5.17 thf(fact_250_power4__eq__xxxx,axiom,
% 4.97/5.17 ! [X2: complex] :
% 4.97/5.17 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.97/5.17
% 4.97/5.17 % power4_eq_xxxx
% 4.97/5.17 thf(fact_251_power2__commute,axiom,
% 4.97/5.17 ! [X2: real,Y: real] :
% 4.97/5.17 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_real @ ( minus_minus_real @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_commute
% 4.97/5.17 thf(fact_252_power2__commute,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat] :
% 4.97/5.17 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_rat @ ( minus_minus_rat @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_commute
% 4.97/5.17 thf(fact_253_power2__commute,axiom,
% 4.97/5.17 ! [X2: int,Y: int] :
% 4.97/5.17 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_int @ ( minus_minus_int @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_commute
% 4.97/5.17 thf(fact_254_power2__commute,axiom,
% 4.97/5.17 ! [X2: complex,Y: complex] :
% 4.97/5.17 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_complex @ ( minus_minus_complex @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_commute
% 4.97/5.17 thf(fact_255_divide__numeral__1,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % divide_numeral_1
% 4.97/5.17 thf(fact_256_divide__numeral__1,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % divide_numeral_1
% 4.97/5.17 thf(fact_257_divide__numeral__1,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % divide_numeral_1
% 4.97/5.17 thf(fact_258_num_Oexhaust,axiom,
% 4.97/5.17 ! [Y: num] :
% 4.97/5.17 ( ( Y != one )
% 4.97/5.17 => ( ! [X22: num] :
% 4.97/5.17 ( Y
% 4.97/5.17 != ( bit0 @ X22 ) )
% 4.97/5.17 => ~ ! [X32: num] :
% 4.97/5.17 ( Y
% 4.97/5.17 != ( bit1 @ X32 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % num.exhaust
% 4.97/5.17 thf(fact_259_numeral__Bit0,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 4.97/5.17 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit0
% 4.97/5.17 thf(fact_260_numeral__Bit0,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 4.97/5.17 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit0
% 4.97/5.17 thf(fact_261_numeral__Bit0,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 4.97/5.17 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit0
% 4.97/5.17 thf(fact_262_numeral__Bit0,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 4.97/5.17 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit0
% 4.97/5.17 thf(fact_263_numeral__Bit0,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 4.97/5.17 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_Bit0
% 4.97/5.17 thf(fact_264_power__add,axiom,
% 4.97/5.17 ! [A: real,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.17 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add
% 4.97/5.17 thf(fact_265_power__add,axiom,
% 4.97/5.17 ! [A: rat,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.17 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add
% 4.97/5.17 thf(fact_266_power__add,axiom,
% 4.97/5.17 ! [A: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.17 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add
% 4.97/5.17 thf(fact_267_power__add,axiom,
% 4.97/5.17 ! [A: int,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.17 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add
% 4.97/5.17 thf(fact_268_power__add,axiom,
% 4.97/5.17 ! [A: complex,M: nat,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.17 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_add
% 4.97/5.17 thf(fact_269_power__commuting__commutes,axiom,
% 4.97/5.17 ! [X2: real,Y: real,N: nat] :
% 4.97/5.17 ( ( ( times_times_real @ X2 @ Y )
% 4.97/5.17 = ( times_times_real @ Y @ X2 ) )
% 4.97/5.17 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ Y )
% 4.97/5.17 = ( times_times_real @ Y @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commuting_commutes
% 4.97/5.17 thf(fact_270_power__commuting__commutes,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat,N: nat] :
% 4.97/5.17 ( ( ( times_times_rat @ X2 @ Y )
% 4.97/5.17 = ( times_times_rat @ Y @ X2 ) )
% 4.97/5.17 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ Y )
% 4.97/5.17 = ( times_times_rat @ Y @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commuting_commutes
% 4.97/5.17 thf(fact_271_power__commuting__commutes,axiom,
% 4.97/5.17 ! [X2: nat,Y: nat,N: nat] :
% 4.97/5.17 ( ( ( times_times_nat @ X2 @ Y )
% 4.97/5.17 = ( times_times_nat @ Y @ X2 ) )
% 4.97/5.17 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ Y )
% 4.97/5.17 = ( times_times_nat @ Y @ ( power_power_nat @ X2 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commuting_commutes
% 4.97/5.17 thf(fact_272_power__commuting__commutes,axiom,
% 4.97/5.17 ! [X2: int,Y: int,N: nat] :
% 4.97/5.17 ( ( ( times_times_int @ X2 @ Y )
% 4.97/5.17 = ( times_times_int @ Y @ X2 ) )
% 4.97/5.17 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ Y )
% 4.97/5.17 = ( times_times_int @ Y @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commuting_commutes
% 4.97/5.17 thf(fact_273_power__commuting__commutes,axiom,
% 4.97/5.17 ! [X2: complex,Y: complex,N: nat] :
% 4.97/5.17 ( ( ( times_times_complex @ X2 @ Y )
% 4.97/5.17 = ( times_times_complex @ Y @ X2 ) )
% 4.97/5.17 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ Y )
% 4.97/5.17 = ( times_times_complex @ Y @ ( power_power_complex @ X2 @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commuting_commutes
% 4.97/5.17 thf(fact_274_power__mult__distrib,axiom,
% 4.97/5.17 ! [A: real,B: real,N: nat] :
% 4.97/5.17 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 4.97/5.17 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_distrib
% 4.97/5.17 thf(fact_275_power__mult__distrib,axiom,
% 4.97/5.17 ! [A: rat,B: rat,N: nat] :
% 4.97/5.17 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 4.97/5.17 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_distrib
% 4.97/5.17 thf(fact_276_power__mult__distrib,axiom,
% 4.97/5.17 ! [A: nat,B: nat,N: nat] :
% 4.97/5.17 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 4.97/5.17 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_distrib
% 4.97/5.17 thf(fact_277_power__mult__distrib,axiom,
% 4.97/5.17 ! [A: int,B: int,N: nat] :
% 4.97/5.17 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 4.97/5.17 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_distrib
% 4.97/5.17 thf(fact_278_power__mult__distrib,axiom,
% 4.97/5.17 ! [A: complex,B: complex,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 4.97/5.17 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_mult_distrib
% 4.97/5.17 thf(fact_279_power__commutes,axiom,
% 4.97/5.17 ! [A: real,N: nat] :
% 4.97/5.17 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 4.97/5.17 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commutes
% 4.97/5.17 thf(fact_280_power__commutes,axiom,
% 4.97/5.17 ! [A: rat,N: nat] :
% 4.97/5.17 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 4.97/5.17 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commutes
% 4.97/5.17 thf(fact_281_power__commutes,axiom,
% 4.97/5.17 ! [A: nat,N: nat] :
% 4.97/5.17 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 4.97/5.17 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commutes
% 4.97/5.17 thf(fact_282_power__commutes,axiom,
% 4.97/5.17 ! [A: int,N: nat] :
% 4.97/5.17 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 4.97/5.17 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commutes
% 4.97/5.17 thf(fact_283_power__commutes,axiom,
% 4.97/5.17 ! [A: complex,N: nat] :
% 4.97/5.17 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 4.97/5.17 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_commutes
% 4.97/5.17 thf(fact_284_left__add__twice,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 4.97/5.17 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_twice
% 4.97/5.17 thf(fact_285_left__add__twice,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.97/5.17 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_twice
% 4.97/5.17 thf(fact_286_left__add__twice,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.17 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_twice
% 4.97/5.17 thf(fact_287_left__add__twice,axiom,
% 4.97/5.17 ! [A: nat,B: nat] :
% 4.97/5.17 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.97/5.17 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_twice
% 4.97/5.17 thf(fact_288_left__add__twice,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.97/5.17 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % left_add_twice
% 4.97/5.17 thf(fact_289_mult__2__right,axiom,
% 4.97/5.17 ! [Z: complex] :
% 4.97/5.17 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_complex @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2_right
% 4.97/5.17 thf(fact_290_mult__2__right,axiom,
% 4.97/5.17 ! [Z: real] :
% 4.97/5.17 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2_right
% 4.97/5.17 thf(fact_291_mult__2__right,axiom,
% 4.97/5.17 ! [Z: rat] :
% 4.97/5.17 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2_right
% 4.97/5.17 thf(fact_292_mult__2__right,axiom,
% 4.97/5.17 ! [Z: nat] :
% 4.97/5.17 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2_right
% 4.97/5.17 thf(fact_293_mult__2__right,axiom,
% 4.97/5.17 ! [Z: int] :
% 4.97/5.17 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2_right
% 4.97/5.17 thf(fact_294_mult__2,axiom,
% 4.97/5.17 ! [Z: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 4.97/5.17 = ( plus_plus_complex @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2
% 4.97/5.17 thf(fact_295_mult__2,axiom,
% 4.97/5.17 ! [Z: real] :
% 4.97/5.17 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 4.97/5.17 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2
% 4.97/5.17 thf(fact_296_mult__2,axiom,
% 4.97/5.17 ! [Z: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 4.97/5.17 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2
% 4.97/5.17 thf(fact_297_mult__2,axiom,
% 4.97/5.17 ! [Z: nat] :
% 4.97/5.17 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 4.97/5.17 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2
% 4.97/5.17 thf(fact_298_mult__2,axiom,
% 4.97/5.17 ! [Z: int] :
% 4.97/5.17 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 4.97/5.17 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_2
% 4.97/5.17 thf(fact_299_power2__sum,axiom,
% 4.97/5.17 ! [X2: complex,Y: complex] :
% 4.97/5.17 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_sum
% 4.97/5.17 thf(fact_300_power2__sum,axiom,
% 4.97/5.17 ! [X2: real,Y: real] :
% 4.97/5.17 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_sum
% 4.97/5.17 thf(fact_301_power2__sum,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat] :
% 4.97/5.17 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_sum
% 4.97/5.17 thf(fact_302_power2__sum,axiom,
% 4.97/5.17 ! [X2: nat,Y: nat] :
% 4.97/5.17 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_sum
% 4.97/5.17 thf(fact_303_power2__sum,axiom,
% 4.97/5.17 ! [X2: int,Y: int] :
% 4.97/5.17 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_sum
% 4.97/5.17 thf(fact_304_mult__numeral__1__right,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1_right
% 4.97/5.17 thf(fact_305_mult__numeral__1__right,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1_right
% 4.97/5.17 thf(fact_306_mult__numeral__1__right,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1_right
% 4.97/5.17 thf(fact_307_mult__numeral__1__right,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1_right
% 4.97/5.17 thf(fact_308_mult__numeral__1__right,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1_right
% 4.97/5.17 thf(fact_309_mult__numeral__1,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1
% 4.97/5.17 thf(fact_310_mult__numeral__1,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1
% 4.97/5.17 thf(fact_311_mult__numeral__1,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1
% 4.97/5.17 thf(fact_312_mult__numeral__1,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1
% 4.97/5.17 thf(fact_313_mult__numeral__1,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % mult_numeral_1
% 4.97/5.17 thf(fact_314_real__average__minus__second,axiom,
% 4.97/5.17 ! [B: real,A: real] :
% 4.97/5.17 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 4.97/5.17 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % real_average_minus_second
% 4.97/5.17 thf(fact_315_real__average__minus__first,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 4.97/5.17 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % real_average_minus_first
% 4.97/5.17 thf(fact_316__092_060open_0622_A_K_A_I2_A_094_A_In_A_L_An_J_A_L_A_I1_A_N_Ac_J_A_K_A2_A_094_An_A_N_Ac_A_L_A1_A_P_A2_J_A_092_060le_062_A2_A_K_A_I2_A_094_A_In_A_L_An_J_A_L_A_N_A_I5_A_P_A10_J_A_K_A1_A_N_A15_A_P_A10_A_L_A1_A_P_A2_J_092_060close_062,axiom,
% 4.97/5.17 ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( times_times_real @ ( minus_minus_real @ one_one_real @ c ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) ) ) @ c ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_nat @ na @ na ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ one_one_real ) ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % \<open>2 * (2 ^ (n + n) + (1 - c) * 2 ^ n - c + 1 / 2) \<le> 2 * (2 ^ (n + n) + - (5 / 10) * 1 - 15 / 10 + 1 / 2)\<close>
% 4.97/5.17 thf(fact_317_L2__set__mult__ineq__lemma,axiom,
% 4.97/5.17 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % L2_set_mult_ineq_lemma
% 4.97/5.17 thf(fact_318_sum__squares__bound,axiom,
% 4.97/5.17 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % sum_squares_bound
% 4.97/5.17 thf(fact_319_sum__squares__bound,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % sum_squares_bound
% 4.97/5.17 thf(fact_320_le__add__diff__inverse2,axiom,
% 4.97/5.17 ! [B: real,A: real] :
% 4.97/5.17 ( ( ord_less_eq_real @ B @ A )
% 4.97/5.17 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse2
% 4.97/5.17 thf(fact_321_le__add__diff__inverse2,axiom,
% 4.97/5.17 ! [B: rat,A: rat] :
% 4.97/5.17 ( ( ord_less_eq_rat @ B @ A )
% 4.97/5.17 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse2
% 4.97/5.17 thf(fact_322_le__add__diff__inverse2,axiom,
% 4.97/5.17 ! [B: nat,A: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ B @ A )
% 4.97/5.17 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse2
% 4.97/5.17 thf(fact_323_le__add__diff__inverse2,axiom,
% 4.97/5.17 ! [B: int,A: int] :
% 4.97/5.17 ( ( ord_less_eq_int @ B @ A )
% 4.97/5.17 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse2
% 4.97/5.17 thf(fact_324_le__add__diff__inverse,axiom,
% 4.97/5.17 ! [B: real,A: real] :
% 4.97/5.17 ( ( ord_less_eq_real @ B @ A )
% 4.97/5.17 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse
% 4.97/5.17 thf(fact_325_le__add__diff__inverse,axiom,
% 4.97/5.17 ! [B: rat,A: rat] :
% 4.97/5.17 ( ( ord_less_eq_rat @ B @ A )
% 4.97/5.17 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse
% 4.97/5.17 thf(fact_326_le__add__diff__inverse,axiom,
% 4.97/5.17 ! [B: nat,A: nat] :
% 4.97/5.17 ( ( ord_less_eq_nat @ B @ A )
% 4.97/5.17 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse
% 4.97/5.17 thf(fact_327_le__add__diff__inverse,axiom,
% 4.97/5.17 ! [B: int,A: int] :
% 4.97/5.17 ( ( ord_less_eq_int @ B @ A )
% 4.97/5.17 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.97/5.17 = A ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_add_diff_inverse
% 4.97/5.17 thf(fact_328_mi__ma__2__deg,axiom,
% 4.97/5.17 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 4.97/5.17 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 4.97/5.17 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.97/5.17 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mi_ma_2_deg
% 4.97/5.17 thf(fact_329_four__x__squared,axiom,
% 4.97/5.17 ! [X2: real] :
% 4.97/5.17 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.17 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % four_x_squared
% 4.97/5.17 thf(fact_330_two__realpow__ge__one,axiom,
% 4.97/5.17 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % two_realpow_ge_one
% 4.97/5.17 thf(fact_331_div__exp__eq,axiom,
% 4.97/5.17 ! [A: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % div_exp_eq
% 4.97/5.17 thf(fact_332_div__exp__eq,axiom,
% 4.97/5.17 ! [A: int,M: nat,N: nat] :
% 4.97/5.17 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % div_exp_eq
% 4.97/5.17 thf(fact_333_not__Some__eq,axiom,
% 4.97/5.17 ! [X2: option4927543243414619207at_nat] :
% 4.97/5.17 ( ( ! [Y2: product_prod_nat_nat] :
% 4.97/5.17 ( X2
% 4.97/5.17 != ( some_P7363390416028606310at_nat @ Y2 ) ) )
% 4.97/5.17 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_Some_eq
% 4.97/5.17 thf(fact_334_not__Some__eq,axiom,
% 4.97/5.17 ! [X2: option_num] :
% 4.97/5.17 ( ( ! [Y2: num] :
% 4.97/5.17 ( X2
% 4.97/5.17 != ( some_num @ Y2 ) ) )
% 4.97/5.17 = ( X2 = none_num ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_Some_eq
% 4.97/5.17 thf(fact_335_power__one__right,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( power_power_real @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_right
% 4.97/5.17 thf(fact_336_power__one__right,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( power_power_nat @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_right
% 4.97/5.17 thf(fact_337_power__one__right,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( power_power_int @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_right
% 4.97/5.17 thf(fact_338_power__one__right,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( power_power_complex @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % power_one_right
% 4.97/5.17 thf(fact_339_option_Oinject,axiom,
% 4.97/5.17 ! [X23: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 4.97/5.17 ( ( ( some_P7363390416028606310at_nat @ X23 )
% 4.97/5.17 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 4.97/5.17 = ( X23 = Y22 ) ) ).
% 4.97/5.17
% 4.97/5.17 % option.inject
% 4.97/5.17 thf(fact_340_option_Oinject,axiom,
% 4.97/5.17 ! [X23: num,Y22: num] :
% 4.97/5.17 ( ( ( some_num @ X23 )
% 4.97/5.17 = ( some_num @ Y22 ) )
% 4.97/5.17 = ( X23 = Y22 ) ) ).
% 4.97/5.17
% 4.97/5.17 % option.inject
% 4.97/5.17 thf(fact_341_pow__sum,axiom,
% 4.97/5.17 ! [A: nat,B: nat] :
% 4.97/5.17 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 4.97/5.17 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % pow_sum
% 4.97/5.17 thf(fact_342_numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_less_iff
% 4.97/5.17 thf(fact_343_numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_less_iff
% 4.97/5.17 thf(fact_344_numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_less_iff
% 4.97/5.17 thf(fact_345_numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_less_iff
% 4.97/5.17 thf(fact_346_neg__numeral__eq__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( M = N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_eq_iff
% 4.97/5.17 thf(fact_347_neg__numeral__eq__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( M = N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_eq_iff
% 4.97/5.17 thf(fact_348_neg__numeral__eq__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( M = N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_eq_iff
% 4.97/5.17 thf(fact_349_neg__numeral__eq__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( M = N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_eq_iff
% 4.97/5.17 thf(fact_350_neg__numeral__eq__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( M = N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_eq_iff
% 4.97/5.17 thf(fact_351_mult__minus__left,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 4.97/5.17 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_left
% 4.97/5.17 thf(fact_352_mult__minus__left,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 4.97/5.17 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_left
% 4.97/5.17 thf(fact_353_mult__minus__left,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_left
% 4.97/5.17 thf(fact_354_mult__minus__left,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_left
% 4.97/5.17 thf(fact_355_mult__minus__left,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.97/5.17 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_left
% 4.97/5.17 thf(fact_356_minus__mult__minus,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.97/5.17 = ( times_times_real @ A @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_minus
% 4.97/5.17 thf(fact_357_minus__mult__minus,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.97/5.17 = ( times_times_int @ A @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_minus
% 4.97/5.17 thf(fact_358_minus__mult__minus,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.17 = ( times_times_complex @ A @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_minus
% 4.97/5.17 thf(fact_359_minus__mult__minus,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.17 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_minus
% 4.97/5.17 thf(fact_360_minus__mult__minus,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.97/5.17 = ( times_times_rat @ A @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_minus
% 4.97/5.17 thf(fact_361_mult__minus__right,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_right
% 4.97/5.17 thf(fact_362_mult__minus__right,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_right
% 4.97/5.17 thf(fact_363_mult__minus__right,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_right
% 4.97/5.17 thf(fact_364_mult__minus__right,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_right
% 4.97/5.17 thf(fact_365_mult__minus__right,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus_right
% 4.97/5.17 thf(fact_366_bits__div__by__1,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % bits_div_by_1
% 4.97/5.17 thf(fact_367_bits__div__by__1,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( divide_divide_int @ A @ one_one_int )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % bits_div_by_1
% 4.97/5.17 thf(fact_368_div__by__1,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % div_by_1
% 4.97/5.17 thf(fact_369_div__by__1,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( divide_divide_real @ A @ one_one_real )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % div_by_1
% 4.97/5.17 thf(fact_370_div__by__1,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( divide_divide_rat @ A @ one_one_rat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % div_by_1
% 4.97/5.17 thf(fact_371_div__by__1,axiom,
% 4.97/5.17 ! [A: nat] :
% 4.97/5.17 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % div_by_1
% 4.97/5.17 thf(fact_372_div__by__1,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( divide_divide_int @ A @ one_one_int )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % div_by_1
% 4.97/5.17 thf(fact_373_set__n__deg__not__0,axiom,
% 4.97/5.17 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 4.97/5.17 ( ! [X4: vEBT_VEBT] :
% 4.97/5.17 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.17 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.97/5.17 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.97/5.17 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.17 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % set_n_deg_not_0
% 4.97/5.17 thf(fact_374_real__divide__square__eq,axiom,
% 4.97/5.17 ! [R: real,A: real] :
% 4.97/5.17 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 4.97/5.17 = ( divide_divide_real @ A @ R ) ) ).
% 4.97/5.17
% 4.97/5.17 % real_divide_square_eq
% 4.97/5.17 thf(fact_375_not__None__eq,axiom,
% 4.97/5.17 ! [X2: option4927543243414619207at_nat] :
% 4.97/5.17 ( ( X2 != none_P5556105721700978146at_nat )
% 4.97/5.17 = ( ? [Y2: product_prod_nat_nat] :
% 4.97/5.17 ( X2
% 4.97/5.17 = ( some_P7363390416028606310at_nat @ Y2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_None_eq
% 4.97/5.17 thf(fact_376_not__None__eq,axiom,
% 4.97/5.17 ! [X2: option_num] :
% 4.97/5.17 ( ( X2 != none_num )
% 4.97/5.17 = ( ? [Y2: num] :
% 4.97/5.17 ( X2
% 4.97/5.17 = ( some_num @ Y2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_None_eq
% 4.97/5.17 thf(fact_377_neg__numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( ord_less_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_iff
% 4.97/5.17 thf(fact_378_neg__numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( ord_less_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_iff
% 4.97/5.17 thf(fact_379_neg__numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( ord_less_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_iff
% 4.97/5.17 thf(fact_380_neg__numeral__less__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( ord_less_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_iff
% 4.97/5.17 thf(fact_381_power__inject__exp,axiom,
% 4.97/5.17 ! [A: real,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.17 => ( ( ( power_power_real @ A @ M )
% 4.97/5.17 = ( power_power_real @ A @ N ) )
% 4.97/5.17 = ( M = N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_inject_exp
% 4.97/5.17 thf(fact_382_power__inject__exp,axiom,
% 4.97/5.17 ! [A: rat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.17 => ( ( ( power_power_rat @ A @ M )
% 4.97/5.17 = ( power_power_rat @ A @ N ) )
% 4.97/5.17 = ( M = N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_inject_exp
% 4.97/5.17 thf(fact_383_power__inject__exp,axiom,
% 4.97/5.17 ! [A: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.17 => ( ( ( power_power_nat @ A @ M )
% 4.97/5.17 = ( power_power_nat @ A @ N ) )
% 4.97/5.17 = ( M = N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_inject_exp
% 4.97/5.17 thf(fact_384_power__inject__exp,axiom,
% 4.97/5.17 ! [A: int,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.17 => ( ( ( power_power_int @ A @ M )
% 4.97/5.17 = ( power_power_int @ A @ N ) )
% 4.97/5.17 = ( M = N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_inject_exp
% 4.97/5.17 thf(fact_385_add__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_386_add__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_387_add__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_388_add__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_389_add__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_390_mult__minus1__right,axiom,
% 4.97/5.17 ! [Z: real] :
% 4.97/5.17 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.17 = ( uminus_uminus_real @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1_right
% 4.97/5.17 thf(fact_391_mult__minus1__right,axiom,
% 4.97/5.17 ! [Z: int] :
% 4.97/5.17 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.17 = ( uminus_uminus_int @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1_right
% 4.97/5.17 thf(fact_392_mult__minus1__right,axiom,
% 4.97/5.17 ! [Z: complex] :
% 4.97/5.17 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1_right
% 4.97/5.17 thf(fact_393_mult__minus1__right,axiom,
% 4.97/5.17 ! [Z: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1_right
% 4.97/5.17 thf(fact_394_mult__minus1__right,axiom,
% 4.97/5.17 ! [Z: rat] :
% 4.97/5.17 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.17 = ( uminus_uminus_rat @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1_right
% 4.97/5.17 thf(fact_395_mult__minus1,axiom,
% 4.97/5.17 ! [Z: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 4.97/5.17 = ( uminus_uminus_real @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1
% 4.97/5.17 thf(fact_396_mult__minus1,axiom,
% 4.97/5.17 ! [Z: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 4.97/5.17 = ( uminus_uminus_int @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1
% 4.97/5.17 thf(fact_397_mult__minus1,axiom,
% 4.97/5.17 ! [Z: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1
% 4.97/5.17 thf(fact_398_mult__minus1,axiom,
% 4.97/5.17 ! [Z: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1
% 4.97/5.17 thf(fact_399_mult__minus1,axiom,
% 4.97/5.17 ! [Z: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 4.97/5.17 = ( uminus_uminus_rat @ Z ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_minus1
% 4.97/5.17 thf(fact_400_one__less__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( ord_less_num @ one @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_less_numeral_iff
% 4.97/5.17 thf(fact_401_one__less__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( ord_less_num @ one @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_less_numeral_iff
% 4.97/5.17 thf(fact_402_one__less__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 4.97/5.17 = ( ord_less_num @ one @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_less_numeral_iff
% 4.97/5.17 thf(fact_403_one__less__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( ord_less_num @ one @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % one_less_numeral_iff
% 4.97/5.17 thf(fact_404_divide__less__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [B: real,W: num,A: real] :
% 4.97/5.17 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 4.97/5.17 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_less_eq_numeral1(1)
% 4.97/5.17 thf(fact_405_divide__less__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [B: rat,W: num,A: rat] :
% 4.97/5.17 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 4.97/5.17 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_less_eq_numeral1(1)
% 4.97/5.17 thf(fact_406_less__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [A: real,B: real,W: num] :
% 4.97/5.17 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.97/5.17 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_divide_eq_numeral1(1)
% 4.97/5.17 thf(fact_407_less__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.17 ! [A: rat,B: rat,W: num] :
% 4.97/5.17 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.97/5.17 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_divide_eq_numeral1(1)
% 4.97/5.17 thf(fact_408_neg__one__eq__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_real @ one_one_real )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_eq_numeral_iff
% 4.97/5.17 thf(fact_409_neg__one__eq__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_int @ one_one_int )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_eq_numeral_iff
% 4.97/5.17 thf(fact_410_neg__one__eq__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_eq_numeral_iff
% 4.97/5.17 thf(fact_411_neg__one__eq__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_eq_numeral_iff
% 4.97/5.17 thf(fact_412_neg__one__eq__numeral__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_rat @ one_one_rat )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_eq_numeral_iff
% 4.97/5.17 thf(fact_413_numeral__eq__neg__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_eq_neg_one_iff
% 4.97/5.17 thf(fact_414_numeral__eq__neg__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_eq_neg_one_iff
% 4.97/5.17 thf(fact_415_numeral__eq__neg__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_eq_neg_one_iff
% 4.97/5.17 thf(fact_416_numeral__eq__neg__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_eq_neg_one_iff
% 4.97/5.17 thf(fact_417_numeral__eq__neg__one__iff,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.17 = ( N = one ) ) ).
% 4.97/5.17
% 4.97/5.17 % numeral_eq_neg_one_iff
% 4.97/5.17 thf(fact_418_minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 4.97/5.17 = one_one_real ) ).
% 4.97/5.17
% 4.97/5.17 % minus_one_mult_self
% 4.97/5.17 thf(fact_419_minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 4.97/5.17 = one_one_int ) ).
% 4.97/5.17
% 4.97/5.17 % minus_one_mult_self
% 4.97/5.17 thf(fact_420_minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 4.97/5.17 = one_one_complex ) ).
% 4.97/5.17
% 4.97/5.17 % minus_one_mult_self
% 4.97/5.17 thf(fact_421_minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 4.97/5.17 = one_one_Code_integer ) ).
% 4.97/5.17
% 4.97/5.17 % minus_one_mult_self
% 4.97/5.17 thf(fact_422_minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 4.97/5.17 = one_one_rat ) ).
% 4.97/5.17
% 4.97/5.17 % minus_one_mult_self
% 4.97/5.17 thf(fact_423_left__minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat,A: real] :
% 4.97/5.17 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % left_minus_one_mult_self
% 4.97/5.17 thf(fact_424_left__minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat,A: int] :
% 4.97/5.17 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % left_minus_one_mult_self
% 4.97/5.17 thf(fact_425_left__minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat,A: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % left_minus_one_mult_self
% 4.97/5.17 thf(fact_426_left__minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat,A: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % left_minus_one_mult_self
% 4.97/5.17 thf(fact_427_left__minus__one__mult__self,axiom,
% 4.97/5.17 ! [N: nat,A: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 4.97/5.17 = A ) ).
% 4.97/5.17
% 4.97/5.17 % left_minus_one_mult_self
% 4.97/5.17 thf(fact_428_power__strict__increasing__iff,axiom,
% 4.97/5.17 ! [B: real,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_real @ one_one_real @ B )
% 4.97/5.17 => ( ( ord_less_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y ) )
% 4.97/5.17 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing_iff
% 4.97/5.17 thf(fact_429_power__strict__increasing__iff,axiom,
% 4.97/5.17 ! [B: rat,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_rat @ one_one_rat @ B )
% 4.97/5.17 => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 4.97/5.17 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing_iff
% 4.97/5.17 thf(fact_430_power__strict__increasing__iff,axiom,
% 4.97/5.17 ! [B: nat,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_nat @ one_one_nat @ B )
% 4.97/5.17 => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 4.97/5.17 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing_iff
% 4.97/5.17 thf(fact_431_power__strict__increasing__iff,axiom,
% 4.97/5.17 ! [B: int,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_int @ one_one_int @ B )
% 4.97/5.17 => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 4.97/5.17 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing_iff
% 4.97/5.17 thf(fact_432_semiring__norm_I168_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: real] :
% 4.97/5.17 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 4.97/5.17 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(168)
% 4.97/5.17 thf(fact_433_semiring__norm_I168_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: int] :
% 4.97/5.17 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 4.97/5.17 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(168)
% 4.97/5.17 thf(fact_434_semiring__norm_I168_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: complex] :
% 4.97/5.17 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 4.97/5.17 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(168)
% 4.97/5.17 thf(fact_435_semiring__norm_I168_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: code_integer] :
% 4.97/5.17 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 4.97/5.17 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(168)
% 4.97/5.17 thf(fact_436_semiring__norm_I168_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: rat] :
% 4.97/5.17 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 4.97/5.17 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(168)
% 4.97/5.17 thf(fact_437_diff__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(3)
% 4.97/5.17 thf(fact_438_diff__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(3)
% 4.97/5.17 thf(fact_439_diff__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(3)
% 4.97/5.17 thf(fact_440_diff__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(3)
% 4.97/5.17 thf(fact_441_diff__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(3)
% 4.97/5.17 thf(fact_442_diff__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(2)
% 4.97/5.17 thf(fact_443_diff__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(2)
% 4.97/5.17 thf(fact_444_diff__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(2)
% 4.97/5.17 thf(fact_445_diff__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(2)
% 4.97/5.17 thf(fact_446_diff__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_simps(2)
% 4.97/5.17 thf(fact_447_semiring__norm_I172_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(172)
% 4.97/5.17 thf(fact_448_semiring__norm_I172_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(172)
% 4.97/5.17 thf(fact_449_semiring__norm_I172_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(172)
% 4.97/5.17 thf(fact_450_semiring__norm_I172_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(172)
% 4.97/5.17 thf(fact_451_semiring__norm_I172_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(172)
% 4.97/5.17 thf(fact_452_semiring__norm_I171_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: real] :
% 4.97/5.17 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(171)
% 4.97/5.17 thf(fact_453_semiring__norm_I171_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: int] :
% 4.97/5.17 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(171)
% 4.97/5.17 thf(fact_454_semiring__norm_I171_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(171)
% 4.97/5.17 thf(fact_455_semiring__norm_I171_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(171)
% 4.97/5.17 thf(fact_456_semiring__norm_I171_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 4.97/5.17 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(171)
% 4.97/5.17 thf(fact_457_semiring__norm_I170_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 4.97/5.17 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(170)
% 4.97/5.17 thf(fact_458_semiring__norm_I170_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 4.97/5.17 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(170)
% 4.97/5.17 thf(fact_459_semiring__norm_I170_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 4.97/5.17 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(170)
% 4.97/5.17 thf(fact_460_semiring__norm_I170_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 4.97/5.17 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(170)
% 4.97/5.17 thf(fact_461_semiring__norm_I170_J,axiom,
% 4.97/5.17 ! [V: num,W: num,Y: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 4.97/5.17 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 4.97/5.17
% 4.97/5.17 % semiring_norm(170)
% 4.97/5.17 thf(fact_462_mult__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_463_mult__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_464_mult__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_465_mult__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_466_mult__neg__numeral__simps_I3_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(3)
% 4.97/5.17 thf(fact_467_mult__neg__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(2)
% 4.97/5.17 thf(fact_468_mult__neg__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(2)
% 4.97/5.17 thf(fact_469_mult__neg__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(2)
% 4.97/5.17 thf(fact_470_mult__neg__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(2)
% 4.97/5.17 thf(fact_471_mult__neg__numeral__simps_I2_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(2)
% 4.97/5.17 thf(fact_472_mult__neg__numeral__simps_I1_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(1)
% 4.97/5.17 thf(fact_473_mult__neg__numeral__simps_I1_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(1)
% 4.97/5.17 thf(fact_474_mult__neg__numeral__simps_I1_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(1)
% 4.97/5.17 thf(fact_475_mult__neg__numeral__simps_I1_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(1)
% 4.97/5.17 thf(fact_476_mult__neg__numeral__simps_I1_J,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % mult_neg_numeral_simps(1)
% 4.97/5.17 thf(fact_477_neg__numeral__le__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( ord_less_eq_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_le_iff
% 4.97/5.17 thf(fact_478_neg__numeral__le__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( ord_less_eq_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_le_iff
% 4.97/5.17 thf(fact_479_neg__numeral__le__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( ord_less_eq_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_le_iff
% 4.97/5.17 thf(fact_480_neg__numeral__le__iff,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( ord_less_eq_num @ N @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_le_iff
% 4.97/5.17 thf(fact_481_not__neg__one__le__neg__numeral__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_le_neg_numeral_iff
% 4.97/5.17 thf(fact_482_not__neg__one__le__neg__numeral__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_le_neg_numeral_iff
% 4.97/5.17 thf(fact_483_not__neg__one__le__neg__numeral__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_le_neg_numeral_iff
% 4.97/5.17 thf(fact_484_not__neg__one__le__neg__numeral__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_le_neg_numeral_iff
% 4.97/5.17 thf(fact_485_divide__le__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [B: real,W: num,A: real] :
% 4.97/5.17 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 4.97/5.17 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_le_eq_numeral1(2)
% 4.97/5.17 thf(fact_486_divide__le__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [B: rat,W: num,A: rat] :
% 4.97/5.17 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 4.97/5.17 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_le_eq_numeral1(2)
% 4.97/5.17 thf(fact_487_le__divide__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [A: real,B: real,W: num] :
% 4.97/5.17 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 4.97/5.17 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_divide_eq_numeral1(2)
% 4.97/5.17 thf(fact_488_le__divide__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [A: rat,B: rat,W: num] :
% 4.97/5.17 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 4.97/5.17 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % le_divide_eq_numeral1(2)
% 4.97/5.17 thf(fact_489_neg__numeral__less__neg__one__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_neg_one_iff
% 4.97/5.17 thf(fact_490_neg__numeral__less__neg__one__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_neg_one_iff
% 4.97/5.17 thf(fact_491_neg__numeral__less__neg__one__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_neg_one_iff
% 4.97/5.17 thf(fact_492_neg__numeral__less__neg__one__iff,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.17 = ( M != one ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_neg_one_iff
% 4.97/5.17 thf(fact_493_divide__less__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [B: real,W: num,A: real] :
% 4.97/5.17 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 4.97/5.17 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_less_eq_numeral1(2)
% 4.97/5.17 thf(fact_494_divide__less__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [B: rat,W: num,A: rat] :
% 4.97/5.17 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 4.97/5.17 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 4.97/5.17
% 4.97/5.17 % divide_less_eq_numeral1(2)
% 4.97/5.17 thf(fact_495_less__divide__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [A: real,B: real,W: num] :
% 4.97/5.17 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 4.97/5.17 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_divide_eq_numeral1(2)
% 4.97/5.17 thf(fact_496_less__divide__eq__numeral1_I2_J,axiom,
% 4.97/5.17 ! [A: rat,B: rat,W: num] :
% 4.97/5.17 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 4.97/5.17 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_divide_eq_numeral1(2)
% 4.97/5.17 thf(fact_497_power__increasing__iff,axiom,
% 4.97/5.17 ! [B: real,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_real @ one_one_real @ B )
% 4.97/5.17 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y ) )
% 4.97/5.17 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing_iff
% 4.97/5.17 thf(fact_498_power__increasing__iff,axiom,
% 4.97/5.17 ! [B: rat,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_rat @ one_one_rat @ B )
% 4.97/5.17 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 4.97/5.17 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing_iff
% 4.97/5.17 thf(fact_499_power__increasing__iff,axiom,
% 4.97/5.17 ! [B: nat,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_nat @ one_one_nat @ B )
% 4.97/5.17 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 4.97/5.17 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing_iff
% 4.97/5.17 thf(fact_500_power__increasing__iff,axiom,
% 4.97/5.17 ! [B: int,X2: nat,Y: nat] :
% 4.97/5.17 ( ( ord_less_int @ one_one_int @ B )
% 4.97/5.17 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 4.97/5.17 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_increasing_iff
% 4.97/5.17 thf(fact_501_power2__minus,axiom,
% 4.97/5.17 ! [A: real] :
% 4.97/5.17 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_minus
% 4.97/5.17 thf(fact_502_power2__minus,axiom,
% 4.97/5.17 ! [A: int] :
% 4.97/5.17 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_minus
% 4.97/5.17 thf(fact_503_power2__minus,axiom,
% 4.97/5.17 ! [A: complex] :
% 4.97/5.17 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_minus
% 4.97/5.17 thf(fact_504_power2__minus,axiom,
% 4.97/5.17 ! [A: code_integer] :
% 4.97/5.17 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_minus
% 4.97/5.17 thf(fact_505_power2__minus,axiom,
% 4.97/5.17 ! [A: rat] :
% 4.97/5.17 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.17 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power2_minus
% 4.97/5.17 thf(fact_506_add__neg__numeral__special_I9_J,axiom,
% 4.97/5.17 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_special(9)
% 4.97/5.17 thf(fact_507_add__neg__numeral__special_I9_J,axiom,
% 4.97/5.17 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_special(9)
% 4.97/5.17 thf(fact_508_add__neg__numeral__special_I9_J,axiom,
% 4.97/5.17 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_special(9)
% 4.97/5.17 thf(fact_509_add__neg__numeral__special_I9_J,axiom,
% 4.97/5.17 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_special(9)
% 4.97/5.17 thf(fact_510_add__neg__numeral__special_I9_J,axiom,
% 4.97/5.17 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % add_neg_numeral_special(9)
% 4.97/5.17 thf(fact_511_diff__numeral__special_I11_J,axiom,
% 4.97/5.17 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.17 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(11)
% 4.97/5.17 thf(fact_512_diff__numeral__special_I11_J,axiom,
% 4.97/5.17 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.17 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(11)
% 4.97/5.17 thf(fact_513_diff__numeral__special_I11_J,axiom,
% 4.97/5.17 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(11)
% 4.97/5.17 thf(fact_514_diff__numeral__special_I11_J,axiom,
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.17 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(11)
% 4.97/5.17 thf(fact_515_diff__numeral__special_I11_J,axiom,
% 4.97/5.17 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.17 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(11)
% 4.97/5.17 thf(fact_516_diff__numeral__special_I10_J,axiom,
% 4.97/5.17 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(10)
% 4.97/5.17 thf(fact_517_diff__numeral__special_I10_J,axiom,
% 4.97/5.17 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(10)
% 4.97/5.17 thf(fact_518_diff__numeral__special_I10_J,axiom,
% 4.97/5.17 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(10)
% 4.97/5.17 thf(fact_519_diff__numeral__special_I10_J,axiom,
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(10)
% 4.97/5.17 thf(fact_520_diff__numeral__special_I10_J,axiom,
% 4.97/5.17 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(10)
% 4.97/5.17 thf(fact_521_Power_Oring__1__class_Opower__minus__even,axiom,
% 4.97/5.17 ! [A: real,N: nat] :
% 4.97/5.17 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Power.ring_1_class.power_minus_even
% 4.97/5.17 thf(fact_522_Power_Oring__1__class_Opower__minus__even,axiom,
% 4.97/5.17 ! [A: int,N: nat] :
% 4.97/5.17 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Power.ring_1_class.power_minus_even
% 4.97/5.17 thf(fact_523_Power_Oring__1__class_Opower__minus__even,axiom,
% 4.97/5.17 ! [A: complex,N: nat] :
% 4.97/5.17 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Power.ring_1_class.power_minus_even
% 4.97/5.17 thf(fact_524_Power_Oring__1__class_Opower__minus__even,axiom,
% 4.97/5.17 ! [A: code_integer,N: nat] :
% 4.97/5.17 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Power.ring_1_class.power_minus_even
% 4.97/5.17 thf(fact_525_Power_Oring__1__class_Opower__minus__even,axiom,
% 4.97/5.17 ! [A: rat,N: nat] :
% 4.97/5.17 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % Power.ring_1_class.power_minus_even
% 4.97/5.17 thf(fact_526_diff__numeral__special_I4_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 4.97/5.17 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(4)
% 4.97/5.17 thf(fact_527_diff__numeral__special_I4_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 4.97/5.17 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(4)
% 4.97/5.17 thf(fact_528_diff__numeral__special_I4_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(4)
% 4.97/5.17 thf(fact_529_diff__numeral__special_I4_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(4)
% 4.97/5.17 thf(fact_530_diff__numeral__special_I4_J,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 4.97/5.17 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(4)
% 4.97/5.17 thf(fact_531_diff__numeral__special_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(3)
% 4.97/5.17 thf(fact_532_diff__numeral__special_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(3)
% 4.97/5.17 thf(fact_533_diff__numeral__special_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 4.97/5.17 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(3)
% 4.97/5.17 thf(fact_534_diff__numeral__special_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 4.97/5.17 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(3)
% 4.97/5.17 thf(fact_535_diff__numeral__special_I3_J,axiom,
% 4.97/5.17 ! [N: num] :
% 4.97/5.17 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 4.97/5.17 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % diff_numeral_special(3)
% 4.97/5.17 thf(fact_536_power__minus1__even,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = one_one_real ) ).
% 4.97/5.17
% 4.97/5.17 % power_minus1_even
% 4.97/5.17 thf(fact_537_power__minus1__even,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = one_one_int ) ).
% 4.97/5.17
% 4.97/5.17 % power_minus1_even
% 4.97/5.17 thf(fact_538_power__minus1__even,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = one_one_complex ) ).
% 4.97/5.17
% 4.97/5.17 % power_minus1_even
% 4.97/5.17 thf(fact_539_power__minus1__even,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = one_one_Code_integer ) ).
% 4.97/5.17
% 4.97/5.17 % power_minus1_even
% 4.97/5.17 thf(fact_540_power__minus1__even,axiom,
% 4.97/5.17 ! [N: nat] :
% 4.97/5.17 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.17 = one_one_rat ) ).
% 4.97/5.17
% 4.97/5.17 % power_minus1_even
% 4.97/5.17 thf(fact_541__C4_Ohyps_C_I5_J,axiom,
% 4.97/5.17 ! [I2: nat] :
% 4.97/5.17 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.97/5.17 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X5 ) )
% 4.97/5.17 = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % "4.hyps"(5)
% 4.97/5.17 thf(fact_542_linorder__neqE__linordered__idom,axiom,
% 4.97/5.17 ! [X2: real,Y: real] :
% 4.97/5.17 ( ( X2 != Y )
% 4.97/5.17 => ( ~ ( ord_less_real @ X2 @ Y )
% 4.97/5.17 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % linorder_neqE_linordered_idom
% 4.97/5.17 thf(fact_543_linorder__neqE__linordered__idom,axiom,
% 4.97/5.17 ! [X2: rat,Y: rat] :
% 4.97/5.17 ( ( X2 != Y )
% 4.97/5.17 => ( ~ ( ord_less_rat @ X2 @ Y )
% 4.97/5.17 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % linorder_neqE_linordered_idom
% 4.97/5.17 thf(fact_544_linorder__neqE__linordered__idom,axiom,
% 4.97/5.17 ! [X2: int,Y: int] :
% 4.97/5.17 ( ( X2 != Y )
% 4.97/5.17 => ( ~ ( ord_less_int @ X2 @ Y )
% 4.97/5.17 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % linorder_neqE_linordered_idom
% 4.97/5.17 thf(fact_545_not__numeral__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_numeral
% 4.97/5.17 thf(fact_546_not__numeral__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_numeral
% 4.97/5.17 thf(fact_547_not__numeral__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_numeral
% 4.97/5.17 thf(fact_548_not__numeral__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_numeral
% 4.97/5.17 thf(fact_549_neg__numeral__less__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_numeral
% 4.97/5.17 thf(fact_550_neg__numeral__less__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_numeral
% 4.97/5.17 thf(fact_551_neg__numeral__less__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_numeral
% 4.97/5.17 thf(fact_552_neg__numeral__less__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_numeral
% 4.97/5.17 thf(fact_553_less__minus__one__simps_I2_J,axiom,
% 4.97/5.17 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(2)
% 4.97/5.17 thf(fact_554_less__minus__one__simps_I2_J,axiom,
% 4.97/5.17 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(2)
% 4.97/5.17 thf(fact_555_less__minus__one__simps_I2_J,axiom,
% 4.97/5.17 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(2)
% 4.97/5.17 thf(fact_556_less__minus__one__simps_I2_J,axiom,
% 4.97/5.17 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(2)
% 4.97/5.17 thf(fact_557_less__minus__one__simps_I4_J,axiom,
% 4.97/5.17 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(4)
% 4.97/5.17 thf(fact_558_less__minus__one__simps_I4_J,axiom,
% 4.97/5.17 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(4)
% 4.97/5.17 thf(fact_559_less__minus__one__simps_I4_J,axiom,
% 4.97/5.17 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(4)
% 4.97/5.17 thf(fact_560_less__minus__one__simps_I4_J,axiom,
% 4.97/5.17 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.17
% 4.97/5.17 % less_minus_one_simps(4)
% 4.97/5.17 thf(fact_561_square__eq__iff,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( ( times_times_real @ A @ A )
% 4.97/5.17 = ( times_times_real @ B @ B ) )
% 4.97/5.17 = ( ( A = B )
% 4.97/5.17 | ( A
% 4.97/5.17 = ( uminus_uminus_real @ B ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % square_eq_iff
% 4.97/5.17 thf(fact_562_square__eq__iff,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( ( times_times_int @ A @ A )
% 4.97/5.17 = ( times_times_int @ B @ B ) )
% 4.97/5.17 = ( ( A = B )
% 4.97/5.17 | ( A
% 4.97/5.17 = ( uminus_uminus_int @ B ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % square_eq_iff
% 4.97/5.17 thf(fact_563_square__eq__iff,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( ( times_times_complex @ A @ A )
% 4.97/5.17 = ( times_times_complex @ B @ B ) )
% 4.97/5.17 = ( ( A = B )
% 4.97/5.17 | ( A
% 4.97/5.17 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % square_eq_iff
% 4.97/5.17 thf(fact_564_square__eq__iff,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( ( times_3573771949741848930nteger @ A @ A )
% 4.97/5.17 = ( times_3573771949741848930nteger @ B @ B ) )
% 4.97/5.17 = ( ( A = B )
% 4.97/5.17 | ( A
% 4.97/5.17 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % square_eq_iff
% 4.97/5.17 thf(fact_565_square__eq__iff,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( ( times_times_rat @ A @ A )
% 4.97/5.17 = ( times_times_rat @ B @ B ) )
% 4.97/5.17 = ( ( A = B )
% 4.97/5.17 | ( A
% 4.97/5.17 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % square_eq_iff
% 4.97/5.17 thf(fact_566_minus__mult__commute,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 4.97/5.17 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_commute
% 4.97/5.17 thf(fact_567_minus__mult__commute,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 4.97/5.17 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_commute
% 4.97/5.17 thf(fact_568_minus__mult__commute,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.97/5.17 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_commute
% 4.97/5.17 thf(fact_569_minus__mult__commute,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 4.97/5.17 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_commute
% 4.97/5.17 thf(fact_570_minus__mult__commute,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.97/5.17 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_mult_commute
% 4.97/5.17 thf(fact_571_minus__diff__minus,axiom,
% 4.97/5.17 ! [A: real,B: real] :
% 4.97/5.17 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.97/5.17 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_diff_minus
% 4.97/5.17 thf(fact_572_minus__diff__minus,axiom,
% 4.97/5.17 ! [A: int,B: int] :
% 4.97/5.17 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.97/5.17 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_diff_minus
% 4.97/5.17 thf(fact_573_minus__diff__minus,axiom,
% 4.97/5.17 ! [A: complex,B: complex] :
% 4.97/5.17 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.17 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_diff_minus
% 4.97/5.17 thf(fact_574_minus__diff__minus,axiom,
% 4.97/5.17 ! [A: code_integer,B: code_integer] :
% 4.97/5.17 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.17 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_diff_minus
% 4.97/5.17 thf(fact_575_minus__diff__minus,axiom,
% 4.97/5.17 ! [A: rat,B: rat] :
% 4.97/5.17 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.97/5.17 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % minus_diff_minus
% 4.97/5.17 thf(fact_576_not__neg__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_less_neg_numeral
% 4.97/5.17 thf(fact_577_not__neg__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_less_neg_numeral
% 4.97/5.17 thf(fact_578_not__neg__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_less_neg_numeral
% 4.97/5.17 thf(fact_579_not__neg__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_neg_one_less_neg_numeral
% 4.97/5.17 thf(fact_580_not__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_one_less_neg_numeral
% 4.97/5.17 thf(fact_581_not__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_one_less_neg_numeral
% 4.97/5.17 thf(fact_582_not__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_one_less_neg_numeral
% 4.97/5.17 thf(fact_583_not__one__less__neg__numeral,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_one_less_neg_numeral
% 4.97/5.17 thf(fact_584_not__numeral__less__neg__one,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_one
% 4.97/5.17 thf(fact_585_not__numeral__less__neg__one,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_one
% 4.97/5.17 thf(fact_586_not__numeral__less__neg__one,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_one
% 4.97/5.17 thf(fact_587_not__numeral__less__neg__one,axiom,
% 4.97/5.17 ! [M: num] :
% 4.97/5.17 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.17
% 4.97/5.17 % not_numeral_less_neg_one
% 4.97/5.17 thf(fact_588_neg__one__less__numeral,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_less_numeral
% 4.97/5.17 thf(fact_589_neg__one__less__numeral,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_less_numeral
% 4.97/5.17 thf(fact_590_neg__one__less__numeral,axiom,
% 4.97/5.17 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_less_numeral
% 4.97/5.17 thf(fact_591_neg__one__less__numeral,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_one_less_numeral
% 4.97/5.17 thf(fact_592_neg__numeral__less__one,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_one
% 4.97/5.17 thf(fact_593_neg__numeral__less__one,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_one
% 4.97/5.17 thf(fact_594_neg__numeral__less__one,axiom,
% 4.97/5.17 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_one
% 4.97/5.17 thf(fact_595_neg__numeral__less__one,axiom,
% 4.97/5.17 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_less_one
% 4.97/5.17 thf(fact_596_power__strict__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: real] :
% 4.97/5.17 ( ( ord_less_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.17 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing
% 4.97/5.17 thf(fact_597_power__strict__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: rat] :
% 4.97/5.17 ( ( ord_less_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.17 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing
% 4.97/5.17 thf(fact_598_power__strict__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: nat] :
% 4.97/5.17 ( ( ord_less_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.17 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing
% 4.97/5.17 thf(fact_599_power__strict__increasing,axiom,
% 4.97/5.17 ! [N: nat,N2: nat,A: int] :
% 4.97/5.17 ( ( ord_less_nat @ N @ N2 )
% 4.97/5.17 => ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.17 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_strict_increasing
% 4.97/5.17 thf(fact_600_power__less__imp__less__exp,axiom,
% 4.97/5.17 ! [A: real,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.17 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 4.97/5.17 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_less_imp_less_exp
% 4.97/5.17 thf(fact_601_power__less__imp__less__exp,axiom,
% 4.97/5.17 ! [A: rat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.17 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 4.97/5.17 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_less_imp_less_exp
% 4.97/5.17 thf(fact_602_power__less__imp__less__exp,axiom,
% 4.97/5.17 ! [A: nat,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.17 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 4.97/5.17 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_less_imp_less_exp
% 4.97/5.17 thf(fact_603_power__less__imp__less__exp,axiom,
% 4.97/5.17 ! [A: int,M: nat,N: nat] :
% 4.97/5.17 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.17 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 4.97/5.17 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.17
% 4.97/5.17 % power_less_imp_less_exp
% 4.97/5.17 thf(fact_604_neg__numeral__neq__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 4.97/5.17 != ( numeral_numeral_real @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_neq_numeral
% 4.97/5.17 thf(fact_605_neg__numeral__neq__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 4.97/5.17 != ( numeral_numeral_int @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_neq_numeral
% 4.97/5.17 thf(fact_606_neg__numeral__neq__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 4.97/5.17 != ( numera6690914467698888265omplex @ N ) ) ).
% 4.97/5.17
% 4.97/5.17 % neg_numeral_neq_numeral
% 4.97/5.17 thf(fact_607_neg__numeral__neq__numeral,axiom,
% 4.97/5.17 ! [M: num,N: num] :
% 4.97/5.17 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 4.97/5.17 != ( numera6620942414471956472nteger @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_neq_numeral
% 4.97/5.18 thf(fact_608_neg__numeral__neq__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 4.97/5.18 != ( numeral_numeral_rat @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_neq_numeral
% 4.97/5.18 thf(fact_609_numeral__neq__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( numeral_numeral_real @ M )
% 4.97/5.18 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_numeral
% 4.97/5.18 thf(fact_610_numeral__neq__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( numeral_numeral_int @ M )
% 4.97/5.18 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_numeral
% 4.97/5.18 thf(fact_611_numeral__neq__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( numera6690914467698888265omplex @ M )
% 4.97/5.18 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_numeral
% 4.97/5.18 thf(fact_612_numeral__neq__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( numera6620942414471956472nteger @ M )
% 4.97/5.18 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_numeral
% 4.97/5.18 thf(fact_613_numeral__neq__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( numeral_numeral_rat @ M )
% 4.97/5.18 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_numeral
% 4.97/5.18 thf(fact_614_is__num__normalize_I8_J,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.97/5.18 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % is_num_normalize(8)
% 4.97/5.18 thf(fact_615_is__num__normalize_I8_J,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.97/5.18 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % is_num_normalize(8)
% 4.97/5.18 thf(fact_616_is__num__normalize_I8_J,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.97/5.18 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % is_num_normalize(8)
% 4.97/5.18 thf(fact_617_is__num__normalize_I8_J,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.97/5.18 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % is_num_normalize(8)
% 4.97/5.18 thf(fact_618_is__num__normalize_I8_J,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.18 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % is_num_normalize(8)
% 4.97/5.18 thf(fact_619_one__neq__neg__one,axiom,
% 4.97/5.18 ( one_one_real
% 4.97/5.18 != ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_one
% 4.97/5.18 thf(fact_620_one__neq__neg__one,axiom,
% 4.97/5.18 ( one_one_int
% 4.97/5.18 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_one
% 4.97/5.18 thf(fact_621_one__neq__neg__one,axiom,
% 4.97/5.18 ( one_one_complex
% 4.97/5.18 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_one
% 4.97/5.18 thf(fact_622_one__neq__neg__one,axiom,
% 4.97/5.18 ( one_one_Code_integer
% 4.97/5.18 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_one
% 4.97/5.18 thf(fact_623_one__neq__neg__one,axiom,
% 4.97/5.18 ( one_one_rat
% 4.97/5.18 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_one
% 4.97/5.18 thf(fact_624_less__numeral__extra_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 4.97/5.18
% 4.97/5.18 % less_numeral_extra(4)
% 4.97/5.18 thf(fact_625_less__numeral__extra_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 4.97/5.18
% 4.97/5.18 % less_numeral_extra(4)
% 4.97/5.18 thf(fact_626_less__numeral__extra_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 4.97/5.18
% 4.97/5.18 % less_numeral_extra(4)
% 4.97/5.18 thf(fact_627_less__numeral__extra_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 4.97/5.18
% 4.97/5.18 % less_numeral_extra(4)
% 4.97/5.18 thf(fact_628_square__eq__1__iff,axiom,
% 4.97/5.18 ! [X2: real] :
% 4.97/5.18 ( ( ( times_times_real @ X2 @ X2 )
% 4.97/5.18 = one_one_real )
% 4.97/5.18 = ( ( X2 = one_one_real )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_eq_1_iff
% 4.97/5.18 thf(fact_629_square__eq__1__iff,axiom,
% 4.97/5.18 ! [X2: int] :
% 4.97/5.18 ( ( ( times_times_int @ X2 @ X2 )
% 4.97/5.18 = one_one_int )
% 4.97/5.18 = ( ( X2 = one_one_int )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_eq_1_iff
% 4.97/5.18 thf(fact_630_square__eq__1__iff,axiom,
% 4.97/5.18 ! [X2: complex] :
% 4.97/5.18 ( ( ( times_times_complex @ X2 @ X2 )
% 4.97/5.18 = one_one_complex )
% 4.97/5.18 = ( ( X2 = one_one_complex )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_eq_1_iff
% 4.97/5.18 thf(fact_631_square__eq__1__iff,axiom,
% 4.97/5.18 ! [X2: code_integer] :
% 4.97/5.18 ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 4.97/5.18 = one_one_Code_integer )
% 4.97/5.18 = ( ( X2 = one_one_Code_integer )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_eq_1_iff
% 4.97/5.18 thf(fact_632_square__eq__1__iff,axiom,
% 4.97/5.18 ! [X2: rat] :
% 4.97/5.18 ( ( ( times_times_rat @ X2 @ X2 )
% 4.97/5.18 = one_one_rat )
% 4.97/5.18 = ( ( X2 = one_one_rat )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_eq_1_iff
% 4.97/5.18 thf(fact_633_less__1__mult,axiom,
% 4.97/5.18 ! [M: real,N: real] :
% 4.97/5.18 ( ( ord_less_real @ one_one_real @ M )
% 4.97/5.18 => ( ( ord_less_real @ one_one_real @ N )
% 4.97/5.18 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_1_mult
% 4.97/5.18 thf(fact_634_less__1__mult,axiom,
% 4.97/5.18 ! [M: rat,N: rat] :
% 4.97/5.18 ( ( ord_less_rat @ one_one_rat @ M )
% 4.97/5.18 => ( ( ord_less_rat @ one_one_rat @ N )
% 4.97/5.18 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_1_mult
% 4.97/5.18 thf(fact_635_less__1__mult,axiom,
% 4.97/5.18 ! [M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_nat @ one_one_nat @ M )
% 4.97/5.18 => ( ( ord_less_nat @ one_one_nat @ N )
% 4.97/5.18 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_1_mult
% 4.97/5.18 thf(fact_636_less__1__mult,axiom,
% 4.97/5.18 ! [M: int,N: int] :
% 4.97/5.18 ( ( ord_less_int @ one_one_int @ M )
% 4.97/5.18 => ( ( ord_less_int @ one_one_int @ N )
% 4.97/5.18 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_1_mult
% 4.97/5.18 thf(fact_637_add__mono1,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( ord_less_real @ A @ B )
% 4.97/5.18 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono1
% 4.97/5.18 thf(fact_638_add__mono1,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( ord_less_rat @ A @ B )
% 4.97/5.18 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono1
% 4.97/5.18 thf(fact_639_add__mono1,axiom,
% 4.97/5.18 ! [A: nat,B: nat] :
% 4.97/5.18 ( ( ord_less_nat @ A @ B )
% 4.97/5.18 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono1
% 4.97/5.18 thf(fact_640_add__mono1,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( ord_less_int @ A @ B )
% 4.97/5.18 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono1
% 4.97/5.18 thf(fact_641_less__add__one,axiom,
% 4.97/5.18 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_one
% 4.97/5.18 thf(fact_642_less__add__one,axiom,
% 4.97/5.18 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_one
% 4.97/5.18 thf(fact_643_less__add__one,axiom,
% 4.97/5.18 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_one
% 4.97/5.18 thf(fact_644_less__add__one,axiom,
% 4.97/5.18 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_one
% 4.97/5.18 thf(fact_645_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ~ ( ord_less_real @ A @ B )
% 4.97/5.18 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.97/5.18 = A ) ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_semidom_class.add_diff_inverse
% 4.97/5.18 thf(fact_646_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ~ ( ord_less_rat @ A @ B )
% 4.97/5.18 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.97/5.18 = A ) ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_semidom_class.add_diff_inverse
% 4.97/5.18 thf(fact_647_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.97/5.18 ! [A: nat,B: nat] :
% 4.97/5.18 ( ~ ( ord_less_nat @ A @ B )
% 4.97/5.18 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.97/5.18 = A ) ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_semidom_class.add_diff_inverse
% 4.97/5.18 thf(fact_648_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ~ ( ord_less_int @ A @ B )
% 4.97/5.18 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.97/5.18 = A ) ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_semidom_class.add_diff_inverse
% 4.97/5.18 thf(fact_649_real__minus__mult__self__le,axiom,
% 4.97/5.18 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 4.97/5.18
% 4.97/5.18 % real_minus_mult_self_le
% 4.97/5.18 thf(fact_650_minus__real__def,axiom,
% 4.97/5.18 ( minus_minus_real
% 4.97/5.18 = ( ^ [X3: real,Y2: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y2 ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_real_def
% 4.97/5.18 thf(fact_651_neg__numeral__le__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_numeral
% 4.97/5.18 thf(fact_652_neg__numeral__le__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_numeral
% 4.97/5.18 thf(fact_653_neg__numeral__le__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_numeral
% 4.97/5.18 thf(fact_654_neg__numeral__le__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_numeral
% 4.97/5.18 thf(fact_655_not__numeral__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_numeral
% 4.97/5.18 thf(fact_656_not__numeral__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_numeral
% 4.97/5.18 thf(fact_657_not__numeral__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_numeral
% 4.97/5.18 thf(fact_658_not__numeral__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_numeral
% 4.97/5.18 thf(fact_659_le__minus__one__simps_I2_J,axiom,
% 4.97/5.18 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(2)
% 4.97/5.18 thf(fact_660_le__minus__one__simps_I2_J,axiom,
% 4.97/5.18 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(2)
% 4.97/5.18 thf(fact_661_le__minus__one__simps_I2_J,axiom,
% 4.97/5.18 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(2)
% 4.97/5.18 thf(fact_662_le__minus__one__simps_I2_J,axiom,
% 4.97/5.18 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(2)
% 4.97/5.18 thf(fact_663_le__minus__one__simps_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(4)
% 4.97/5.18 thf(fact_664_le__minus__one__simps_I4_J,axiom,
% 4.97/5.18 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(4)
% 4.97/5.18 thf(fact_665_le__minus__one__simps_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(4)
% 4.97/5.18 thf(fact_666_le__minus__one__simps_I4_J,axiom,
% 4.97/5.18 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % le_minus_one_simps(4)
% 4.97/5.18 thf(fact_667_less__add__iff1,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff1
% 4.97/5.18 thf(fact_668_less__add__iff1,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff1
% 4.97/5.18 thf(fact_669_less__add__iff1,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff1
% 4.97/5.18 thf(fact_670_less__add__iff2,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff2
% 4.97/5.18 thf(fact_671_less__add__iff2,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff2
% 4.97/5.18 thf(fact_672_less__add__iff2,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_add_iff2
% 4.97/5.18 thf(fact_673_numeral__times__minus__swap,axiom,
% 4.97/5.18 ! [W: num,X2: real] :
% 4.97/5.18 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X2 ) )
% 4.97/5.18 = ( times_times_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_times_minus_swap
% 4.97/5.18 thf(fact_674_numeral__times__minus__swap,axiom,
% 4.97/5.18 ! [W: num,X2: int] :
% 4.97/5.18 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X2 ) )
% 4.97/5.18 = ( times_times_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_times_minus_swap
% 4.97/5.18 thf(fact_675_numeral__times__minus__swap,axiom,
% 4.97/5.18 ! [W: num,X2: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X2 ) )
% 4.97/5.18 = ( times_times_complex @ X2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_times_minus_swap
% 4.97/5.18 thf(fact_676_numeral__times__minus__swap,axiom,
% 4.97/5.18 ! [W: num,X2: code_integer] :
% 4.97/5.18 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X2 ) )
% 4.97/5.18 = ( times_3573771949741848930nteger @ X2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_times_minus_swap
% 4.97/5.18 thf(fact_677_numeral__times__minus__swap,axiom,
% 4.97/5.18 ! [W: num,X2: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X2 ) )
% 4.97/5.18 = ( times_times_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_times_minus_swap
% 4.97/5.18 thf(fact_678_one__neq__neg__numeral,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( one_one_real
% 4.97/5.18 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_numeral
% 4.97/5.18 thf(fact_679_one__neq__neg__numeral,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( one_one_int
% 4.97/5.18 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_numeral
% 4.97/5.18 thf(fact_680_one__neq__neg__numeral,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( one_one_complex
% 4.97/5.18 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_numeral
% 4.97/5.18 thf(fact_681_one__neq__neg__numeral,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( one_one_Code_integer
% 4.97/5.18 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_numeral
% 4.97/5.18 thf(fact_682_one__neq__neg__numeral,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( one_one_rat
% 4.97/5.18 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % one_neq_neg_numeral
% 4.97/5.18 thf(fact_683_numeral__neq__neg__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( ( numeral_numeral_real @ N )
% 4.97/5.18 != ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_one
% 4.97/5.18 thf(fact_684_numeral__neq__neg__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( ( numeral_numeral_int @ N )
% 4.97/5.18 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_one
% 4.97/5.18 thf(fact_685_numeral__neq__neg__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( ( numera6690914467698888265omplex @ N )
% 4.97/5.18 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_one
% 4.97/5.18 thf(fact_686_numeral__neq__neg__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( ( numera6620942414471956472nteger @ N )
% 4.97/5.18 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_one
% 4.97/5.18 thf(fact_687_numeral__neq__neg__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ( ( numeral_numeral_rat @ N )
% 4.97/5.18 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % numeral_neq_neg_one
% 4.97/5.18 thf(fact_688_not__numeral__less__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_less_one
% 4.97/5.18 thf(fact_689_not__numeral__less__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_less_one
% 4.97/5.18 thf(fact_690_not__numeral__less__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_less_one
% 4.97/5.18 thf(fact_691_not__numeral__less__one,axiom,
% 4.97/5.18 ! [N: num] :
% 4.97/5.18 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_less_one
% 4.97/5.18 thf(fact_692_nat__less__add__iff2,axiom,
% 4.97/5.18 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.18 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.18 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_less_add_iff2
% 4.97/5.18 thf(fact_693_nat__less__add__iff1,axiom,
% 4.97/5.18 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ J @ I )
% 4.97/5.18 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 4.97/5.18 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_less_add_iff1
% 4.97/5.18 thf(fact_694_numerals_I1_J,axiom,
% 4.97/5.18 ( ( numeral_numeral_nat @ one )
% 4.97/5.18 = one_one_nat ) ).
% 4.97/5.18
% 4.97/5.18 % numerals(1)
% 4.97/5.18 thf(fact_695_ex__power__ivl2,axiom,
% 4.97/5.18 ! [B: nat,K: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.97/5.18 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.97/5.18 => ? [N3: nat] :
% 4.97/5.18 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 4.97/5.18 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ex_power_ivl2
% 4.97/5.18 thf(fact_696_ex__power__ivl1,axiom,
% 4.97/5.18 ! [B: nat,K: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.97/5.18 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 4.97/5.18 => ? [N3: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 4.97/5.18 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ex_power_ivl1
% 4.97/5.18 thf(fact_697_neg__numeral__le__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_one
% 4.97/5.18 thf(fact_698_neg__numeral__le__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_one
% 4.97/5.18 thf(fact_699_neg__numeral__le__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_one
% 4.97/5.18 thf(fact_700_neg__numeral__le__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_one
% 4.97/5.18 thf(fact_701_neg__one__le__numeral,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_one_le_numeral
% 4.97/5.18 thf(fact_702_neg__one__le__numeral,axiom,
% 4.97/5.18 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_one_le_numeral
% 4.97/5.18 thf(fact_703_neg__one__le__numeral,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_one_le_numeral
% 4.97/5.18 thf(fact_704_neg__one__le__numeral,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_one_le_numeral
% 4.97/5.18 thf(fact_705_neg__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_neg_one
% 4.97/5.18 thf(fact_706_neg__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_neg_one
% 4.97/5.18 thf(fact_707_neg__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_neg_one
% 4.97/5.18 thf(fact_708_neg__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_numeral_le_neg_one
% 4.97/5.18 thf(fact_709_not__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_one
% 4.97/5.18 thf(fact_710_not__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_one
% 4.97/5.18 thf(fact_711_not__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_one
% 4.97/5.18 thf(fact_712_not__numeral__le__neg__one,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_numeral_le_neg_one
% 4.97/5.18 thf(fact_713_not__one__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_one_le_neg_numeral
% 4.97/5.18 thf(fact_714_not__one__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_one_le_neg_numeral
% 4.97/5.18 thf(fact_715_not__one__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_one_le_neg_numeral
% 4.97/5.18 thf(fact_716_not__one__le__neg__numeral,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % not_one_le_neg_numeral
% 4.97/5.18 thf(fact_717_mult__1s__ring__1_I2_J,axiom,
% 4.97/5.18 ! [B: real] :
% 4.97/5.18 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 4.97/5.18 = ( uminus_uminus_real @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(2)
% 4.97/5.18 thf(fact_718_mult__1s__ring__1_I2_J,axiom,
% 4.97/5.18 ! [B: int] :
% 4.97/5.18 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 4.97/5.18 = ( uminus_uminus_int @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(2)
% 4.97/5.18 thf(fact_719_mult__1s__ring__1_I2_J,axiom,
% 4.97/5.18 ! [B: complex] :
% 4.97/5.18 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(2)
% 4.97/5.18 thf(fact_720_mult__1s__ring__1_I2_J,axiom,
% 4.97/5.18 ! [B: code_integer] :
% 4.97/5.18 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(2)
% 4.97/5.18 thf(fact_721_mult__1s__ring__1_I2_J,axiom,
% 4.97/5.18 ! [B: rat] :
% 4.97/5.18 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 4.97/5.18 = ( uminus_uminus_rat @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(2)
% 4.97/5.18 thf(fact_722_mult__1s__ring__1_I1_J,axiom,
% 4.97/5.18 ! [B: real] :
% 4.97/5.18 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 4.97/5.18 = ( uminus_uminus_real @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(1)
% 4.97/5.18 thf(fact_723_mult__1s__ring__1_I1_J,axiom,
% 4.97/5.18 ! [B: int] :
% 4.97/5.18 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 4.97/5.18 = ( uminus_uminus_int @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(1)
% 4.97/5.18 thf(fact_724_mult__1s__ring__1_I1_J,axiom,
% 4.97/5.18 ! [B: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(1)
% 4.97/5.18 thf(fact_725_mult__1s__ring__1_I1_J,axiom,
% 4.97/5.18 ! [B: code_integer] :
% 4.97/5.18 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(1)
% 4.97/5.18 thf(fact_726_mult__1s__ring__1_I1_J,axiom,
% 4.97/5.18 ! [B: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 4.97/5.18 = ( uminus_uminus_rat @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1s_ring_1(1)
% 4.97/5.18 thf(fact_727_uminus__numeral__One,axiom,
% 4.97/5.18 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 4.97/5.18 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_numeral_One
% 4.97/5.18 thf(fact_728_uminus__numeral__One,axiom,
% 4.97/5.18 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 4.97/5.18 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_numeral_One
% 4.97/5.18 thf(fact_729_uminus__numeral__One,axiom,
% 4.97/5.18 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_numeral_One
% 4.97/5.18 thf(fact_730_uminus__numeral__One,axiom,
% 4.97/5.18 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_numeral_One
% 4.97/5.18 thf(fact_731_uminus__numeral__One,axiom,
% 4.97/5.18 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 4.97/5.18 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_numeral_One
% 4.97/5.18 thf(fact_732_power__minus,axiom,
% 4.97/5.18 ! [A: real,N: nat] :
% 4.97/5.18 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 4.97/5.18 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus
% 4.97/5.18 thf(fact_733_power__minus,axiom,
% 4.97/5.18 ! [A: int,N: nat] :
% 4.97/5.18 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 4.97/5.18 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus
% 4.97/5.18 thf(fact_734_power__minus,axiom,
% 4.97/5.18 ! [A: complex,N: nat] :
% 4.97/5.18 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 4.97/5.18 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus
% 4.97/5.18 thf(fact_735_power__minus,axiom,
% 4.97/5.18 ! [A: code_integer,N: nat] :
% 4.97/5.18 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 4.97/5.18 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus
% 4.97/5.18 thf(fact_736_power__minus,axiom,
% 4.97/5.18 ! [A: rat,N: nat] :
% 4.97/5.18 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 4.97/5.18 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus
% 4.97/5.18 thf(fact_737_power__minus__Bit0,axiom,
% 4.97/5.18 ! [X2: real,K: num] :
% 4.97/5.18 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 4.97/5.18 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit0
% 4.97/5.18 thf(fact_738_power__minus__Bit0,axiom,
% 4.97/5.18 ! [X2: int,K: num] :
% 4.97/5.18 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 4.97/5.18 = ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit0
% 4.97/5.18 thf(fact_739_power__minus__Bit0,axiom,
% 4.97/5.18 ! [X2: complex,K: num] :
% 4.97/5.18 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 4.97/5.18 = ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit0
% 4.97/5.18 thf(fact_740_power__minus__Bit0,axiom,
% 4.97/5.18 ! [X2: code_integer,K: num] :
% 4.97/5.18 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 4.97/5.18 = ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit0
% 4.97/5.18 thf(fact_741_power__minus__Bit0,axiom,
% 4.97/5.18 ! [X2: rat,K: num] :
% 4.97/5.18 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 4.97/5.18 = ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit0
% 4.97/5.18 thf(fact_742_power__gt1__lemma,axiom,
% 4.97/5.18 ! [A: real,N: nat] :
% 4.97/5.18 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.18 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_gt1_lemma
% 4.97/5.18 thf(fact_743_power__gt1__lemma,axiom,
% 4.97/5.18 ! [A: rat,N: nat] :
% 4.97/5.18 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.18 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_gt1_lemma
% 4.97/5.18 thf(fact_744_power__gt1__lemma,axiom,
% 4.97/5.18 ! [A: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.18 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_gt1_lemma
% 4.97/5.18 thf(fact_745_power__gt1__lemma,axiom,
% 4.97/5.18 ! [A: int,N: nat] :
% 4.97/5.18 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.18 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_gt1_lemma
% 4.97/5.18 thf(fact_746_power__less__power__Suc,axiom,
% 4.97/5.18 ! [A: real,N: nat] :
% 4.97/5.18 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.18 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_less_power_Suc
% 4.97/5.18 thf(fact_747_power__less__power__Suc,axiom,
% 4.97/5.18 ! [A: rat,N: nat] :
% 4.97/5.18 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.18 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_less_power_Suc
% 4.97/5.18 thf(fact_748_power__less__power__Suc,axiom,
% 4.97/5.18 ! [A: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.18 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_less_power_Suc
% 4.97/5.18 thf(fact_749_power__less__power__Suc,axiom,
% 4.97/5.18 ! [A: int,N: nat] :
% 4.97/5.18 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.18 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_less_power_Suc
% 4.97/5.18 thf(fact_750_power__minus__Bit1,axiom,
% 4.97/5.18 ! [X2: real,K: num] :
% 4.97/5.18 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 4.97/5.18 = ( uminus_uminus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit1
% 4.97/5.18 thf(fact_751_power__minus__Bit1,axiom,
% 4.97/5.18 ! [X2: int,K: num] :
% 4.97/5.18 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 4.97/5.18 = ( uminus_uminus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit1
% 4.97/5.18 thf(fact_752_power__minus__Bit1,axiom,
% 4.97/5.18 ! [X2: complex,K: num] :
% 4.97/5.18 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit1
% 4.97/5.18 thf(fact_753_power__minus__Bit1,axiom,
% 4.97/5.18 ! [X2: code_integer,K: num] :
% 4.97/5.18 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit1
% 4.97/5.18 thf(fact_754_power__minus__Bit1,axiom,
% 4.97/5.18 ! [X2: rat,K: num] :
% 4.97/5.18 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 4.97/5.18 = ( uminus_uminus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_minus_Bit1
% 4.97/5.18 thf(fact_755_less__exp,axiom,
% 4.97/5.18 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_exp
% 4.97/5.18 thf(fact_756_complete__real,axiom,
% 4.97/5.18 ! [S: set_real] :
% 4.97/5.18 ( ? [X: real] : ( member_real @ X @ S )
% 4.97/5.18 => ( ? [Z2: real] :
% 4.97/5.18 ! [X4: real] :
% 4.97/5.18 ( ( member_real @ X4 @ S )
% 4.97/5.18 => ( ord_less_eq_real @ X4 @ Z2 ) )
% 4.97/5.18 => ? [Y3: real] :
% 4.97/5.18 ( ! [X: real] :
% 4.97/5.18 ( ( member_real @ X @ S )
% 4.97/5.18 => ( ord_less_eq_real @ X @ Y3 ) )
% 4.97/5.18 & ! [Z2: real] :
% 4.97/5.18 ( ! [X4: real] :
% 4.97/5.18 ( ( member_real @ X4 @ S )
% 4.97/5.18 => ( ord_less_eq_real @ X4 @ Z2 ) )
% 4.97/5.18 => ( ord_less_eq_real @ Y3 @ Z2 ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % complete_real
% 4.97/5.18 thf(fact_757_field__less__half__sum,axiom,
% 4.97/5.18 ! [X2: real,Y: real] :
% 4.97/5.18 ( ( ord_less_real @ X2 @ Y )
% 4.97/5.18 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % field_less_half_sum
% 4.97/5.18 thf(fact_758_field__less__half__sum,axiom,
% 4.97/5.18 ! [X2: rat,Y: rat] :
% 4.97/5.18 ( ( ord_less_rat @ X2 @ Y )
% 4.97/5.18 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % field_less_half_sum
% 4.97/5.18 thf(fact_759_realpow__square__minus__le,axiom,
% 4.97/5.18 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % realpow_square_minus_le
% 4.97/5.18 thf(fact_760_power2__eq__iff,axiom,
% 4.97/5.18 ! [X2: real,Y: real] :
% 4.97/5.18 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = ( ( X2 = Y )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_iff
% 4.97/5.18 thf(fact_761_power2__eq__iff,axiom,
% 4.97/5.18 ! [X2: int,Y: int] :
% 4.97/5.18 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = ( ( X2 = Y )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_iff
% 4.97/5.18 thf(fact_762_power2__eq__iff,axiom,
% 4.97/5.18 ! [X2: complex,Y: complex] :
% 4.97/5.18 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = ( ( X2 = Y )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_iff
% 4.97/5.18 thf(fact_763_power2__eq__iff,axiom,
% 4.97/5.18 ! [X2: code_integer,Y: code_integer] :
% 4.97/5.18 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = ( ( X2 = Y )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_iff
% 4.97/5.18 thf(fact_764_power2__eq__iff,axiom,
% 4.97/5.18 ! [X2: rat,Y: rat] :
% 4.97/5.18 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = ( ( X2 = Y )
% 4.97/5.18 | ( X2
% 4.97/5.18 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_iff
% 4.97/5.18 thf(fact_765_power__le__imp__le__exp,axiom,
% 4.97/5.18 ! [A: real,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.18 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 4.97/5.18 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_le_imp_le_exp
% 4.97/5.18 thf(fact_766_power__le__imp__le__exp,axiom,
% 4.97/5.18 ! [A: rat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.18 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 4.97/5.18 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_le_imp_le_exp
% 4.97/5.18 thf(fact_767_power__le__imp__le__exp,axiom,
% 4.97/5.18 ! [A: nat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.18 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 4.97/5.18 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_le_imp_le_exp
% 4.97/5.18 thf(fact_768_power__le__imp__le__exp,axiom,
% 4.97/5.18 ! [A: int,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.18 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 4.97/5.18 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power_le_imp_le_exp
% 4.97/5.18 thf(fact_769_nat__1__add__1,axiom,
% 4.97/5.18 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.97/5.18 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_1_add_1
% 4.97/5.18 thf(fact_770_minus__power__mult__self,axiom,
% 4.97/5.18 ! [A: real,N: nat] :
% 4.97/5.18 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 4.97/5.18 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_power_mult_self
% 4.97/5.18 thf(fact_771_minus__power__mult__self,axiom,
% 4.97/5.18 ! [A: int,N: nat] :
% 4.97/5.18 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 4.97/5.18 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_power_mult_self
% 4.97/5.18 thf(fact_772_minus__power__mult__self,axiom,
% 4.97/5.18 ! [A: complex,N: nat] :
% 4.97/5.18 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 4.97/5.18 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_power_mult_self
% 4.97/5.18 thf(fact_773_minus__power__mult__self,axiom,
% 4.97/5.18 ! [A: code_integer,N: nat] :
% 4.97/5.18 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 4.97/5.18 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_power_mult_self
% 4.97/5.18 thf(fact_774_minus__power__mult__self,axiom,
% 4.97/5.18 ! [A: rat,N: nat] :
% 4.97/5.18 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 4.97/5.18 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_power_mult_self
% 4.97/5.18 thf(fact_775_power2__eq__1__iff,axiom,
% 4.97/5.18 ! [A: real] :
% 4.97/5.18 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = one_one_real )
% 4.97/5.18 = ( ( A = one_one_real )
% 4.97/5.18 | ( A
% 4.97/5.18 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_1_iff
% 4.97/5.18 thf(fact_776_power2__eq__1__iff,axiom,
% 4.97/5.18 ! [A: int] :
% 4.97/5.18 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = one_one_int )
% 4.97/5.18 = ( ( A = one_one_int )
% 4.97/5.18 | ( A
% 4.97/5.18 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_1_iff
% 4.97/5.18 thf(fact_777_power2__eq__1__iff,axiom,
% 4.97/5.18 ! [A: complex] :
% 4.97/5.18 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = one_one_complex )
% 4.97/5.18 = ( ( A = one_one_complex )
% 4.97/5.18 | ( A
% 4.97/5.18 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_1_iff
% 4.97/5.18 thf(fact_778_power2__eq__1__iff,axiom,
% 4.97/5.18 ! [A: code_integer] :
% 4.97/5.18 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = one_one_Code_integer )
% 4.97/5.18 = ( ( A = one_one_Code_integer )
% 4.97/5.18 | ( A
% 4.97/5.18 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_1_iff
% 4.97/5.18 thf(fact_779_power2__eq__1__iff,axiom,
% 4.97/5.18 ! [A: rat] :
% 4.97/5.18 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = one_one_rat )
% 4.97/5.18 = ( ( A = one_one_rat )
% 4.97/5.18 | ( A
% 4.97/5.18 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % power2_eq_1_iff
% 4.97/5.18 thf(fact_780_square__le__1,axiom,
% 4.97/5.18 ! [X2: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 4.97/5.18 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 4.97/5.18 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_le_1
% 4.97/5.18 thf(fact_781_square__le__1,axiom,
% 4.97/5.18 ! [X2: code_integer] :
% 4.97/5.18 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 4.97/5.18 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 4.97/5.18 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_le_1
% 4.97/5.18 thf(fact_782_square__le__1,axiom,
% 4.97/5.18 ! [X2: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 4.97/5.18 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 4.97/5.18 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_le_1
% 4.97/5.18 thf(fact_783_square__le__1,axiom,
% 4.97/5.18 ! [X2: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 4.97/5.18 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 4.97/5.18 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_le_1
% 4.97/5.18 thf(fact_784_ring__class_Oring__distribs_I2_J,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(2)
% 4.97/5.18 thf(fact_785_ring__class_Oring__distribs_I2_J,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(2)
% 4.97/5.18 thf(fact_786_ring__class_Oring__distribs_I2_J,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(2)
% 4.97/5.18 thf(fact_787_ring__class_Oring__distribs_I2_J,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(2)
% 4.97/5.18 thf(fact_788_ring__class_Oring__distribs_I1_J,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(1)
% 4.97/5.18 thf(fact_789_ring__class_Oring__distribs_I1_J,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(1)
% 4.97/5.18 thf(fact_790_ring__class_Oring__distribs_I1_J,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(1)
% 4.97/5.18 thf(fact_791_ring__class_Oring__distribs_I1_J,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ring_class.ring_distribs(1)
% 4.97/5.18 thf(fact_792_comm__semiring__class_Odistrib,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % comm_semiring_class.distrib
% 4.97/5.18 thf(fact_793_comm__semiring__class_Odistrib,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % comm_semiring_class.distrib
% 4.97/5.18 thf(fact_794_comm__semiring__class_Odistrib,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % comm_semiring_class.distrib
% 4.97/5.18 thf(fact_795_comm__semiring__class_Odistrib,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % comm_semiring_class.distrib
% 4.97/5.18 thf(fact_796_comm__semiring__class_Odistrib,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % comm_semiring_class.distrib
% 4.97/5.18 thf(fact_797_distrib__left,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_left
% 4.97/5.18 thf(fact_798_distrib__left,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_left
% 4.97/5.18 thf(fact_799_distrib__left,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.18 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_left
% 4.97/5.18 thf(fact_800_distrib__left,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_left
% 4.97/5.18 thf(fact_801_distrib__left,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_left
% 4.97/5.18 thf(fact_802_distrib__right,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_right
% 4.97/5.18 thf(fact_803_distrib__right,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_right
% 4.97/5.18 thf(fact_804_distrib__right,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_right
% 4.97/5.18 thf(fact_805_distrib__right,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_right
% 4.97/5.18 thf(fact_806_distrib__right,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % distrib_right
% 4.97/5.18 thf(fact_807_combine__common__factor,axiom,
% 4.97/5.18 ! [A: real,E: real,B: real,C: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_common_factor
% 4.97/5.18 thf(fact_808_combine__common__factor,axiom,
% 4.97/5.18 ! [A: rat,E: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_common_factor
% 4.97/5.18 thf(fact_809_combine__common__factor,axiom,
% 4.97/5.18 ! [A: nat,E: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 4.97/5.18 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_common_factor
% 4.97/5.18 thf(fact_810_combine__common__factor,axiom,
% 4.97/5.18 ! [A: int,E: int,B: int,C: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_common_factor
% 4.97/5.18 thf(fact_811_combine__common__factor,axiom,
% 4.97/5.18 ! [A: complex,E: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_common_factor
% 4.97/5.18 thf(fact_812_left__diff__distrib,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.18 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib
% 4.97/5.18 thf(fact_813_left__diff__distrib,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib
% 4.97/5.18 thf(fact_814_left__diff__distrib,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.97/5.18 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib
% 4.97/5.18 thf(fact_815_left__diff__distrib,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 4.97/5.18 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib
% 4.97/5.18 thf(fact_816_right__diff__distrib,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.97/5.18 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib
% 4.97/5.18 thf(fact_817_right__diff__distrib,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.97/5.18 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib
% 4.97/5.18 thf(fact_818_right__diff__distrib,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.97/5.18 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib
% 4.97/5.18 thf(fact_819_right__diff__distrib,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 4.97/5.18 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib
% 4.97/5.18 thf(fact_820_left__diff__distrib_H,axiom,
% 4.97/5.18 ! [B: real,C: real,A: real] :
% 4.97/5.18 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 4.97/5.18 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib'
% 4.97/5.18 thf(fact_821_left__diff__distrib_H,axiom,
% 4.97/5.18 ! [B: rat,C: rat,A: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 4.97/5.18 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib'
% 4.97/5.18 thf(fact_822_left__diff__distrib_H,axiom,
% 4.97/5.18 ! [B: nat,C: nat,A: nat] :
% 4.97/5.18 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 4.97/5.18 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib'
% 4.97/5.18 thf(fact_823_left__diff__distrib_H,axiom,
% 4.97/5.18 ! [B: int,C: int,A: int] :
% 4.97/5.18 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 4.97/5.18 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib'
% 4.97/5.18 thf(fact_824_left__diff__distrib_H,axiom,
% 4.97/5.18 ! [B: complex,C: complex,A: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 4.97/5.18 = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % left_diff_distrib'
% 4.97/5.18 thf(fact_825_right__diff__distrib_H,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.97/5.18 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib'
% 4.97/5.18 thf(fact_826_right__diff__distrib_H,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.97/5.18 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib'
% 4.97/5.18 thf(fact_827_right__diff__distrib_H,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 4.97/5.18 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib'
% 4.97/5.18 thf(fact_828_right__diff__distrib_H,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.97/5.18 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib'
% 4.97/5.18 thf(fact_829_right__diff__distrib_H,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 4.97/5.18 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % right_diff_distrib'
% 4.97/5.18 thf(fact_830_add__diff__add,axiom,
% 4.97/5.18 ! [A: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 4.97/5.18 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_add
% 4.97/5.18 thf(fact_831_add__diff__add,axiom,
% 4.97/5.18 ! [A: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 4.97/5.18 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_add
% 4.97/5.18 thf(fact_832_add__diff__add,axiom,
% 4.97/5.18 ! [A: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 4.97/5.18 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_add
% 4.97/5.18 thf(fact_833_add__diff__add,axiom,
% 4.97/5.18 ! [A: complex,C: complex,B: complex,D: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D ) )
% 4.97/5.18 = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_add
% 4.97/5.18 thf(fact_834_option_Odistinct_I1_J,axiom,
% 4.97/5.18 ! [X23: product_prod_nat_nat] :
% 4.97/5.18 ( none_P5556105721700978146at_nat
% 4.97/5.18 != ( some_P7363390416028606310at_nat @ X23 ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.distinct(1)
% 4.97/5.18 thf(fact_835_option_Odistinct_I1_J,axiom,
% 4.97/5.18 ! [X23: num] :
% 4.97/5.18 ( none_num
% 4.97/5.18 != ( some_num @ X23 ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.distinct(1)
% 4.97/5.18 thf(fact_836_option_OdiscI,axiom,
% 4.97/5.18 ! [Option: option4927543243414619207at_nat,X23: product_prod_nat_nat] :
% 4.97/5.18 ( ( Option
% 4.97/5.18 = ( some_P7363390416028606310at_nat @ X23 ) )
% 4.97/5.18 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.discI
% 4.97/5.18 thf(fact_837_option_OdiscI,axiom,
% 4.97/5.18 ! [Option: option_num,X23: num] :
% 4.97/5.18 ( ( Option
% 4.97/5.18 = ( some_num @ X23 ) )
% 4.97/5.18 => ( Option != none_num ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.discI
% 4.97/5.18 thf(fact_838_option_Oexhaust,axiom,
% 4.97/5.18 ! [Y: option4927543243414619207at_nat] :
% 4.97/5.18 ( ( Y != none_P5556105721700978146at_nat )
% 4.97/5.18 => ~ ! [X22: product_prod_nat_nat] :
% 4.97/5.18 ( Y
% 4.97/5.18 != ( some_P7363390416028606310at_nat @ X22 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.exhaust
% 4.97/5.18 thf(fact_839_option_Oexhaust,axiom,
% 4.97/5.18 ! [Y: option_num] :
% 4.97/5.18 ( ( Y != none_num )
% 4.97/5.18 => ~ ! [X22: num] :
% 4.97/5.18 ( Y
% 4.97/5.18 != ( some_num @ X22 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % option.exhaust
% 4.97/5.18 thf(fact_840_split__option__ex,axiom,
% 4.97/5.18 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 4.97/5.18 ? [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 4.97/5.18 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 4.97/5.18 ( ( P3 @ none_P5556105721700978146at_nat )
% 4.97/5.18 | ? [X3: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % split_option_ex
% 4.97/5.18 thf(fact_841_split__option__ex,axiom,
% 4.97/5.18 ( ( ^ [P2: option_num > $o] :
% 4.97/5.18 ? [X6: option_num] : ( P2 @ X6 ) )
% 4.97/5.18 = ( ^ [P3: option_num > $o] :
% 4.97/5.18 ( ( P3 @ none_num )
% 4.97/5.18 | ? [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % split_option_ex
% 4.97/5.18 thf(fact_842_split__option__all,axiom,
% 4.97/5.18 ( ( ^ [P2: option4927543243414619207at_nat > $o] :
% 4.97/5.18 ! [X6: option4927543243414619207at_nat] : ( P2 @ X6 ) )
% 4.97/5.18 = ( ^ [P3: option4927543243414619207at_nat > $o] :
% 4.97/5.18 ( ( P3 @ none_P5556105721700978146at_nat )
% 4.97/5.18 & ! [X3: product_prod_nat_nat] : ( P3 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % split_option_all
% 4.97/5.18 thf(fact_843_split__option__all,axiom,
% 4.97/5.18 ( ( ^ [P2: option_num > $o] :
% 4.97/5.18 ! [X6: option_num] : ( P2 @ X6 ) )
% 4.97/5.18 = ( ^ [P3: option_num > $o] :
% 4.97/5.18 ( ( P3 @ none_num )
% 4.97/5.18 & ! [X3: num] : ( P3 @ ( some_num @ X3 ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % split_option_all
% 4.97/5.18 thf(fact_844_combine__options__cases,axiom,
% 4.97/5.18 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 4.97/5.18 ( ( ( X2 = none_P5556105721700978146at_nat )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ( ( Y = none_P5556105721700978146at_nat )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ! [A3: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 4.97/5.18 ( ( X2
% 4.97/5.18 = ( some_P7363390416028606310at_nat @ A3 ) )
% 4.97/5.18 => ( ( Y
% 4.97/5.18 = ( some_P7363390416028606310at_nat @ B2 ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_options_cases
% 4.97/5.18 thf(fact_845_combine__options__cases,axiom,
% 4.97/5.18 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 4.97/5.18 ( ( ( X2 = none_P5556105721700978146at_nat )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ( ( Y = none_num )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ! [A3: product_prod_nat_nat,B2: num] :
% 4.97/5.18 ( ( X2
% 4.97/5.18 = ( some_P7363390416028606310at_nat @ A3 ) )
% 4.97/5.18 => ( ( Y
% 4.97/5.18 = ( some_num @ B2 ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_options_cases
% 4.97/5.18 thf(fact_846_combine__options__cases,axiom,
% 4.97/5.18 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 4.97/5.18 ( ( ( X2 = none_num )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ( ( Y = none_P5556105721700978146at_nat )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ! [A3: num,B2: product_prod_nat_nat] :
% 4.97/5.18 ( ( X2
% 4.97/5.18 = ( some_num @ A3 ) )
% 4.97/5.18 => ( ( Y
% 4.97/5.18 = ( some_P7363390416028606310at_nat @ B2 ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_options_cases
% 4.97/5.18 thf(fact_847_combine__options__cases,axiom,
% 4.97/5.18 ! [X2: option_num,P: option_num > option_num > $o,Y: option_num] :
% 4.97/5.18 ( ( ( X2 = none_num )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ( ( Y = none_num )
% 4.97/5.18 => ( P @ X2 @ Y ) )
% 4.97/5.18 => ( ! [A3: num,B2: num] :
% 4.97/5.18 ( ( X2
% 4.97/5.18 = ( some_num @ A3 ) )
% 4.97/5.18 => ( ( Y
% 4.97/5.18 = ( some_num @ B2 ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) )
% 4.97/5.18 => ( P @ X2 @ Y ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % combine_options_cases
% 4.97/5.18 thf(fact_848_add__le__imp__le__diff,axiom,
% 4.97/5.18 ! [I: real,K: real,N: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.97/5.18 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_imp_le_diff
% 4.97/5.18 thf(fact_849_add__le__imp__le__diff,axiom,
% 4.97/5.18 ! [I: rat,K: rat,N: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.97/5.18 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_imp_le_diff
% 4.97/5.18 thf(fact_850_add__le__imp__le__diff,axiom,
% 4.97/5.18 ! [I: nat,K: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.97/5.18 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_imp_le_diff
% 4.97/5.18 thf(fact_851_add__le__imp__le__diff,axiom,
% 4.97/5.18 ! [I: int,K: int,N: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.97/5.18 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_imp_le_diff
% 4.97/5.18 thf(fact_852_add__le__add__imp__diff__le,axiom,
% 4.97/5.18 ! [I: real,K: real,N: real,J: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 4.97/5.18 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 4.97/5.18 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_add_imp_diff_le
% 4.97/5.18 thf(fact_853_add__le__add__imp__diff__le,axiom,
% 4.97/5.18 ! [I: rat,K: rat,N: rat,J: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 4.97/5.18 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 4.97/5.18 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_add_imp_diff_le
% 4.97/5.18 thf(fact_854_add__le__add__imp__diff__le,axiom,
% 4.97/5.18 ! [I: nat,K: nat,N: nat,J: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 4.97/5.18 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 4.97/5.18 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_add_imp_diff_le
% 4.97/5.18 thf(fact_855_add__le__add__imp__diff__le,axiom,
% 4.97/5.18 ! [I: int,K: int,N: int,J: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 4.97/5.18 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 4.97/5.18 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 4.97/5.18 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_add_imp_diff_le
% 4.97/5.18 thf(fact_856_eq__add__iff1,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 4.97/5.18 = D ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff1
% 4.97/5.18 thf(fact_857_eq__add__iff1,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 4.97/5.18 = D ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff1
% 4.97/5.18 thf(fact_858_eq__add__iff1,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 4.97/5.18 = D ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff1
% 4.97/5.18 thf(fact_859_eq__add__iff1,axiom,
% 4.97/5.18 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 4.97/5.18 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 4.97/5.18 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 4.97/5.18 = D ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff1
% 4.97/5.18 thf(fact_860_eq__add__iff2,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( C
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff2
% 4.97/5.18 thf(fact_861_eq__add__iff2,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( C
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff2
% 4.97/5.18 thf(fact_862_eq__add__iff2,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( C
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff2
% 4.97/5.18 thf(fact_863_eq__add__iff2,axiom,
% 4.97/5.18 ! [A: complex,E: complex,C: complex,B: complex,D: complex] :
% 4.97/5.18 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D ) )
% 4.97/5.18 = ( C
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % eq_add_iff2
% 4.97/5.18 thf(fact_864_square__diff__square__factored,axiom,
% 4.97/5.18 ! [X2: real,Y: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 4.97/5.18 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_square_factored
% 4.97/5.18 thf(fact_865_square__diff__square__factored,axiom,
% 4.97/5.18 ! [X2: rat,Y: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 4.97/5.18 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( minus_minus_rat @ X2 @ Y ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_square_factored
% 4.97/5.18 thf(fact_866_square__diff__square__factored,axiom,
% 4.97/5.18 ! [X2: int,Y: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 4.97/5.18 = ( times_times_int @ ( plus_plus_int @ X2 @ Y ) @ ( minus_minus_int @ X2 @ Y ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_square_factored
% 4.97/5.18 thf(fact_867_square__diff__square__factored,axiom,
% 4.97/5.18 ! [X2: complex,Y: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ ( times_times_complex @ Y @ Y ) )
% 4.97/5.18 = ( times_times_complex @ ( plus_plus_complex @ X2 @ Y ) @ ( minus_minus_complex @ X2 @ Y ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_square_factored
% 4.97/5.18 thf(fact_868_mult__diff__mult,axiom,
% 4.97/5.18 ! [X2: real,Y: real,A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y ) @ ( times_times_real @ A @ B ) )
% 4.97/5.18 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_diff_mult
% 4.97/5.18 thf(fact_869_mult__diff__mult,axiom,
% 4.97/5.18 ! [X2: rat,Y: rat,A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y ) @ ( times_times_rat @ A @ B ) )
% 4.97/5.18 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A ) @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_diff_mult
% 4.97/5.18 thf(fact_870_mult__diff__mult,axiom,
% 4.97/5.18 ! [X2: int,Y: int,A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y ) @ ( times_times_int @ A @ B ) )
% 4.97/5.18 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A ) @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_diff_mult
% 4.97/5.18 thf(fact_871_mult__diff__mult,axiom,
% 4.97/5.18 ! [X2: complex,Y: complex,A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ Y ) @ ( times_times_complex @ A @ B ) )
% 4.97/5.18 = ( plus_plus_complex @ ( times_times_complex @ X2 @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X2 @ A ) @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult_diff_mult
% 4.97/5.18 thf(fact_872_ordered__ring__class_Ole__add__iff1,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff1
% 4.97/5.18 thf(fact_873_ordered__ring__class_Ole__add__iff1,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff1
% 4.97/5.18 thf(fact_874_ordered__ring__class_Ole__add__iff1,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff1
% 4.97/5.18 thf(fact_875_ordered__ring__class_Ole__add__iff2,axiom,
% 4.97/5.18 ! [A: real,E: real,C: real,B: real,D: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff2
% 4.97/5.18 thf(fact_876_ordered__ring__class_Ole__add__iff2,axiom,
% 4.97/5.18 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff2
% 4.97/5.18 thf(fact_877_ordered__ring__class_Ole__add__iff2,axiom,
% 4.97/5.18 ! [A: int,E: int,C: int,B: int,D: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 4.97/5.18 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ordered_ring_class.le_add_iff2
% 4.97/5.18 thf(fact_878_square__diff__one__factored,axiom,
% 4.97/5.18 ! [X2: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 4.97/5.18 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_one_factored
% 4.97/5.18 thf(fact_879_square__diff__one__factored,axiom,
% 4.97/5.18 ! [X2: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 4.97/5.18 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_one_factored
% 4.97/5.18 thf(fact_880_square__diff__one__factored,axiom,
% 4.97/5.18 ! [X2: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 4.97/5.18 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_one_factored
% 4.97/5.18 thf(fact_881_square__diff__one__factored,axiom,
% 4.97/5.18 ! [X2: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ one_one_complex )
% 4.97/5.18 = ( times_times_complex @ ( plus_plus_complex @ X2 @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % square_diff_one_factored
% 4.97/5.18 thf(fact_882_field__sum__of__halves,axiom,
% 4.97/5.18 ! [X2: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = X2 ) ).
% 4.97/5.18
% 4.97/5.18 % field_sum_of_halves
% 4.97/5.18 thf(fact_883_field__sum__of__halves,axiom,
% 4.97/5.18 ! [X2: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.97/5.18 = X2 ) ).
% 4.97/5.18
% 4.97/5.18 % field_sum_of_halves
% 4.97/5.18 thf(fact_884_minus__1__div__2__eq,axiom,
% 4.97/5.18 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_1_div_2_eq
% 4.97/5.18 thf(fact_885_minus__1__div__2__eq,axiom,
% 4.97/5.18 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_1_div_2_eq
% 4.97/5.18 thf(fact_886_invar__vebt_Ointros_I2_J,axiom,
% 4.97/5.18 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 4.97/5.18 ( ! [X4: vEBT_VEBT] :
% 4.97/5.18 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.18 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.97/5.18 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.97/5.18 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.97/5.18 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.18 => ( ( M = N )
% 4.97/5.18 => ( ( Deg
% 4.97/5.18 = ( plus_plus_nat @ N @ M ) )
% 4.97/5.18 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 4.97/5.18 => ( ! [X4: vEBT_VEBT] :
% 4.97/5.18 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.18 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 4.97/5.18 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % invar_vebt.intros(2)
% 4.97/5.18 thf(fact_887_add__self__div__2,axiom,
% 4.97/5.18 ! [M: nat] :
% 4.97/5.18 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.18 = M ) ).
% 4.97/5.18
% 4.97/5.18 % add_self_div_2
% 4.97/5.18 thf(fact_888_Nat_Odiff__diff__right,axiom,
% 4.97/5.18 ! [K: nat,J: nat,I: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.18 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.97/5.18 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % Nat.diff_diff_right
% 4.97/5.18 thf(fact_889_Nat_Oadd__diff__assoc2,axiom,
% 4.97/5.18 ! [K: nat,J: nat,I: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.18 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.97/5.18 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % Nat.add_diff_assoc2
% 4.97/5.18 thf(fact_890_Nat_Oadd__diff__assoc,axiom,
% 4.97/5.18 ! [K: nat,J: nat,I: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.18 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.97/5.18 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % Nat.add_diff_assoc
% 4.97/5.18 thf(fact_891_div__minus1__right,axiom,
% 4.97/5.18 ! [A: int] :
% 4.97/5.18 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.18 = ( uminus_uminus_int @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % div_minus1_right
% 4.97/5.18 thf(fact_892_div__minus1__right,axiom,
% 4.97/5.18 ! [A: code_integer] :
% 4.97/5.18 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % div_minus1_right
% 4.97/5.18 thf(fact_893_divide__minus1,axiom,
% 4.97/5.18 ! [X2: real] :
% 4.97/5.18 ( ( divide_divide_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.18 = ( uminus_uminus_real @ X2 ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_minus1
% 4.97/5.18 thf(fact_894_divide__minus1,axiom,
% 4.97/5.18 ! [X2: complex] :
% 4.97/5.18 ( ( divide1717551699836669952omplex @ X2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_minus1
% 4.97/5.18 thf(fact_895_divide__minus1,axiom,
% 4.97/5.18 ! [X2: rat] :
% 4.97/5.18 ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.18 = ( uminus_uminus_rat @ X2 ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_minus1
% 4.97/5.18 thf(fact_896_diff__minus__eq__add,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 4.97/5.18 = ( plus_plus_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_minus_eq_add
% 4.97/5.18 thf(fact_897_diff__minus__eq__add,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 4.97/5.18 = ( plus_plus_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_minus_eq_add
% 4.97/5.18 thf(fact_898_diff__minus__eq__add,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.18 = ( plus_plus_complex @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_minus_eq_add
% 4.97/5.18 thf(fact_899_diff__minus__eq__add,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.18 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_minus_eq_add
% 4.97/5.18 thf(fact_900_diff__minus__eq__add,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.97/5.18 = ( plus_plus_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_minus_eq_add
% 4.97/5.18 thf(fact_901_uminus__add__conv__diff,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 4.97/5.18 = ( minus_minus_real @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_add_conv_diff
% 4.97/5.18 thf(fact_902_uminus__add__conv__diff,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 4.97/5.18 = ( minus_minus_int @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_add_conv_diff
% 4.97/5.18 thf(fact_903_uminus__add__conv__diff,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 4.97/5.18 = ( minus_minus_complex @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_add_conv_diff
% 4.97/5.18 thf(fact_904_uminus__add__conv__diff,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 4.97/5.18 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_add_conv_diff
% 4.97/5.18 thf(fact_905_uminus__add__conv__diff,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.97/5.18 = ( minus_minus_rat @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % uminus_add_conv_diff
% 4.97/5.18 thf(fact_906_low__inv,axiom,
% 4.97/5.18 ! [X2: nat,N: nat,Y: nat] :
% 4.97/5.18 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.18 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 4.97/5.18 = X2 ) ) ).
% 4.97/5.18
% 4.97/5.18 % low_inv
% 4.97/5.18 thf(fact_907_high__inv,axiom,
% 4.97/5.18 ! [X2: nat,N: nat,Y: nat] :
% 4.97/5.18 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.18 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 4.97/5.18 = Y ) ) ).
% 4.97/5.18
% 4.97/5.18 % high_inv
% 4.97/5.18 thf(fact_908_inthall,axiom,
% 4.97/5.18 ! [Xs: list_real,P: real > $o,N: nat] :
% 4.97/5.18 ( ! [X4: real] :
% 4.97/5.18 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_909_inthall,axiom,
% 4.97/5.18 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 4.97/5.18 ( ! [X4: complex] :
% 4.97/5.18 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_910_inthall,axiom,
% 4.97/5.18 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 4.97/5.18 ( ! [X4: set_nat] :
% 4.97/5.18 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_911_inthall,axiom,
% 4.97/5.18 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 4.97/5.18 ( ! [X4: vEBT_VEBT] :
% 4.97/5.18 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_912_inthall,axiom,
% 4.97/5.18 ! [Xs: list_o,P: $o > $o,N: nat] :
% 4.97/5.18 ( ! [X4: $o] :
% 4.97/5.18 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_913_inthall,axiom,
% 4.97/5.18 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 4.97/5.18 ( ! [X4: nat] :
% 4.97/5.18 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_914_inthall,axiom,
% 4.97/5.18 ! [Xs: list_int,P: int > $o,N: nat] :
% 4.97/5.18 ( ! [X4: int] :
% 4.97/5.18 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 4.97/5.18 => ( P @ X4 ) )
% 4.97/5.18 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.97/5.18 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % inthall
% 4.97/5.18 thf(fact_915_add__left__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( ( plus_plus_real @ A @ B )
% 4.97/5.18 = ( plus_plus_real @ A @ C ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_left_cancel
% 4.97/5.18 thf(fact_916_add__left__cancel,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( ( plus_plus_rat @ A @ B )
% 4.97/5.18 = ( plus_plus_rat @ A @ C ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_left_cancel
% 4.97/5.18 thf(fact_917_add__left__cancel,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( ( plus_plus_nat @ A @ B )
% 4.97/5.18 = ( plus_plus_nat @ A @ C ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_left_cancel
% 4.97/5.18 thf(fact_918_add__left__cancel,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( ( plus_plus_int @ A @ B )
% 4.97/5.18 = ( plus_plus_int @ A @ C ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_left_cancel
% 4.97/5.18 thf(fact_919_add__right__cancel,axiom,
% 4.97/5.18 ! [B: real,A: real,C: real] :
% 4.97/5.18 ( ( ( plus_plus_real @ B @ A )
% 4.97/5.18 = ( plus_plus_real @ C @ A ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_right_cancel
% 4.97/5.18 thf(fact_920_add__right__cancel,axiom,
% 4.97/5.18 ! [B: rat,A: rat,C: rat] :
% 4.97/5.18 ( ( ( plus_plus_rat @ B @ A )
% 4.97/5.18 = ( plus_plus_rat @ C @ A ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_right_cancel
% 4.97/5.18 thf(fact_921_add__right__cancel,axiom,
% 4.97/5.18 ! [B: nat,A: nat,C: nat] :
% 4.97/5.18 ( ( ( plus_plus_nat @ B @ A )
% 4.97/5.18 = ( plus_plus_nat @ C @ A ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_right_cancel
% 4.97/5.18 thf(fact_922_add__right__cancel,axiom,
% 4.97/5.18 ! [B: int,A: int,C: int] :
% 4.97/5.18 ( ( ( plus_plus_int @ B @ A )
% 4.97/5.18 = ( plus_plus_int @ C @ A ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_right_cancel
% 4.97/5.18 thf(fact_923_add_Oinverse__inverse,axiom,
% 4.97/5.18 ! [A: real] :
% 4.97/5.18 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add.inverse_inverse
% 4.97/5.18 thf(fact_924_add_Oinverse__inverse,axiom,
% 4.97/5.18 ! [A: int] :
% 4.97/5.18 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add.inverse_inverse
% 4.97/5.18 thf(fact_925_add_Oinverse__inverse,axiom,
% 4.97/5.18 ! [A: complex] :
% 4.97/5.18 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add.inverse_inverse
% 4.97/5.18 thf(fact_926_add_Oinverse__inverse,axiom,
% 4.97/5.18 ! [A: code_integer] :
% 4.97/5.18 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add.inverse_inverse
% 4.97/5.18 thf(fact_927_add_Oinverse__inverse,axiom,
% 4.97/5.18 ! [A: rat] :
% 4.97/5.18 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add.inverse_inverse
% 4.97/5.18 thf(fact_928_neg__equal__iff__equal,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( ( uminus_uminus_real @ A )
% 4.97/5.18 = ( uminus_uminus_real @ B ) )
% 4.97/5.18 = ( A = B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_equal_iff_equal
% 4.97/5.18 thf(fact_929_neg__equal__iff__equal,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( ( uminus_uminus_int @ A )
% 4.97/5.18 = ( uminus_uminus_int @ B ) )
% 4.97/5.18 = ( A = B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_equal_iff_equal
% 4.97/5.18 thf(fact_930_neg__equal__iff__equal,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( ( uminus1482373934393186551omplex @ A )
% 4.97/5.18 = ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.18 = ( A = B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_equal_iff_equal
% 4.97/5.18 thf(fact_931_neg__equal__iff__equal,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( ( uminus1351360451143612070nteger @ A )
% 4.97/5.18 = ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.18 = ( A = B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_equal_iff_equal
% 4.97/5.18 thf(fact_932_neg__equal__iff__equal,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( ( uminus_uminus_rat @ A )
% 4.97/5.18 = ( uminus_uminus_rat @ B ) )
% 4.97/5.18 = ( A = B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_equal_iff_equal
% 4.97/5.18 thf(fact_933_VEBT_Oinject_I1_J,axiom,
% 4.97/5.18 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 4.97/5.18 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 4.97/5.18 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 4.97/5.18 = ( ( X11 = Y11 )
% 4.97/5.18 & ( X12 = Y12 )
% 4.97/5.18 & ( X13 = Y13 )
% 4.97/5.18 & ( X14 = Y14 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % VEBT.inject(1)
% 4.97/5.18 thf(fact_934_high__def,axiom,
% 4.97/5.18 ( vEBT_VEBT_high
% 4.97/5.18 = ( ^ [X3: nat,N4: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % high_def
% 4.97/5.18 thf(fact_935_high__bound__aux,axiom,
% 4.97/5.18 ! [Ma: nat,N: nat,M: nat] :
% 4.97/5.18 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 4.97/5.18 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % high_bound_aux
% 4.97/5.18 thf(fact_936_add__le__cancel__right,axiom,
% 4.97/5.18 ! [A: real,C: real,B: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.18 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_right
% 4.97/5.18 thf(fact_937_add__le__cancel__right,axiom,
% 4.97/5.18 ! [A: rat,C: rat,B: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.18 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_right
% 4.97/5.18 thf(fact_938_add__le__cancel__right,axiom,
% 4.97/5.18 ! [A: nat,C: nat,B: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.18 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_right
% 4.97/5.18 thf(fact_939_add__le__cancel__right,axiom,
% 4.97/5.18 ! [A: int,C: int,B: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.18 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_right
% 4.97/5.18 thf(fact_940_add__le__cancel__left,axiom,
% 4.97/5.18 ! [C: real,A: real,B: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.97/5.18 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_left
% 4.97/5.18 thf(fact_941_add__le__cancel__left,axiom,
% 4.97/5.18 ! [C: rat,A: rat,B: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.97/5.18 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_left
% 4.97/5.18 thf(fact_942_add__le__cancel__left,axiom,
% 4.97/5.18 ! [C: nat,A: nat,B: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.97/5.18 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_left
% 4.97/5.18 thf(fact_943_add__le__cancel__left,axiom,
% 4.97/5.18 ! [C: int,A: int,B: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.97/5.18 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_le_cancel_left
% 4.97/5.18 thf(fact_944_add__less__cancel__left,axiom,
% 4.97/5.18 ! [C: real,A: real,B: real] :
% 4.97/5.18 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.97/5.18 = ( ord_less_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_left
% 4.97/5.18 thf(fact_945_add__less__cancel__left,axiom,
% 4.97/5.18 ! [C: rat,A: rat,B: rat] :
% 4.97/5.18 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.97/5.18 = ( ord_less_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_left
% 4.97/5.18 thf(fact_946_add__less__cancel__left,axiom,
% 4.97/5.18 ! [C: nat,A: nat,B: nat] :
% 4.97/5.18 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.97/5.18 = ( ord_less_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_left
% 4.97/5.18 thf(fact_947_add__less__cancel__left,axiom,
% 4.97/5.18 ! [C: int,A: int,B: int] :
% 4.97/5.18 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.97/5.18 = ( ord_less_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_left
% 4.97/5.18 thf(fact_948_add__less__cancel__right,axiom,
% 4.97/5.18 ! [A: real,C: real,B: real] :
% 4.97/5.18 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.18 = ( ord_less_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_right
% 4.97/5.18 thf(fact_949_add__less__cancel__right,axiom,
% 4.97/5.18 ! [A: rat,C: rat,B: rat] :
% 4.97/5.18 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.18 = ( ord_less_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_right
% 4.97/5.18 thf(fact_950_add__less__cancel__right,axiom,
% 4.97/5.18 ! [A: nat,C: nat,B: nat] :
% 4.97/5.18 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.18 = ( ord_less_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_right
% 4.97/5.18 thf(fact_951_add__less__cancel__right,axiom,
% 4.97/5.18 ! [A: int,C: int,B: int] :
% 4.97/5.18 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.18 = ( ord_less_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_less_cancel_right
% 4.97/5.18 thf(fact_952_neg__le__iff__le,axiom,
% 4.97/5.18 ! [B: real,A: real] :
% 4.97/5.18 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 4.97/5.18 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_le_iff_le
% 4.97/5.18 thf(fact_953_neg__le__iff__le,axiom,
% 4.97/5.18 ! [B: code_integer,A: code_integer] :
% 4.97/5.18 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.18 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_le_iff_le
% 4.97/5.18 thf(fact_954_neg__le__iff__le,axiom,
% 4.97/5.18 ! [B: rat,A: rat] :
% 4.97/5.18 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 4.97/5.18 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_le_iff_le
% 4.97/5.18 thf(fact_955_neg__le__iff__le,axiom,
% 4.97/5.18 ! [B: int,A: int] :
% 4.97/5.18 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 4.97/5.18 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_le_iff_le
% 4.97/5.18 thf(fact_956_mult__1,axiom,
% 4.97/5.18 ! [A: real] :
% 4.97/5.18 ( ( times_times_real @ one_one_real @ A )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1
% 4.97/5.18 thf(fact_957_mult__1,axiom,
% 4.97/5.18 ! [A: rat] :
% 4.97/5.18 ( ( times_times_rat @ one_one_rat @ A )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1
% 4.97/5.18 thf(fact_958_mult__1,axiom,
% 4.97/5.18 ! [A: nat] :
% 4.97/5.18 ( ( times_times_nat @ one_one_nat @ A )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1
% 4.97/5.18 thf(fact_959_mult__1,axiom,
% 4.97/5.18 ! [A: int] :
% 4.97/5.18 ( ( times_times_int @ one_one_int @ A )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1
% 4.97/5.18 thf(fact_960_mult__1,axiom,
% 4.97/5.18 ! [A: complex] :
% 4.97/5.18 ( ( times_times_complex @ one_one_complex @ A )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult_1
% 4.97/5.18 thf(fact_961_mult_Oright__neutral,axiom,
% 4.97/5.18 ! [A: real] :
% 4.97/5.18 ( ( times_times_real @ A @ one_one_real )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult.right_neutral
% 4.97/5.18 thf(fact_962_mult_Oright__neutral,axiom,
% 4.97/5.18 ! [A: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ one_one_rat )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult.right_neutral
% 4.97/5.18 thf(fact_963_mult_Oright__neutral,axiom,
% 4.97/5.18 ! [A: nat] :
% 4.97/5.18 ( ( times_times_nat @ A @ one_one_nat )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult.right_neutral
% 4.97/5.18 thf(fact_964_mult_Oright__neutral,axiom,
% 4.97/5.18 ! [A: int] :
% 4.97/5.18 ( ( times_times_int @ A @ one_one_int )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult.right_neutral
% 4.97/5.18 thf(fact_965_mult_Oright__neutral,axiom,
% 4.97/5.18 ! [A: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ one_one_complex )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % mult.right_neutral
% 4.97/5.18 thf(fact_966_neg__less__iff__less,axiom,
% 4.97/5.18 ! [B: real,A: real] :
% 4.97/5.18 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 4.97/5.18 = ( ord_less_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_less_iff_less
% 4.97/5.18 thf(fact_967_neg__less__iff__less,axiom,
% 4.97/5.18 ! [B: int,A: int] :
% 4.97/5.18 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 4.97/5.18 = ( ord_less_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_less_iff_less
% 4.97/5.18 thf(fact_968_neg__less__iff__less,axiom,
% 4.97/5.18 ! [B: code_integer,A: code_integer] :
% 4.97/5.18 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.18 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_less_iff_less
% 4.97/5.18 thf(fact_969_neg__less__iff__less,axiom,
% 4.97/5.18 ! [B: rat,A: rat] :
% 4.97/5.18 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 4.97/5.18 = ( ord_less_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % neg_less_iff_less
% 4.97/5.18 thf(fact_970_add__diff__cancel__right_H,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right'
% 4.97/5.18 thf(fact_971_add__diff__cancel__right_H,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right'
% 4.97/5.18 thf(fact_972_add__diff__cancel__right_H,axiom,
% 4.97/5.18 ! [A: nat,B: nat] :
% 4.97/5.18 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right'
% 4.97/5.18 thf(fact_973_add__diff__cancel__right_H,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right'
% 4.97/5.18 thf(fact_974_add__diff__cancel__right_H,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right'
% 4.97/5.18 thf(fact_975_add__diff__cancel__right,axiom,
% 4.97/5.18 ! [A: real,C: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.18 = ( minus_minus_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right
% 4.97/5.18 thf(fact_976_add__diff__cancel__right,axiom,
% 4.97/5.18 ! [A: rat,C: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.18 = ( minus_minus_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right
% 4.97/5.18 thf(fact_977_add__diff__cancel__right,axiom,
% 4.97/5.18 ! [A: nat,C: nat,B: nat] :
% 4.97/5.18 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.18 = ( minus_minus_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right
% 4.97/5.18 thf(fact_978_add__diff__cancel__right,axiom,
% 4.97/5.18 ! [A: int,C: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.18 = ( minus_minus_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right
% 4.97/5.18 thf(fact_979_add__diff__cancel__right,axiom,
% 4.97/5.18 ! [A: complex,C: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 4.97/5.18 = ( minus_minus_complex @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_right
% 4.97/5.18 thf(fact_980_add__diff__cancel__left_H,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left'
% 4.97/5.18 thf(fact_981_add__diff__cancel__left_H,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left'
% 4.97/5.18 thf(fact_982_add__diff__cancel__left_H,axiom,
% 4.97/5.18 ! [A: nat,B: nat] :
% 4.97/5.18 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left'
% 4.97/5.18 thf(fact_983_add__diff__cancel__left_H,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left'
% 4.97/5.18 thf(fact_984_add__diff__cancel__left_H,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left'
% 4.97/5.18 thf(fact_985_add__diff__cancel__left,axiom,
% 4.97/5.18 ! [C: real,A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.97/5.18 = ( minus_minus_real @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left
% 4.97/5.18 thf(fact_986_add__diff__cancel__left,axiom,
% 4.97/5.18 ! [C: rat,A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.97/5.18 = ( minus_minus_rat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left
% 4.97/5.18 thf(fact_987_add__diff__cancel__left,axiom,
% 4.97/5.18 ! [C: nat,A: nat,B: nat] :
% 4.97/5.18 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.97/5.18 = ( minus_minus_nat @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left
% 4.97/5.18 thf(fact_988_add__diff__cancel__left,axiom,
% 4.97/5.18 ! [C: int,A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.97/5.18 = ( minus_minus_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left
% 4.97/5.18 thf(fact_989_add__diff__cancel__left,axiom,
% 4.97/5.18 ! [C: complex,A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 4.97/5.18 = ( minus_minus_complex @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel_left
% 4.97/5.18 thf(fact_990_diff__add__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % diff_add_cancel
% 4.97/5.18 thf(fact_991_diff__add__cancel,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % diff_add_cancel
% 4.97/5.18 thf(fact_992_diff__add__cancel,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % diff_add_cancel
% 4.97/5.18 thf(fact_993_diff__add__cancel,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % diff_add_cancel
% 4.97/5.18 thf(fact_994_add__diff__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel
% 4.97/5.18 thf(fact_995_add__diff__cancel,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel
% 4.97/5.18 thf(fact_996_add__diff__cancel,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel
% 4.97/5.18 thf(fact_997_add__diff__cancel,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 4.97/5.18 = A ) ).
% 4.97/5.18
% 4.97/5.18 % add_diff_cancel
% 4.97/5.18 thf(fact_998_times__divide__eq__right,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 4.97/5.18 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_right
% 4.97/5.18 thf(fact_999_times__divide__eq__right,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.97/5.18 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_right
% 4.97/5.18 thf(fact_1000_times__divide__eq__right,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.97/5.18 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_right
% 4.97/5.18 thf(fact_1001_divide__divide__eq__right,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 4.97/5.18 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_right
% 4.97/5.18 thf(fact_1002_divide__divide__eq__right,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.97/5.18 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_right
% 4.97/5.18 thf(fact_1003_divide__divide__eq__right,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.97/5.18 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_right
% 4.97/5.18 thf(fact_1004_divide__divide__eq__left,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 4.97/5.18 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_left
% 4.97/5.18 thf(fact_1005_divide__divide__eq__left,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 4.97/5.18 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_left
% 4.97/5.18 thf(fact_1006_divide__divide__eq__left,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 4.97/5.18 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % divide_divide_eq_left
% 4.97/5.18 thf(fact_1007_times__divide__eq__left,axiom,
% 4.97/5.18 ! [B: complex,C: complex,A: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 4.97/5.18 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_left
% 4.97/5.18 thf(fact_1008_times__divide__eq__left,axiom,
% 4.97/5.18 ! [B: real,C: real,A: real] :
% 4.97/5.18 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.97/5.18 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_left
% 4.97/5.18 thf(fact_1009_times__divide__eq__left,axiom,
% 4.97/5.18 ! [B: rat,C: rat,A: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.97/5.18 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 4.97/5.18
% 4.97/5.18 % times_divide_eq_left
% 4.97/5.18 thf(fact_1010_add__minus__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_minus_cancel
% 4.97/5.18 thf(fact_1011_add__minus__cancel,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_minus_cancel
% 4.97/5.18 thf(fact_1012_add__minus__cancel,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_minus_cancel
% 4.97/5.18 thf(fact_1013_add__minus__cancel,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_minus_cancel
% 4.97/5.18 thf(fact_1014_add__minus__cancel,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % add_minus_cancel
% 4.97/5.18 thf(fact_1015_minus__add__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_cancel
% 4.97/5.18 thf(fact_1016_minus__add__cancel,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_cancel
% 4.97/5.18 thf(fact_1017_minus__add__cancel,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_cancel
% 4.97/5.18 thf(fact_1018_minus__add__cancel,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_cancel
% 4.97/5.18 thf(fact_1019_minus__add__cancel,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.18 = B ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_cancel
% 4.97/5.18 thf(fact_1020_minus__add__distrib,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.97/5.18 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_distrib
% 4.97/5.18 thf(fact_1021_minus__add__distrib,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.97/5.18 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_distrib
% 4.97/5.18 thf(fact_1022_minus__add__distrib,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.97/5.18 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_distrib
% 4.97/5.18 thf(fact_1023_minus__add__distrib,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.97/5.18 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_distrib
% 4.97/5.18 thf(fact_1024_minus__add__distrib,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.18 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_add_distrib
% 4.97/5.18 thf(fact_1025_minus__diff__eq,axiom,
% 4.97/5.18 ! [A: real,B: real] :
% 4.97/5.18 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 4.97/5.18 = ( minus_minus_real @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_diff_eq
% 4.97/5.18 thf(fact_1026_minus__diff__eq,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 4.97/5.18 = ( minus_minus_int @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_diff_eq
% 4.97/5.18 thf(fact_1027_minus__diff__eq,axiom,
% 4.97/5.18 ! [A: complex,B: complex] :
% 4.97/5.18 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 4.97/5.18 = ( minus_minus_complex @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_diff_eq
% 4.97/5.18 thf(fact_1028_minus__diff__eq,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 4.97/5.18 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_diff_eq
% 4.97/5.18 thf(fact_1029_minus__diff__eq,axiom,
% 4.97/5.18 ! [A: rat,B: rat] :
% 4.97/5.18 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 4.97/5.18 = ( minus_minus_rat @ B @ A ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_diff_eq
% 4.97/5.18 thf(fact_1030_div__minus__minus,axiom,
% 4.97/5.18 ! [A: int,B: int] :
% 4.97/5.18 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.97/5.18 = ( divide_divide_int @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % div_minus_minus
% 4.97/5.18 thf(fact_1031_div__minus__minus,axiom,
% 4.97/5.18 ! [A: code_integer,B: code_integer] :
% 4.97/5.18 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.18 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 4.97/5.18
% 4.97/5.18 % div_minus_minus
% 4.97/5.18 thf(fact_1032_nat__add__left__cancel__less,axiom,
% 4.97/5.18 ! [K: nat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 4.97/5.18 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_add_left_cancel_less
% 4.97/5.18 thf(fact_1033_nat__add__left__cancel__le,axiom,
% 4.97/5.18 ! [K: nat,M: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 4.97/5.18 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_add_left_cancel_le
% 4.97/5.18 thf(fact_1034_diff__diff__cancel,axiom,
% 4.97/5.18 ! [I: nat,N: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ I @ N )
% 4.97/5.18 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 4.97/5.18 = I ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_diff_cancel
% 4.97/5.18 thf(fact_1035_diff__diff__left,axiom,
% 4.97/5.18 ! [I: nat,J: nat,K: nat] :
% 4.97/5.18 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 4.97/5.18 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % diff_diff_left
% 4.97/5.18 thf(fact_1036_nat__mult__eq__1__iff,axiom,
% 4.97/5.18 ! [M: nat,N: nat] :
% 4.97/5.18 ( ( ( times_times_nat @ M @ N )
% 4.97/5.18 = one_one_nat )
% 4.97/5.18 = ( ( M = one_one_nat )
% 4.97/5.18 & ( N = one_one_nat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_mult_eq_1_iff
% 4.97/5.18 thf(fact_1037_nat__1__eq__mult__iff,axiom,
% 4.97/5.18 ! [M: nat,N: nat] :
% 4.97/5.18 ( ( one_one_nat
% 4.97/5.18 = ( times_times_nat @ M @ N ) )
% 4.97/5.18 = ( ( M = one_one_nat )
% 4.97/5.18 & ( N = one_one_nat ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % nat_1_eq_mult_iff
% 4.97/5.18 thf(fact_1038_semiring__norm_I78_J,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 4.97/5.18 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(78)
% 4.97/5.18 thf(fact_1039_semiring__norm_I75_J,axiom,
% 4.97/5.18 ! [M: num] :
% 4.97/5.18 ~ ( ord_less_num @ M @ one ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(75)
% 4.97/5.18 thf(fact_1040_semiring__norm_I80_J,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 4.97/5.18 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(80)
% 4.97/5.18 thf(fact_1041__C4_Ohyps_C_I9_J,axiom,
% 4.97/5.18 ( ( mi != ma )
% 4.97/5.18 => ! [I2: nat] :
% 4.97/5.18 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.97/5.18 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 4.97/5.18 = I2 )
% 4.97/5.18 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 4.97/5.18 & ! [X: nat] :
% 4.97/5.18 ( ( ( ( vEBT_VEBT_high @ X @ na )
% 4.97/5.18 = I2 )
% 4.97/5.18 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ X @ na ) ) )
% 4.97/5.18 => ( ( ord_less_nat @ mi @ X )
% 4.97/5.18 & ( ord_less_eq_nat @ X @ ma ) ) ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % "4.hyps"(9)
% 4.97/5.18 thf(fact_1042_semiring__norm_I76_J,axiom,
% 4.97/5.18 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(76)
% 4.97/5.18 thf(fact_1043_both__member__options__ding,axiom,
% 4.97/5.18 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 4.97/5.18 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 4.97/5.18 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.97/5.18 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.97/5.18 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % both_member_options_ding
% 4.97/5.18 thf(fact_1044_semiring__norm_I81_J,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 4.97/5.18 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(81)
% 4.97/5.18 thf(fact_1045_semiring__norm_I77_J,axiom,
% 4.97/5.18 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(77)
% 4.97/5.18 thf(fact_1046_both__member__options__from__complete__tree__to__child,axiom,
% 4.97/5.18 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 4.97/5.18 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.97/5.18 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.97/5.18 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.97/5.18 | ( X2 = Mi )
% 4.97/5.18 | ( X2 = Ma ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % both_member_options_from_complete_tree_to_child
% 4.97/5.18 thf(fact_1047_both__member__options__from__chilf__to__complete__tree,axiom,
% 4.97/5.18 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.97/5.18 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.97/5.18 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.97/5.18 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.97/5.18 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % both_member_options_from_chilf_to_complete_tree
% 4.97/5.18 thf(fact_1048_semiring__norm_I79_J,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 4.97/5.18 = ( ord_less_eq_num @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(79)
% 4.97/5.18 thf(fact_1049_semiring__norm_I74_J,axiom,
% 4.97/5.18 ! [M: num,N: num] :
% 4.97/5.18 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 4.97/5.18 = ( ord_less_num @ M @ N ) ) ).
% 4.97/5.18
% 4.97/5.18 % semiring_norm(74)
% 4.97/5.18 thf(fact_1050_less__eq__real__def,axiom,
% 4.97/5.18 ( ord_less_eq_real
% 4.97/5.18 = ( ^ [X3: real,Y2: real] :
% 4.97/5.18 ( ( ord_less_real @ X3 @ Y2 )
% 4.97/5.18 | ( X3 = Y2 ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % less_eq_real_def
% 4.97/5.18 thf(fact_1051_minus__1__div__exp__eq__int,axiom,
% 4.97/5.18 ! [N: nat] :
% 4.97/5.18 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 4.97/5.18 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.18
% 4.97/5.18 % minus_1_div_exp_eq_int
% 4.97/5.18 thf(fact_1052_real__arch__pow,axiom,
% 4.97/5.18 ! [X2: real,Y: real] :
% 4.97/5.18 ( ( ord_less_real @ one_one_real @ X2 )
% 4.97/5.18 => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % real_arch_pow
% 4.97/5.18 thf(fact_1053_linordered__field__no__lb,axiom,
% 4.97/5.18 ! [X: real] :
% 4.97/5.18 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_field_no_lb
% 4.97/5.18 thf(fact_1054_linordered__field__no__lb,axiom,
% 4.97/5.18 ! [X: rat] :
% 4.97/5.18 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_field_no_lb
% 4.97/5.18 thf(fact_1055_linordered__field__no__ub,axiom,
% 4.97/5.18 ! [X: real] :
% 4.97/5.18 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_field_no_ub
% 4.97/5.18 thf(fact_1056_linordered__field__no__ub,axiom,
% 4.97/5.18 ! [X: rat] :
% 4.97/5.18 ? [X_12: rat] : ( ord_less_rat @ X @ X_12 ) ).
% 4.97/5.18
% 4.97/5.18 % linordered_field_no_ub
% 4.97/5.18 thf(fact_1057_mult_Oleft__commute,axiom,
% 4.97/5.18 ! [B: real,A: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 4.97/5.18 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.left_commute
% 4.97/5.18 thf(fact_1058_mult_Oleft__commute,axiom,
% 4.97/5.18 ! [B: rat,A: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 4.97/5.18 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.left_commute
% 4.97/5.18 thf(fact_1059_mult_Oleft__commute,axiom,
% 4.97/5.18 ! [B: nat,A: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 4.97/5.18 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.left_commute
% 4.97/5.18 thf(fact_1060_mult_Oleft__commute,axiom,
% 4.97/5.18 ! [B: int,A: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 4.97/5.18 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.left_commute
% 4.97/5.18 thf(fact_1061_mult_Oleft__commute,axiom,
% 4.97/5.18 ! [B: complex,A: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 4.97/5.18 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.left_commute
% 4.97/5.18 thf(fact_1062_mult_Ocommute,axiom,
% 4.97/5.18 ( times_times_real
% 4.97/5.18 = ( ^ [A4: real,B3: real] : ( times_times_real @ B3 @ A4 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.commute
% 4.97/5.18 thf(fact_1063_mult_Ocommute,axiom,
% 4.97/5.18 ( times_times_rat
% 4.97/5.18 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ B3 @ A4 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.commute
% 4.97/5.18 thf(fact_1064_mult_Ocommute,axiom,
% 4.97/5.18 ( times_times_nat
% 4.97/5.18 = ( ^ [A4: nat,B3: nat] : ( times_times_nat @ B3 @ A4 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.commute
% 4.97/5.18 thf(fact_1065_mult_Ocommute,axiom,
% 4.97/5.18 ( times_times_int
% 4.97/5.18 = ( ^ [A4: int,B3: int] : ( times_times_int @ B3 @ A4 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.commute
% 4.97/5.18 thf(fact_1066_mult_Ocommute,axiom,
% 4.97/5.18 ( times_times_complex
% 4.97/5.18 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ B3 @ A4 ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.commute
% 4.97/5.18 thf(fact_1067_mult_Oassoc,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.assoc
% 4.97/5.18 thf(fact_1068_mult_Oassoc,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.assoc
% 4.97/5.18 thf(fact_1069_mult_Oassoc,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.assoc
% 4.97/5.18 thf(fact_1070_mult_Oassoc,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.assoc
% 4.97/5.18 thf(fact_1071_mult_Oassoc,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % mult.assoc
% 4.97/5.18 thf(fact_1072_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_mult_class.mult_ac(1)
% 4.97/5.18 thf(fact_1073_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_mult_class.mult_ac(1)
% 4.97/5.18 thf(fact_1074_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_mult_class.mult_ac(1)
% 4.97/5.18 thf(fact_1075_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_mult_class.mult_ac(1)
% 4.97/5.18 thf(fact_1076_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.97/5.18 ! [A: complex,B: complex,C: complex] :
% 4.97/5.18 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 4.97/5.18 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_mult_class.mult_ac(1)
% 4.97/5.18 thf(fact_1077_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_add_class.add_ac(1)
% 4.97/5.18 thf(fact_1078_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_add_class.add_ac(1)
% 4.97/5.18 thf(fact_1079_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_add_class.add_ac(1)
% 4.97/5.18 thf(fact_1080_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % ab_semigroup_add_class.add_ac(1)
% 4.97/5.18 thf(fact_1081_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.97/5.18 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.18 ( ( ( I = J )
% 4.97/5.18 & ( K = L ) )
% 4.97/5.18 => ( ( plus_plus_real @ I @ K )
% 4.97/5.18 = ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono_thms_linordered_semiring(4)
% 4.97/5.18 thf(fact_1082_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.97/5.18 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.18 ( ( ( I = J )
% 4.97/5.18 & ( K = L ) )
% 4.97/5.18 => ( ( plus_plus_rat @ I @ K )
% 4.97/5.18 = ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono_thms_linordered_semiring(4)
% 4.97/5.18 thf(fact_1083_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.97/5.18 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.18 ( ( ( I = J )
% 4.97/5.18 & ( K = L ) )
% 4.97/5.18 => ( ( plus_plus_nat @ I @ K )
% 4.97/5.18 = ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono_thms_linordered_semiring(4)
% 4.97/5.18 thf(fact_1084_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.97/5.18 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.18 ( ( ( I = J )
% 4.97/5.18 & ( K = L ) )
% 4.97/5.18 => ( ( plus_plus_int @ I @ K )
% 4.97/5.18 = ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add_mono_thms_linordered_semiring(4)
% 4.97/5.18 thf(fact_1085_group__cancel_Oadd1,axiom,
% 4.97/5.18 ! [A2: real,K: real,A: real,B: real] :
% 4.97/5.18 ( ( A2
% 4.97/5.18 = ( plus_plus_real @ K @ A ) )
% 4.97/5.18 => ( ( plus_plus_real @ A2 @ B )
% 4.97/5.18 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add1
% 4.97/5.18 thf(fact_1086_group__cancel_Oadd1,axiom,
% 4.97/5.18 ! [A2: rat,K: rat,A: rat,B: rat] :
% 4.97/5.18 ( ( A2
% 4.97/5.18 = ( plus_plus_rat @ K @ A ) )
% 4.97/5.18 => ( ( plus_plus_rat @ A2 @ B )
% 4.97/5.18 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add1
% 4.97/5.18 thf(fact_1087_group__cancel_Oadd1,axiom,
% 4.97/5.18 ! [A2: nat,K: nat,A: nat,B: nat] :
% 4.97/5.18 ( ( A2
% 4.97/5.18 = ( plus_plus_nat @ K @ A ) )
% 4.97/5.18 => ( ( plus_plus_nat @ A2 @ B )
% 4.97/5.18 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add1
% 4.97/5.18 thf(fact_1088_group__cancel_Oadd1,axiom,
% 4.97/5.18 ! [A2: int,K: int,A: int,B: int] :
% 4.97/5.18 ( ( A2
% 4.97/5.18 = ( plus_plus_int @ K @ A ) )
% 4.97/5.18 => ( ( plus_plus_int @ A2 @ B )
% 4.97/5.18 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add1
% 4.97/5.18 thf(fact_1089_group__cancel_Oadd2,axiom,
% 4.97/5.18 ! [B4: real,K: real,B: real,A: real] :
% 4.97/5.18 ( ( B4
% 4.97/5.18 = ( plus_plus_real @ K @ B ) )
% 4.97/5.18 => ( ( plus_plus_real @ A @ B4 )
% 4.97/5.18 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add2
% 4.97/5.18 thf(fact_1090_group__cancel_Oadd2,axiom,
% 4.97/5.18 ! [B4: rat,K: rat,B: rat,A: rat] :
% 4.97/5.18 ( ( B4
% 4.97/5.18 = ( plus_plus_rat @ K @ B ) )
% 4.97/5.18 => ( ( plus_plus_rat @ A @ B4 )
% 4.97/5.18 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add2
% 4.97/5.18 thf(fact_1091_group__cancel_Oadd2,axiom,
% 4.97/5.18 ! [B4: nat,K: nat,B: nat,A: nat] :
% 4.97/5.18 ( ( B4
% 4.97/5.18 = ( plus_plus_nat @ K @ B ) )
% 4.97/5.18 => ( ( plus_plus_nat @ A @ B4 )
% 4.97/5.18 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add2
% 4.97/5.18 thf(fact_1092_group__cancel_Oadd2,axiom,
% 4.97/5.18 ! [B4: int,K: int,B: int,A: int] :
% 4.97/5.18 ( ( B4
% 4.97/5.18 = ( plus_plus_int @ K @ B ) )
% 4.97/5.18 => ( ( plus_plus_int @ A @ B4 )
% 4.97/5.18 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % group_cancel.add2
% 4.97/5.18 thf(fact_1093_add_Oassoc,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add.assoc
% 4.97/5.18 thf(fact_1094_add_Oassoc,axiom,
% 4.97/5.18 ! [A: rat,B: rat,C: rat] :
% 4.97/5.18 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add.assoc
% 4.97/5.18 thf(fact_1095_add_Oassoc,axiom,
% 4.97/5.18 ! [A: nat,B: nat,C: nat] :
% 4.97/5.18 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add.assoc
% 4.97/5.18 thf(fact_1096_add_Oassoc,axiom,
% 4.97/5.18 ! [A: int,B: int,C: int] :
% 4.97/5.18 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.97/5.18 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.18
% 4.97/5.18 % add.assoc
% 4.97/5.18 thf(fact_1097_add_Oleft__cancel,axiom,
% 4.97/5.18 ! [A: real,B: real,C: real] :
% 4.97/5.18 ( ( ( plus_plus_real @ A @ B )
% 4.97/5.18 = ( plus_plus_real @ A @ C ) )
% 4.97/5.18 = ( B = C ) ) ).
% 4.97/5.18
% 4.97/5.18 % add.left_cancel
% 4.97/5.19 thf(fact_1098_add_Oleft__cancel,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ( plus_plus_rat @ A @ B )
% 4.97/5.19 = ( plus_plus_rat @ A @ C ) )
% 4.97/5.19 = ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_cancel
% 4.97/5.19 thf(fact_1099_add_Oleft__cancel,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ( plus_plus_int @ A @ B )
% 4.97/5.19 = ( plus_plus_int @ A @ C ) )
% 4.97/5.19 = ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_cancel
% 4.97/5.19 thf(fact_1100_add_Oright__cancel,axiom,
% 4.97/5.19 ! [B: real,A: real,C: real] :
% 4.97/5.19 ( ( ( plus_plus_real @ B @ A )
% 4.97/5.19 = ( plus_plus_real @ C @ A ) )
% 4.97/5.19 = ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.right_cancel
% 4.97/5.19 thf(fact_1101_add_Oright__cancel,axiom,
% 4.97/5.19 ! [B: rat,A: rat,C: rat] :
% 4.97/5.19 ( ( ( plus_plus_rat @ B @ A )
% 4.97/5.19 = ( plus_plus_rat @ C @ A ) )
% 4.97/5.19 = ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.right_cancel
% 4.97/5.19 thf(fact_1102_add_Oright__cancel,axiom,
% 4.97/5.19 ! [B: int,A: int,C: int] :
% 4.97/5.19 ( ( ( plus_plus_int @ B @ A )
% 4.97/5.19 = ( plus_plus_int @ C @ A ) )
% 4.97/5.19 = ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.right_cancel
% 4.97/5.19 thf(fact_1103_add_Ocommute,axiom,
% 4.97/5.19 ( plus_plus_real
% 4.97/5.19 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ B3 @ A4 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.commute
% 4.97/5.19 thf(fact_1104_add_Ocommute,axiom,
% 4.97/5.19 ( plus_plus_rat
% 4.97/5.19 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ B3 @ A4 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.commute
% 4.97/5.19 thf(fact_1105_add_Ocommute,axiom,
% 4.97/5.19 ( plus_plus_nat
% 4.97/5.19 = ( ^ [A4: nat,B3: nat] : ( plus_plus_nat @ B3 @ A4 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.commute
% 4.97/5.19 thf(fact_1106_add_Ocommute,axiom,
% 4.97/5.19 ( plus_plus_int
% 4.97/5.19 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ B3 @ A4 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.commute
% 4.97/5.19 thf(fact_1107_add_Oleft__commute,axiom,
% 4.97/5.19 ! [B: real,A: real,C: real] :
% 4.97/5.19 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 4.97/5.19 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_commute
% 4.97/5.19 thf(fact_1108_add_Oleft__commute,axiom,
% 4.97/5.19 ! [B: rat,A: rat,C: rat] :
% 4.97/5.19 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 4.97/5.19 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_commute
% 4.97/5.19 thf(fact_1109_add_Oleft__commute,axiom,
% 4.97/5.19 ! [B: nat,A: nat,C: nat] :
% 4.97/5.19 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 4.97/5.19 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_commute
% 4.97/5.19 thf(fact_1110_add_Oleft__commute,axiom,
% 4.97/5.19 ! [B: int,A: int,C: int] :
% 4.97/5.19 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 4.97/5.19 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.left_commute
% 4.97/5.19 thf(fact_1111_add__left__imp__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ( plus_plus_real @ A @ B )
% 4.97/5.19 = ( plus_plus_real @ A @ C ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_imp_eq
% 4.97/5.19 thf(fact_1112_add__left__imp__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ( plus_plus_rat @ A @ B )
% 4.97/5.19 = ( plus_plus_rat @ A @ C ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_imp_eq
% 4.97/5.19 thf(fact_1113_add__left__imp__eq,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ( plus_plus_nat @ A @ B )
% 4.97/5.19 = ( plus_plus_nat @ A @ C ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_imp_eq
% 4.97/5.19 thf(fact_1114_add__left__imp__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ( plus_plus_int @ A @ B )
% 4.97/5.19 = ( plus_plus_int @ A @ C ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_imp_eq
% 4.97/5.19 thf(fact_1115_add__right__imp__eq,axiom,
% 4.97/5.19 ! [B: real,A: real,C: real] :
% 4.97/5.19 ( ( ( plus_plus_real @ B @ A )
% 4.97/5.19 = ( plus_plus_real @ C @ A ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_imp_eq
% 4.97/5.19 thf(fact_1116_add__right__imp__eq,axiom,
% 4.97/5.19 ! [B: rat,A: rat,C: rat] :
% 4.97/5.19 ( ( ( plus_plus_rat @ B @ A )
% 4.97/5.19 = ( plus_plus_rat @ C @ A ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_imp_eq
% 4.97/5.19 thf(fact_1117_add__right__imp__eq,axiom,
% 4.97/5.19 ! [B: nat,A: nat,C: nat] :
% 4.97/5.19 ( ( ( plus_plus_nat @ B @ A )
% 4.97/5.19 = ( plus_plus_nat @ C @ A ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_imp_eq
% 4.97/5.19 thf(fact_1118_add__right__imp__eq,axiom,
% 4.97/5.19 ! [B: int,A: int,C: int] :
% 4.97/5.19 ( ( ( plus_plus_int @ B @ A )
% 4.97/5.19 = ( plus_plus_int @ C @ A ) )
% 4.97/5.19 => ( B = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_imp_eq
% 4.97/5.19 thf(fact_1119_one__reorient,axiom,
% 4.97/5.19 ! [X2: complex] :
% 4.97/5.19 ( ( one_one_complex = X2 )
% 4.97/5.19 = ( X2 = one_one_complex ) ) ).
% 4.97/5.19
% 4.97/5.19 % one_reorient
% 4.97/5.19 thf(fact_1120_one__reorient,axiom,
% 4.97/5.19 ! [X2: real] :
% 4.97/5.19 ( ( one_one_real = X2 )
% 4.97/5.19 = ( X2 = one_one_real ) ) ).
% 4.97/5.19
% 4.97/5.19 % one_reorient
% 4.97/5.19 thf(fact_1121_one__reorient,axiom,
% 4.97/5.19 ! [X2: rat] :
% 4.97/5.19 ( ( one_one_rat = X2 )
% 4.97/5.19 = ( X2 = one_one_rat ) ) ).
% 4.97/5.19
% 4.97/5.19 % one_reorient
% 4.97/5.19 thf(fact_1122_one__reorient,axiom,
% 4.97/5.19 ! [X2: nat] :
% 4.97/5.19 ( ( one_one_nat = X2 )
% 4.97/5.19 = ( X2 = one_one_nat ) ) ).
% 4.97/5.19
% 4.97/5.19 % one_reorient
% 4.97/5.19 thf(fact_1123_one__reorient,axiom,
% 4.97/5.19 ! [X2: int] :
% 4.97/5.19 ( ( one_one_int = X2 )
% 4.97/5.19 = ( X2 = one_one_int ) ) ).
% 4.97/5.19
% 4.97/5.19 % one_reorient
% 4.97/5.19 thf(fact_1124_diff__right__commute,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 4.97/5.19 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_commute
% 4.97/5.19 thf(fact_1125_diff__right__commute,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 4.97/5.19 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_commute
% 4.97/5.19 thf(fact_1126_diff__right__commute,axiom,
% 4.97/5.19 ! [A: nat,C: nat,B: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 4.97/5.19 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_commute
% 4.97/5.19 thf(fact_1127_diff__right__commute,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 4.97/5.19 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_commute
% 4.97/5.19 thf(fact_1128_diff__right__commute,axiom,
% 4.97/5.19 ! [A: complex,C: complex,B: complex] :
% 4.97/5.19 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B )
% 4.97/5.19 = ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_commute
% 4.97/5.19 thf(fact_1129_diff__eq__diff__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ( minus_minus_real @ A @ B )
% 4.97/5.19 = ( minus_minus_real @ C @ D ) )
% 4.97/5.19 => ( ( A = B )
% 4.97/5.19 = ( C = D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_eq
% 4.97/5.19 thf(fact_1130_diff__eq__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ( minus_minus_rat @ A @ B )
% 4.97/5.19 = ( minus_minus_rat @ C @ D ) )
% 4.97/5.19 => ( ( A = B )
% 4.97/5.19 = ( C = D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_eq
% 4.97/5.19 thf(fact_1131_diff__eq__diff__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ( minus_minus_int @ A @ B )
% 4.97/5.19 = ( minus_minus_int @ C @ D ) )
% 4.97/5.19 => ( ( A = B )
% 4.97/5.19 = ( C = D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_eq
% 4.97/5.19 thf(fact_1132_diff__eq__diff__eq,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex,D: complex] :
% 4.97/5.19 ( ( ( minus_minus_complex @ A @ B )
% 4.97/5.19 = ( minus_minus_complex @ C @ D ) )
% 4.97/5.19 => ( ( A = B )
% 4.97/5.19 = ( C = D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_eq
% 4.97/5.19 thf(fact_1133_equation__minus__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( uminus_uminus_real @ B ) )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % equation_minus_iff
% 4.97/5.19 thf(fact_1134_equation__minus__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( uminus_uminus_int @ B ) )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % equation_minus_iff
% 4.97/5.19 thf(fact_1135_equation__minus__iff,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % equation_minus_iff
% 4.97/5.19 thf(fact_1136_equation__minus__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % equation_minus_iff
% 4.97/5.19 thf(fact_1137_equation__minus__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( uminus_uminus_rat @ B ) )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % equation_minus_iff
% 4.97/5.19 thf(fact_1138_minus__equation__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ( uminus_uminus_real @ A )
% 4.97/5.19 = B )
% 4.97/5.19 = ( ( uminus_uminus_real @ B )
% 4.97/5.19 = A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_equation_iff
% 4.97/5.19 thf(fact_1139_minus__equation__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ( uminus_uminus_int @ A )
% 4.97/5.19 = B )
% 4.97/5.19 = ( ( uminus_uminus_int @ B )
% 4.97/5.19 = A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_equation_iff
% 4.97/5.19 thf(fact_1140_minus__equation__iff,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( ( uminus1482373934393186551omplex @ A )
% 4.97/5.19 = B )
% 4.97/5.19 = ( ( uminus1482373934393186551omplex @ B )
% 4.97/5.19 = A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_equation_iff
% 4.97/5.19 thf(fact_1141_minus__equation__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ( uminus1351360451143612070nteger @ A )
% 4.97/5.19 = B )
% 4.97/5.19 = ( ( uminus1351360451143612070nteger @ B )
% 4.97/5.19 = A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_equation_iff
% 4.97/5.19 thf(fact_1142_minus__equation__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ( uminus_uminus_rat @ A )
% 4.97/5.19 = B )
% 4.97/5.19 = ( ( uminus_uminus_rat @ B )
% 4.97/5.19 = A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_equation_iff
% 4.97/5.19 thf(fact_1143_nat__neq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( M != N )
% 4.97/5.19 = ( ( ord_less_nat @ M @ N )
% 4.97/5.19 | ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat_neq_iff
% 4.97/5.19 thf(fact_1144_less__not__refl,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ~ ( ord_less_nat @ N @ N ) ).
% 4.97/5.19
% 4.97/5.19 % less_not_refl
% 4.97/5.19 thf(fact_1145_less__not__refl2,axiom,
% 4.97/5.19 ! [N: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_nat @ N @ M )
% 4.97/5.19 => ( M != N ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_not_refl2
% 4.97/5.19 thf(fact_1146_less__not__refl3,axiom,
% 4.97/5.19 ! [S2: nat,T: nat] :
% 4.97/5.19 ( ( ord_less_nat @ S2 @ T )
% 4.97/5.19 => ( S2 != T ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_not_refl3
% 4.97/5.19 thf(fact_1147_less__irrefl__nat,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ~ ( ord_less_nat @ N @ N ) ).
% 4.97/5.19
% 4.97/5.19 % less_irrefl_nat
% 4.97/5.19 thf(fact_1148_nat__less__induct,axiom,
% 4.97/5.19 ! [P: nat > $o,N: nat] :
% 4.97/5.19 ( ! [N3: nat] :
% 4.97/5.19 ( ! [M2: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M2 @ N3 )
% 4.97/5.19 => ( P @ M2 ) )
% 4.97/5.19 => ( P @ N3 ) )
% 4.97/5.19 => ( P @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat_less_induct
% 4.97/5.19 thf(fact_1149_infinite__descent,axiom,
% 4.97/5.19 ! [P: nat > $o,N: nat] :
% 4.97/5.19 ( ! [N3: nat] :
% 4.97/5.19 ( ~ ( P @ N3 )
% 4.97/5.19 => ? [M2: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M2 @ N3 )
% 4.97/5.19 & ~ ( P @ M2 ) ) )
% 4.97/5.19 => ( P @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % infinite_descent
% 4.97/5.19 thf(fact_1150_linorder__neqE__nat,axiom,
% 4.97/5.19 ! [X2: nat,Y: nat] :
% 4.97/5.19 ( ( X2 != Y )
% 4.97/5.19 => ( ~ ( ord_less_nat @ X2 @ Y )
% 4.97/5.19 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % linorder_neqE_nat
% 4.97/5.19 thf(fact_1151_le__refl,axiom,
% 4.97/5.19 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 4.97/5.19
% 4.97/5.19 % le_refl
% 4.97/5.19 thf(fact_1152_le__trans,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ( ord_less_eq_nat @ J @ K )
% 4.97/5.19 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_trans
% 4.97/5.19 thf(fact_1153_eq__imp__le,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( M = N )
% 4.97/5.19 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_imp_le
% 4.97/5.19 thf(fact_1154_le__antisym,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.19 => ( M = N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_antisym
% 4.97/5.19 thf(fact_1155_nat__le__linear,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 | ( ord_less_eq_nat @ N @ M ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat_le_linear
% 4.97/5.19 thf(fact_1156_Nat_Oex__has__greatest__nat,axiom,
% 4.97/5.19 ! [P: nat > $o,K: nat,B: nat] :
% 4.97/5.19 ( ( P @ K )
% 4.97/5.19 => ( ! [Y3: nat] :
% 4.97/5.19 ( ( P @ Y3 )
% 4.97/5.19 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.97/5.19 => ? [X4: nat] :
% 4.97/5.19 ( ( P @ X4 )
% 4.97/5.19 & ! [Y4: nat] :
% 4.97/5.19 ( ( P @ Y4 )
% 4.97/5.19 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.ex_has_greatest_nat
% 4.97/5.19 thf(fact_1157_div__le__mono,axiom,
% 4.97/5.19 ! [M: nat,N: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_le_mono
% 4.97/5.19 thf(fact_1158_div__le__dividend,axiom,
% 4.97/5.19 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 4.97/5.19
% 4.97/5.19 % div_le_dividend
% 4.97/5.19 thf(fact_1159_size__neq__size__imp__neq,axiom,
% 4.97/5.19 ! [X2: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 4.97/5.19 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 4.97/5.19 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 4.97/5.19 => ( X2 != Y ) ) ).
% 4.97/5.19
% 4.97/5.19 % size_neq_size_imp_neq
% 4.97/5.19 thf(fact_1160_size__neq__size__imp__neq,axiom,
% 4.97/5.19 ! [X2: list_o,Y: list_o] :
% 4.97/5.19 ( ( ( size_size_list_o @ X2 )
% 4.97/5.19 != ( size_size_list_o @ Y ) )
% 4.97/5.19 => ( X2 != Y ) ) ).
% 4.97/5.19
% 4.97/5.19 % size_neq_size_imp_neq
% 4.97/5.19 thf(fact_1161_size__neq__size__imp__neq,axiom,
% 4.97/5.19 ! [X2: list_nat,Y: list_nat] :
% 4.97/5.19 ( ( ( size_size_list_nat @ X2 )
% 4.97/5.19 != ( size_size_list_nat @ Y ) )
% 4.97/5.19 => ( X2 != Y ) ) ).
% 4.97/5.19
% 4.97/5.19 % size_neq_size_imp_neq
% 4.97/5.19 thf(fact_1162_size__neq__size__imp__neq,axiom,
% 4.97/5.19 ! [X2: list_int,Y: list_int] :
% 4.97/5.19 ( ( ( size_size_list_int @ X2 )
% 4.97/5.19 != ( size_size_list_int @ Y ) )
% 4.97/5.19 => ( X2 != Y ) ) ).
% 4.97/5.19
% 4.97/5.19 % size_neq_size_imp_neq
% 4.97/5.19 thf(fact_1163_size__neq__size__imp__neq,axiom,
% 4.97/5.19 ! [X2: num,Y: num] :
% 4.97/5.19 ( ( ( size_size_num @ X2 )
% 4.97/5.19 != ( size_size_num @ Y ) )
% 4.97/5.19 => ( X2 != Y ) ) ).
% 4.97/5.19
% 4.97/5.19 % size_neq_size_imp_neq
% 4.97/5.19 thf(fact_1164_diff__commute,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 4.97/5.19 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_commute
% 4.97/5.19 thf(fact_1165_div__mult2__eq,axiom,
% 4.97/5.19 ! [M: nat,N: nat,Q2: nat] :
% 4.97/5.19 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 4.97/5.19 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_mult2_eq
% 4.97/5.19 thf(fact_1166_nat__mult__1__right,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( times_times_nat @ N @ one_one_nat )
% 4.97/5.19 = N ) ).
% 4.97/5.19
% 4.97/5.19 % nat_mult_1_right
% 4.97/5.19 thf(fact_1167_nat__mult__1,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( times_times_nat @ one_one_nat @ N )
% 4.97/5.19 = N ) ).
% 4.97/5.19
% 4.97/5.19 % nat_mult_1
% 4.97/5.19 thf(fact_1168_invar__vebt_Ointros_I4_J,axiom,
% 4.97/5.19 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.97/5.19 ( ! [X4: vEBT_VEBT] :
% 4.97/5.19 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.19 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.97/5.19 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.97/5.19 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.97/5.19 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( M = N )
% 4.97/5.19 => ( ( Deg
% 4.97/5.19 = ( plus_plus_nat @ N @ M ) )
% 4.97/5.19 => ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X5 ) )
% 4.97/5.19 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 4.97/5.19 => ( ( ( Mi = Ma )
% 4.97/5.19 => ! [X4: vEBT_VEBT] :
% 4.97/5.19 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.19 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 4.97/5.19 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.97/5.19 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.97/5.19 => ( ( ( Mi != Ma )
% 4.97/5.19 => ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 4.97/5.19 = I3 )
% 4.97/5.19 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 4.97/5.19 & ! [X4: nat] :
% 4.97/5.19 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 4.97/5.19 = I3 )
% 4.97/5.19 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 4.97/5.19 => ( ( ord_less_nat @ Mi @ X4 )
% 4.97/5.19 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 4.97/5.19 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % invar_vebt.intros(4)
% 4.97/5.19 thf(fact_1169_add__le__imp__le__right,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.19 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_right
% 4.97/5.19 thf(fact_1170_add__le__imp__le__right,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.19 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_right
% 4.97/5.19 thf(fact_1171_add__le__imp__le__right,axiom,
% 4.97/5.19 ! [A: nat,C: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.19 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_right
% 4.97/5.19 thf(fact_1172_add__le__imp__le__right,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.19 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_right
% 4.97/5.19 thf(fact_1173_add__le__imp__le__left,axiom,
% 4.97/5.19 ! [C: real,A: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.97/5.19 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_left
% 4.97/5.19 thf(fact_1174_add__le__imp__le__left,axiom,
% 4.97/5.19 ! [C: rat,A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.97/5.19 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_left
% 4.97/5.19 thf(fact_1175_add__le__imp__le__left,axiom,
% 4.97/5.19 ! [C: nat,A: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.97/5.19 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_left
% 4.97/5.19 thf(fact_1176_add__le__imp__le__left,axiom,
% 4.97/5.19 ! [C: int,A: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.97/5.19 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_imp_le_left
% 4.97/5.19 thf(fact_1177_le__iff__add,axiom,
% 4.97/5.19 ( ord_less_eq_nat
% 4.97/5.19 = ( ^ [A4: nat,B3: nat] :
% 4.97/5.19 ? [C2: nat] :
% 4.97/5.19 ( B3
% 4.97/5.19 = ( plus_plus_nat @ A4 @ C2 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_iff_add
% 4.97/5.19 thf(fact_1178_add__right__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_mono
% 4.97/5.19 thf(fact_1179_add__right__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_mono
% 4.97/5.19 thf(fact_1180_add__right__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_mono
% 4.97/5.19 thf(fact_1181_add__right__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_right_mono
% 4.97/5.19 thf(fact_1182_less__eqE,axiom,
% 4.97/5.19 ! [A: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ~ ! [C3: nat] :
% 4.97/5.19 ( B
% 4.97/5.19 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_eqE
% 4.97/5.19 thf(fact_1183_add__left__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_mono
% 4.97/5.19 thf(fact_1184_add__left__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_mono
% 4.97/5.19 thf(fact_1185_add__left__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_mono
% 4.97/5.19 thf(fact_1186_add__left__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_left_mono
% 4.97/5.19 thf(fact_1187_add__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_real @ C @ D )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono
% 4.97/5.19 thf(fact_1188_add__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_rat @ C @ D )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono
% 4.97/5.19 thf(fact_1189_add__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_nat @ C @ D )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono
% 4.97/5.19 thf(fact_1190_add__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_int @ C @ D )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono
% 4.97/5.19 thf(fact_1191_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_eq_real @ I @ J )
% 4.97/5.19 & ( ord_less_eq_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(1)
% 4.97/5.19 thf(fact_1192_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_eq_rat @ I @ J )
% 4.97/5.19 & ( ord_less_eq_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(1)
% 4.97/5.19 thf(fact_1193_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 & ( ord_less_eq_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(1)
% 4.97/5.19 thf(fact_1194_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_eq_int @ I @ J )
% 4.97/5.19 & ( ord_less_eq_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(1)
% 4.97/5.19 thf(fact_1195_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_eq_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(2)
% 4.97/5.19 thf(fact_1196_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_eq_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(2)
% 4.97/5.19 thf(fact_1197_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_eq_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(2)
% 4.97/5.19 thf(fact_1198_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_eq_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(2)
% 4.97/5.19 thf(fact_1199_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_eq_real @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(3)
% 4.97/5.19 thf(fact_1200_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_eq_rat @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(3)
% 4.97/5.19 thf(fact_1201_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(3)
% 4.97/5.19 thf(fact_1202_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_eq_int @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_semiring(3)
% 4.97/5.19 thf(fact_1203_diff__eq__diff__less__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ( minus_minus_real @ A @ B )
% 4.97/5.19 = ( minus_minus_real @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less_eq
% 4.97/5.19 thf(fact_1204_diff__eq__diff__less__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ( minus_minus_rat @ A @ B )
% 4.97/5.19 = ( minus_minus_rat @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less_eq
% 4.97/5.19 thf(fact_1205_diff__eq__diff__less__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ( minus_minus_int @ A @ B )
% 4.97/5.19 = ( minus_minus_int @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less_eq
% 4.97/5.19 thf(fact_1206_diff__right__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_mono
% 4.97/5.19 thf(fact_1207_diff__right__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_mono
% 4.97/5.19 thf(fact_1208_diff__right__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_right_mono
% 4.97/5.19 thf(fact_1209_diff__left__mono,axiom,
% 4.97/5.19 ! [B: real,A: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ B @ A )
% 4.97/5.19 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_left_mono
% 4.97/5.19 thf(fact_1210_diff__left__mono,axiom,
% 4.97/5.19 ! [B: rat,A: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ B @ A )
% 4.97/5.19 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_left_mono
% 4.97/5.19 thf(fact_1211_diff__left__mono,axiom,
% 4.97/5.19 ! [B: int,A: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ B @ A )
% 4.97/5.19 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_left_mono
% 4.97/5.19 thf(fact_1212_diff__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,D: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_real @ D @ C )
% 4.97/5.19 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_mono
% 4.97/5.19 thf(fact_1213_diff__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_rat @ D @ C )
% 4.97/5.19 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_mono
% 4.97/5.19 thf(fact_1214_diff__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,D: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_int @ D @ C )
% 4.97/5.19 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_mono
% 4.97/5.19 thf(fact_1215_add__mono__thms__linordered__field_I5_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_real @ I @ J )
% 4.97/5.19 & ( ord_less_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(5)
% 4.97/5.19 thf(fact_1216_add__mono__thms__linordered__field_I5_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_rat @ I @ J )
% 4.97/5.19 & ( ord_less_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(5)
% 4.97/5.19 thf(fact_1217_add__mono__thms__linordered__field_I5_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_nat @ I @ J )
% 4.97/5.19 & ( ord_less_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(5)
% 4.97/5.19 thf(fact_1218_add__mono__thms__linordered__field_I5_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_int @ I @ J )
% 4.97/5.19 & ( ord_less_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(5)
% 4.97/5.19 thf(fact_1219_add__mono__thms__linordered__field_I2_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(2)
% 4.97/5.19 thf(fact_1220_add__mono__thms__linordered__field_I2_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(2)
% 4.97/5.19 thf(fact_1221_add__mono__thms__linordered__field_I2_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(2)
% 4.97/5.19 thf(fact_1222_add__mono__thms__linordered__field_I2_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( I = J )
% 4.97/5.19 & ( ord_less_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(2)
% 4.97/5.19 thf(fact_1223_add__mono__thms__linordered__field_I1_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_real @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(1)
% 4.97/5.19 thf(fact_1224_add__mono__thms__linordered__field_I1_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_rat @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(1)
% 4.97/5.19 thf(fact_1225_add__mono__thms__linordered__field_I1_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_nat @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(1)
% 4.97/5.19 thf(fact_1226_add__mono__thms__linordered__field_I1_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_int @ I @ J )
% 4.97/5.19 & ( K = L ) )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(1)
% 4.97/5.19 thf(fact_1227_add__strict__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_real @ C @ D )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_mono
% 4.97/5.19 thf(fact_1228_add__strict__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_rat @ C @ D )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_mono
% 4.97/5.19 thf(fact_1229_add__strict__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.97/5.19 ( ( ord_less_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_nat @ C @ D )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_mono
% 4.97/5.19 thf(fact_1230_add__strict__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_int @ C @ D )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_mono
% 4.97/5.19 thf(fact_1231_add__strict__left__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_left_mono
% 4.97/5.19 thf(fact_1232_add__strict__left__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_left_mono
% 4.97/5.19 thf(fact_1233_add__strict__left__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_nat @ A @ B )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_left_mono
% 4.97/5.19 thf(fact_1234_add__strict__left__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_left_mono
% 4.97/5.19 thf(fact_1235_add__strict__right__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_right_mono
% 4.97/5.19 thf(fact_1236_add__strict__right__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_right_mono
% 4.97/5.19 thf(fact_1237_add__strict__right__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_nat @ A @ B )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_right_mono
% 4.97/5.19 thf(fact_1238_add__strict__right__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_strict_right_mono
% 4.97/5.19 thf(fact_1239_add__less__imp__less__left,axiom,
% 4.97/5.19 ! [C: real,A: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.97/5.19 => ( ord_less_real @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_left
% 4.97/5.19 thf(fact_1240_add__less__imp__less__left,axiom,
% 4.97/5.19 ! [C: rat,A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.97/5.19 => ( ord_less_rat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_left
% 4.97/5.19 thf(fact_1241_add__less__imp__less__left,axiom,
% 4.97/5.19 ! [C: nat,A: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.97/5.19 => ( ord_less_nat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_left
% 4.97/5.19 thf(fact_1242_add__less__imp__less__left,axiom,
% 4.97/5.19 ! [C: int,A: int,B: int] :
% 4.97/5.19 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.97/5.19 => ( ord_less_int @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_left
% 4.97/5.19 thf(fact_1243_add__less__imp__less__right,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.97/5.19 => ( ord_less_real @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_right
% 4.97/5.19 thf(fact_1244_add__less__imp__less__right,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.19 => ( ord_less_rat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_right
% 4.97/5.19 thf(fact_1245_add__less__imp__less__right,axiom,
% 4.97/5.19 ! [A: nat,C: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.97/5.19 => ( ord_less_nat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_right
% 4.97/5.19 thf(fact_1246_add__less__imp__less__right,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.97/5.19 => ( ord_less_int @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_imp_less_right
% 4.97/5.19 thf(fact_1247_le__imp__neg__le,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_imp_neg_le
% 4.97/5.19 thf(fact_1248_le__imp__neg__le,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ord_le3102999989581377725nteger @ A @ B )
% 4.97/5.19 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_imp_neg_le
% 4.97/5.19 thf(fact_1249_le__imp__neg__le,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_imp_neg_le
% 4.97/5.19 thf(fact_1250_le__imp__neg__le,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_imp_neg_le
% 4.97/5.19 thf(fact_1251_minus__le__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 4.97/5.19 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_le_iff
% 4.97/5.19 thf(fact_1252_minus__le__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 4.97/5.19 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_le_iff
% 4.97/5.19 thf(fact_1253_minus__le__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.97/5.19 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_le_iff
% 4.97/5.19 thf(fact_1254_minus__le__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 4.97/5.19 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_le_iff
% 4.97/5.19 thf(fact_1255_le__minus__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 4.97/5.19 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_minus_iff
% 4.97/5.19 thf(fact_1256_le__minus__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.19 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_minus_iff
% 4.97/5.19 thf(fact_1257_le__minus__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.97/5.19 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_minus_iff
% 4.97/5.19 thf(fact_1258_le__minus__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 4.97/5.19 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_minus_iff
% 4.97/5.19 thf(fact_1259_diff__strict__right__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_right_mono
% 4.97/5.19 thf(fact_1260_diff__strict__right__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_right_mono
% 4.97/5.19 thf(fact_1261_diff__strict__right__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_right_mono
% 4.97/5.19 thf(fact_1262_diff__strict__left__mono,axiom,
% 4.97/5.19 ! [B: real,A: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ B @ A )
% 4.97/5.19 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_left_mono
% 4.97/5.19 thf(fact_1263_diff__strict__left__mono,axiom,
% 4.97/5.19 ! [B: rat,A: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ B @ A )
% 4.97/5.19 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_left_mono
% 4.97/5.19 thf(fact_1264_diff__strict__left__mono,axiom,
% 4.97/5.19 ! [B: int,A: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ B @ A )
% 4.97/5.19 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_left_mono
% 4.97/5.19 thf(fact_1265_diff__eq__diff__less,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ( minus_minus_real @ A @ B )
% 4.97/5.19 = ( minus_minus_real @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_real @ A @ B )
% 4.97/5.19 = ( ord_less_real @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less
% 4.97/5.19 thf(fact_1266_diff__eq__diff__less,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ( minus_minus_rat @ A @ B )
% 4.97/5.19 = ( minus_minus_rat @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_rat @ A @ B )
% 4.97/5.19 = ( ord_less_rat @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less
% 4.97/5.19 thf(fact_1267_diff__eq__diff__less,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ( minus_minus_int @ A @ B )
% 4.97/5.19 = ( minus_minus_int @ C @ D ) )
% 4.97/5.19 => ( ( ord_less_int @ A @ B )
% 4.97/5.19 = ( ord_less_int @ C @ D ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_diff_less
% 4.97/5.19 thf(fact_1268_diff__strict__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,D: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_real @ D @ C )
% 4.97/5.19 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_mono
% 4.97/5.19 thf(fact_1269_diff__strict__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_rat @ D @ C )
% 4.97/5.19 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_mono
% 4.97/5.19 thf(fact_1270_diff__strict__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,D: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_int @ D @ C )
% 4.97/5.19 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_strict_mono
% 4.97/5.19 thf(fact_1271_mult_Ocomm__neutral,axiom,
% 4.97/5.19 ! [A: real] :
% 4.97/5.19 ( ( times_times_real @ A @ one_one_real )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % mult.comm_neutral
% 4.97/5.19 thf(fact_1272_mult_Ocomm__neutral,axiom,
% 4.97/5.19 ! [A: rat] :
% 4.97/5.19 ( ( times_times_rat @ A @ one_one_rat )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % mult.comm_neutral
% 4.97/5.19 thf(fact_1273_mult_Ocomm__neutral,axiom,
% 4.97/5.19 ! [A: nat] :
% 4.97/5.19 ( ( times_times_nat @ A @ one_one_nat )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % mult.comm_neutral
% 4.97/5.19 thf(fact_1274_mult_Ocomm__neutral,axiom,
% 4.97/5.19 ! [A: int] :
% 4.97/5.19 ( ( times_times_int @ A @ one_one_int )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % mult.comm_neutral
% 4.97/5.19 thf(fact_1275_mult_Ocomm__neutral,axiom,
% 4.97/5.19 ! [A: complex] :
% 4.97/5.19 ( ( times_times_complex @ A @ one_one_complex )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % mult.comm_neutral
% 4.97/5.19 thf(fact_1276_comm__monoid__mult__class_Omult__1,axiom,
% 4.97/5.19 ! [A: real] :
% 4.97/5.19 ( ( times_times_real @ one_one_real @ A )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % comm_monoid_mult_class.mult_1
% 4.97/5.19 thf(fact_1277_comm__monoid__mult__class_Omult__1,axiom,
% 4.97/5.19 ! [A: rat] :
% 4.97/5.19 ( ( times_times_rat @ one_one_rat @ A )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % comm_monoid_mult_class.mult_1
% 4.97/5.19 thf(fact_1278_comm__monoid__mult__class_Omult__1,axiom,
% 4.97/5.19 ! [A: nat] :
% 4.97/5.19 ( ( times_times_nat @ one_one_nat @ A )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % comm_monoid_mult_class.mult_1
% 4.97/5.19 thf(fact_1279_comm__monoid__mult__class_Omult__1,axiom,
% 4.97/5.19 ! [A: int] :
% 4.97/5.19 ( ( times_times_int @ one_one_int @ A )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % comm_monoid_mult_class.mult_1
% 4.97/5.19 thf(fact_1280_comm__monoid__mult__class_Omult__1,axiom,
% 4.97/5.19 ! [A: complex] :
% 4.97/5.19 ( ( times_times_complex @ one_one_complex @ A )
% 4.97/5.19 = A ) ).
% 4.97/5.19
% 4.97/5.19 % comm_monoid_mult_class.mult_1
% 4.97/5.19 thf(fact_1281_less__minus__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 4.97/5.19 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_minus_iff
% 4.97/5.19 thf(fact_1282_less__minus__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 4.97/5.19 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_minus_iff
% 4.97/5.19 thf(fact_1283_less__minus__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.19 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_minus_iff
% 4.97/5.19 thf(fact_1284_less__minus__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 4.97/5.19 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_minus_iff
% 4.97/5.19 thf(fact_1285_minus__less__iff,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 4.97/5.19 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_less_iff
% 4.97/5.19 thf(fact_1286_minus__less__iff,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 4.97/5.19 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_less_iff
% 4.97/5.19 thf(fact_1287_minus__less__iff,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 4.97/5.19 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_less_iff
% 4.97/5.19 thf(fact_1288_minus__less__iff,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 4.97/5.19 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_less_iff
% 4.97/5.19 thf(fact_1289_diff__diff__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq
% 4.97/5.19 thf(fact_1290_diff__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq
% 4.97/5.19 thf(fact_1291_diff__diff__eq,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq
% 4.97/5.19 thf(fact_1292_diff__diff__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq
% 4.97/5.19 thf(fact_1293_diff__diff__eq,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq
% 4.97/5.19 thf(fact_1294_add__implies__diff,axiom,
% 4.97/5.19 ! [C: real,B: real,A: real] :
% 4.97/5.19 ( ( ( plus_plus_real @ C @ B )
% 4.97/5.19 = A )
% 4.97/5.19 => ( C
% 4.97/5.19 = ( minus_minus_real @ A @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_implies_diff
% 4.97/5.19 thf(fact_1295_add__implies__diff,axiom,
% 4.97/5.19 ! [C: rat,B: rat,A: rat] :
% 4.97/5.19 ( ( ( plus_plus_rat @ C @ B )
% 4.97/5.19 = A )
% 4.97/5.19 => ( C
% 4.97/5.19 = ( minus_minus_rat @ A @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_implies_diff
% 4.97/5.19 thf(fact_1296_add__implies__diff,axiom,
% 4.97/5.19 ! [C: nat,B: nat,A: nat] :
% 4.97/5.19 ( ( ( plus_plus_nat @ C @ B )
% 4.97/5.19 = A )
% 4.97/5.19 => ( C
% 4.97/5.19 = ( minus_minus_nat @ A @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_implies_diff
% 4.97/5.19 thf(fact_1297_add__implies__diff,axiom,
% 4.97/5.19 ! [C: int,B: int,A: int] :
% 4.97/5.19 ( ( ( plus_plus_int @ C @ B )
% 4.97/5.19 = A )
% 4.97/5.19 => ( C
% 4.97/5.19 = ( minus_minus_int @ A @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_implies_diff
% 4.97/5.19 thf(fact_1298_add__implies__diff,axiom,
% 4.97/5.19 ! [C: complex,B: complex,A: complex] :
% 4.97/5.19 ( ( ( plus_plus_complex @ C @ B )
% 4.97/5.19 = A )
% 4.97/5.19 => ( C
% 4.97/5.19 = ( minus_minus_complex @ A @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_implies_diff
% 4.97/5.19 thf(fact_1299_diff__add__eq__diff__diff__swap,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.97/5.19 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq_diff_diff_swap
% 4.97/5.19 thf(fact_1300_diff__add__eq__diff__diff__swap,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.97/5.19 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq_diff_diff_swap
% 4.97/5.19 thf(fact_1301_diff__add__eq__diff__diff__swap,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.97/5.19 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq_diff_diff_swap
% 4.97/5.19 thf(fact_1302_diff__add__eq__diff__diff__swap,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 4.97/5.19 = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq_diff_diff_swap
% 4.97/5.19 thf(fact_1303_diff__add__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq
% 4.97/5.19 thf(fact_1304_diff__add__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq
% 4.97/5.19 thf(fact_1305_diff__add__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq
% 4.97/5.19 thf(fact_1306_diff__add__eq,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_eq
% 4.97/5.19 thf(fact_1307_diff__diff__eq2,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.97/5.19 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq2
% 4.97/5.19 thf(fact_1308_diff__diff__eq2,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.97/5.19 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq2
% 4.97/5.19 thf(fact_1309_diff__diff__eq2,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.97/5.19 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq2
% 4.97/5.19 thf(fact_1310_diff__diff__eq2,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 4.97/5.19 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_diff_eq2
% 4.97/5.19 thf(fact_1311_add__diff__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.97/5.19 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_diff_eq
% 4.97/5.19 thf(fact_1312_add__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.97/5.19 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_diff_eq
% 4.97/5.19 thf(fact_1313_add__diff__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.97/5.19 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_diff_eq
% 4.97/5.19 thf(fact_1314_add__diff__eq,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 4.97/5.19 = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_diff_eq
% 4.97/5.19 thf(fact_1315_eq__diff__eq,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( minus_minus_real @ C @ B ) )
% 4.97/5.19 = ( ( plus_plus_real @ A @ B )
% 4.97/5.19 = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_diff_eq
% 4.97/5.19 thf(fact_1316_eq__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( minus_minus_rat @ C @ B ) )
% 4.97/5.19 = ( ( plus_plus_rat @ A @ B )
% 4.97/5.19 = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_diff_eq
% 4.97/5.19 thf(fact_1317_eq__diff__eq,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( minus_minus_int @ C @ B ) )
% 4.97/5.19 = ( ( plus_plus_int @ A @ B )
% 4.97/5.19 = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_diff_eq
% 4.97/5.19 thf(fact_1318_eq__diff__eq,axiom,
% 4.97/5.19 ! [A: complex,C: complex,B: complex] :
% 4.97/5.19 ( ( A
% 4.97/5.19 = ( minus_minus_complex @ C @ B ) )
% 4.97/5.19 = ( ( plus_plus_complex @ A @ B )
% 4.97/5.19 = C ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_diff_eq
% 4.97/5.19 thf(fact_1319_diff__eq__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ( minus_minus_real @ A @ B )
% 4.97/5.19 = C )
% 4.97/5.19 = ( A
% 4.97/5.19 = ( plus_plus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_eq
% 4.97/5.19 thf(fact_1320_diff__eq__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ( minus_minus_rat @ A @ B )
% 4.97/5.19 = C )
% 4.97/5.19 = ( A
% 4.97/5.19 = ( plus_plus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_eq
% 4.97/5.19 thf(fact_1321_diff__eq__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ( minus_minus_int @ A @ B )
% 4.97/5.19 = C )
% 4.97/5.19 = ( A
% 4.97/5.19 = ( plus_plus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_eq
% 4.97/5.19 thf(fact_1322_diff__eq__eq,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( ( minus_minus_complex @ A @ B )
% 4.97/5.19 = C )
% 4.97/5.19 = ( A
% 4.97/5.19 = ( plus_plus_complex @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_eq_eq
% 4.97/5.19 thf(fact_1323_group__cancel_Osub1,axiom,
% 4.97/5.19 ! [A2: real,K: real,A: real,B: real] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_real @ K @ A ) )
% 4.97/5.19 => ( ( minus_minus_real @ A2 @ B )
% 4.97/5.19 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub1
% 4.97/5.19 thf(fact_1324_group__cancel_Osub1,axiom,
% 4.97/5.19 ! [A2: rat,K: rat,A: rat,B: rat] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_rat @ K @ A ) )
% 4.97/5.19 => ( ( minus_minus_rat @ A2 @ B )
% 4.97/5.19 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub1
% 4.97/5.19 thf(fact_1325_group__cancel_Osub1,axiom,
% 4.97/5.19 ! [A2: int,K: int,A: int,B: int] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_int @ K @ A ) )
% 4.97/5.19 => ( ( minus_minus_int @ A2 @ B )
% 4.97/5.19 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub1
% 4.97/5.19 thf(fact_1326_group__cancel_Osub1,axiom,
% 4.97/5.19 ! [A2: complex,K: complex,A: complex,B: complex] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_complex @ K @ A ) )
% 4.97/5.19 => ( ( minus_minus_complex @ A2 @ B )
% 4.97/5.19 = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub1
% 4.97/5.19 thf(fact_1327_divide__divide__eq__left_H,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 4.97/5.19 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_eq_left'
% 4.97/5.19 thf(fact_1328_divide__divide__eq__left_H,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 4.97/5.19 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_eq_left'
% 4.97/5.19 thf(fact_1329_divide__divide__eq__left_H,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 4.97/5.19 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_eq_left'
% 4.97/5.19 thf(fact_1330_divide__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: complex,Y: complex,Z: complex,W: complex] :
% 4.97/5.19 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 4.97/5.19 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_times_eq
% 4.97/5.19 thf(fact_1331_divide__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: real,Y: real,Z: real,W: real] :
% 4.97/5.19 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 4.97/5.19 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_times_eq
% 4.97/5.19 thf(fact_1332_divide__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: rat,Y: rat,Z: rat,W: rat] :
% 4.97/5.19 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 4.97/5.19 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divide_divide_times_eq
% 4.97/5.19 thf(fact_1333_times__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: complex,Y: complex,Z: complex,W: complex] :
% 4.97/5.19 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 4.97/5.19 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % times_divide_times_eq
% 4.97/5.19 thf(fact_1334_times__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: real,Y: real,Z: real,W: real] :
% 4.97/5.19 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 4.97/5.19 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % times_divide_times_eq
% 4.97/5.19 thf(fact_1335_times__divide__times__eq,axiom,
% 4.97/5.19 ! [X2: rat,Y: rat,Z: rat,W: rat] :
% 4.97/5.19 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 4.97/5.19 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % times_divide_times_eq
% 4.97/5.19 thf(fact_1336_add__divide__distrib,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 4.97/5.19 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_divide_distrib
% 4.97/5.19 thf(fact_1337_add__divide__distrib,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.97/5.19 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_divide_distrib
% 4.97/5.19 thf(fact_1338_add__divide__distrib,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_divide_distrib
% 4.97/5.19 thf(fact_1339_group__cancel_Oneg1,axiom,
% 4.97/5.19 ! [A2: real,K: real,A: real] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_real @ K @ A ) )
% 4.97/5.19 => ( ( uminus_uminus_real @ A2 )
% 4.97/5.19 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.neg1
% 4.97/5.19 thf(fact_1340_group__cancel_Oneg1,axiom,
% 4.97/5.19 ! [A2: int,K: int,A: int] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_int @ K @ A ) )
% 4.97/5.19 => ( ( uminus_uminus_int @ A2 )
% 4.97/5.19 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.neg1
% 4.97/5.19 thf(fact_1341_group__cancel_Oneg1,axiom,
% 4.97/5.19 ! [A2: complex,K: complex,A: complex] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_complex @ K @ A ) )
% 4.97/5.19 => ( ( uminus1482373934393186551omplex @ A2 )
% 4.97/5.19 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.neg1
% 4.97/5.19 thf(fact_1342_group__cancel_Oneg1,axiom,
% 4.97/5.19 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 4.97/5.19 => ( ( uminus1351360451143612070nteger @ A2 )
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.neg1
% 4.97/5.19 thf(fact_1343_group__cancel_Oneg1,axiom,
% 4.97/5.19 ! [A2: rat,K: rat,A: rat] :
% 4.97/5.19 ( ( A2
% 4.97/5.19 = ( plus_plus_rat @ K @ A ) )
% 4.97/5.19 => ( ( uminus_uminus_rat @ A2 )
% 4.97/5.19 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.neg1
% 4.97/5.19 thf(fact_1344_add_Oinverse__distrib__swap,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 4.97/5.19 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.inverse_distrib_swap
% 4.97/5.19 thf(fact_1345_add_Oinverse__distrib__swap,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 4.97/5.19 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.inverse_distrib_swap
% 4.97/5.19 thf(fact_1346_add_Oinverse__distrib__swap,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 4.97/5.19 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.inverse_distrib_swap
% 4.97/5.19 thf(fact_1347_add_Oinverse__distrib__swap,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.inverse_distrib_swap
% 4.97/5.19 thf(fact_1348_add_Oinverse__distrib__swap,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.19 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add.inverse_distrib_swap
% 4.97/5.19 thf(fact_1349_diff__divide__distrib,axiom,
% 4.97/5.19 ! [A: complex,B: complex,C: complex] :
% 4.97/5.19 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_divide_distrib
% 4.97/5.19 thf(fact_1350_diff__divide__distrib,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_divide_distrib
% 4.97/5.19 thf(fact_1351_diff__divide__distrib,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_divide_distrib
% 4.97/5.19 thf(fact_1352_minus__diff__commute,axiom,
% 4.97/5.19 ! [B: real,A: real] :
% 4.97/5.19 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 4.97/5.19 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_diff_commute
% 4.97/5.19 thf(fact_1353_minus__diff__commute,axiom,
% 4.97/5.19 ! [B: int,A: int] :
% 4.97/5.19 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 4.97/5.19 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_diff_commute
% 4.97/5.19 thf(fact_1354_minus__diff__commute,axiom,
% 4.97/5.19 ! [B: complex,A: complex] :
% 4.97/5.19 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 4.97/5.19 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_diff_commute
% 4.97/5.19 thf(fact_1355_minus__diff__commute,axiom,
% 4.97/5.19 ! [B: code_integer,A: code_integer] :
% 4.97/5.19 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 4.97/5.19 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_diff_commute
% 4.97/5.19 thf(fact_1356_minus__diff__commute,axiom,
% 4.97/5.19 ! [B: rat,A: rat] :
% 4.97/5.19 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 4.97/5.19 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_diff_commute
% 4.97/5.19 thf(fact_1357_minus__divide__right,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 4.97/5.19 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_right
% 4.97/5.19 thf(fact_1358_minus__divide__right,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 4.97/5.19 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_right
% 4.97/5.19 thf(fact_1359_minus__divide__right,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 4.97/5.19 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_right
% 4.97/5.19 thf(fact_1360_minus__divide__divide,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 4.97/5.19 = ( divide_divide_real @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_divide
% 4.97/5.19 thf(fact_1361_minus__divide__divide,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 4.97/5.19 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_divide
% 4.97/5.19 thf(fact_1362_minus__divide__divide,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 4.97/5.19 = ( divide_divide_rat @ A @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_divide
% 4.97/5.19 thf(fact_1363_minus__divide__left,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 4.97/5.19 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_left
% 4.97/5.19 thf(fact_1364_minus__divide__left,axiom,
% 4.97/5.19 ! [A: complex,B: complex] :
% 4.97/5.19 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 4.97/5.19 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_left
% 4.97/5.19 thf(fact_1365_minus__divide__left,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 4.97/5.19 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % minus_divide_left
% 4.97/5.19 thf(fact_1366_div__minus__right,axiom,
% 4.97/5.19 ! [A: int,B: int] :
% 4.97/5.19 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 4.97/5.19 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_minus_right
% 4.97/5.19 thf(fact_1367_div__minus__right,axiom,
% 4.97/5.19 ! [A: code_integer,B: code_integer] :
% 4.97/5.19 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.19 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_minus_right
% 4.97/5.19 thf(fact_1368_nat__less__le,axiom,
% 4.97/5.19 ( ord_less_nat
% 4.97/5.19 = ( ^ [M3: nat,N4: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M3 @ N4 )
% 4.97/5.19 & ( M3 != N4 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat_less_le
% 4.97/5.19 thf(fact_1369_less__imp__le__nat,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_imp_le_nat
% 4.97/5.19 thf(fact_1370_le__eq__less__or__eq,axiom,
% 4.97/5.19 ( ord_less_eq_nat
% 4.97/5.19 = ( ^ [M3: nat,N4: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M3 @ N4 )
% 4.97/5.19 | ( M3 = N4 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_eq_less_or_eq
% 4.97/5.19 thf(fact_1371_less__or__eq__imp__le,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( ord_less_nat @ M @ N )
% 4.97/5.19 | ( M = N ) )
% 4.97/5.19 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_or_eq_imp_le
% 4.97/5.19 thf(fact_1372_le__neq__implies__less,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ( ( M != N )
% 4.97/5.19 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_neq_implies_less
% 4.97/5.19 thf(fact_1373_less__mono__imp__le__mono,axiom,
% 4.97/5.19 ! [F: nat > nat,I: nat,J: nat] :
% 4.97/5.19 ( ! [I3: nat,J2: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ J2 )
% 4.97/5.19 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 4.97/5.19 => ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_mono_imp_le_mono
% 4.97/5.19 thf(fact_1374_add__lessD1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 4.97/5.19 => ( ord_less_nat @ I @ K ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_lessD1
% 4.97/5.19 thf(fact_1375_add__less__mono,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I @ J )
% 4.97/5.19 => ( ( ord_less_nat @ K @ L )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_mono
% 4.97/5.19 thf(fact_1376_not__add__less1,axiom,
% 4.97/5.19 ! [I: nat,J: nat] :
% 4.97/5.19 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 4.97/5.19
% 4.97/5.19 % not_add_less1
% 4.97/5.19 thf(fact_1377_not__add__less2,axiom,
% 4.97/5.19 ! [J: nat,I: nat] :
% 4.97/5.19 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 4.97/5.19
% 4.97/5.19 % not_add_less2
% 4.97/5.19 thf(fact_1378_add__less__mono1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I @ J )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_mono1
% 4.97/5.19 thf(fact_1379_trans__less__add1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I @ J )
% 4.97/5.19 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % trans_less_add1
% 4.97/5.19 thf(fact_1380_trans__less__add2,axiom,
% 4.97/5.19 ! [I: nat,J: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I @ J )
% 4.97/5.19 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % trans_less_add2
% 4.97/5.19 thf(fact_1381_less__add__eq__less,axiom,
% 4.97/5.19 ! [K: nat,L: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ K @ L )
% 4.97/5.19 => ( ( ( plus_plus_nat @ M @ L )
% 4.97/5.19 = ( plus_plus_nat @ K @ N ) )
% 4.97/5.19 => ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_add_eq_less
% 4.97/5.19 thf(fact_1382_add__leE,axiom,
% 4.97/5.19 ! [M: nat,K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 4.97/5.19 => ~ ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_leE
% 4.97/5.19 thf(fact_1383_le__add1,axiom,
% 4.97/5.19 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_add1
% 4.97/5.19 thf(fact_1384_le__add2,axiom,
% 4.97/5.19 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_add2
% 4.97/5.19 thf(fact_1385_add__leD1,axiom,
% 4.97/5.19 ! [M: nat,K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_leD1
% 4.97/5.19 thf(fact_1386_add__leD2,axiom,
% 4.97/5.19 ! [M: nat,K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ K @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_leD2
% 4.97/5.19 thf(fact_1387_le__Suc__ex,axiom,
% 4.97/5.19 ! [K: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ L )
% 4.97/5.19 => ? [N3: nat] :
% 4.97/5.19 ( L
% 4.97/5.19 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_Suc_ex
% 4.97/5.19 thf(fact_1388_add__le__mono,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ L )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_mono
% 4.97/5.19 thf(fact_1389_add__le__mono1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_mono1
% 4.97/5.19 thf(fact_1390_trans__le__add1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % trans_le_add1
% 4.97/5.19 thf(fact_1391_trans__le__add2,axiom,
% 4.97/5.19 ! [I: nat,J: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % trans_le_add2
% 4.97/5.19 thf(fact_1392_nat__le__iff__add,axiom,
% 4.97/5.19 ( ord_less_eq_nat
% 4.97/5.19 = ( ^ [M3: nat,N4: nat] :
% 4.97/5.19 ? [K2: nat] :
% 4.97/5.19 ( N4
% 4.97/5.19 = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat_le_iff_add
% 4.97/5.19 thf(fact_1393_less__imp__diff__less,axiom,
% 4.97/5.19 ! [J: nat,K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ J @ K )
% 4.97/5.19 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_imp_diff_less
% 4.97/5.19 thf(fact_1394_diff__less__mono2,axiom,
% 4.97/5.19 ! [M: nat,N: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M @ N )
% 4.97/5.19 => ( ( ord_less_nat @ M @ L )
% 4.97/5.19 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_less_mono2
% 4.97/5.19 thf(fact_1395_less__mult__imp__div__less,axiom,
% 4.97/5.19 ! [M: nat,I: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 4.97/5.19 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_mult_imp_div_less
% 4.97/5.19 thf(fact_1396_eq__diff__iff,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ M )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( ( minus_minus_nat @ M @ K )
% 4.97/5.19 = ( minus_minus_nat @ N @ K ) )
% 4.97/5.19 = ( M = N ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % eq_diff_iff
% 4.97/5.19 thf(fact_1397_le__diff__iff,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ M )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_iff
% 4.97/5.19 thf(fact_1398_Nat_Odiff__diff__eq,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ M )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.97/5.19 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.diff_diff_eq
% 4.97/5.19 thf(fact_1399_diff__le__mono,axiom,
% 4.97/5.19 ! [M: nat,N: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_mono
% 4.97/5.19 thf(fact_1400_diff__le__self,axiom,
% 4.97/5.19 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_self
% 4.97/5.19 thf(fact_1401_le__diff__iff_H,axiom,
% 4.97/5.19 ! [A: nat,C: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ C )
% 4.97/5.19 => ( ( ord_less_eq_nat @ B @ C )
% 4.97/5.19 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 4.97/5.19 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_iff'
% 4.97/5.19 thf(fact_1402_diff__le__mono2,axiom,
% 4.97/5.19 ! [M: nat,N: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.19 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_mono2
% 4.97/5.19 thf(fact_1403_le__cube,axiom,
% 4.97/5.19 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_cube
% 4.97/5.19 thf(fact_1404_le__square,axiom,
% 4.97/5.19 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_square
% 4.97/5.19 thf(fact_1405_mult__le__mono,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ L )
% 4.97/5.19 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % mult_le_mono
% 4.97/5.19 thf(fact_1406_mult__le__mono1,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % mult_le_mono1
% 4.97/5.19 thf(fact_1407_mult__le__mono2,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % mult_le_mono2
% 4.97/5.19 thf(fact_1408_div__times__less__eq__dividend,axiom,
% 4.97/5.19 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 4.97/5.19
% 4.97/5.19 % div_times_less_eq_dividend
% 4.97/5.19 thf(fact_1409_times__div__less__eq__dividend,axiom,
% 4.97/5.19 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 4.97/5.19
% 4.97/5.19 % times_div_less_eq_dividend
% 4.97/5.19 thf(fact_1410_Nat_Odiff__cancel,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 4.97/5.19 = ( minus_minus_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.diff_cancel
% 4.97/5.19 thf(fact_1411_diff__cancel2,axiom,
% 4.97/5.19 ! [M: nat,K: nat,N: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( minus_minus_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_cancel2
% 4.97/5.19 thf(fact_1412_diff__add__inverse,axiom,
% 4.97/5.19 ! [N: nat,M: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 4.97/5.19 = M ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_inverse
% 4.97/5.19 thf(fact_1413_diff__add__inverse2,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 4.97/5.19 = M ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add_inverse2
% 4.97/5.19 thf(fact_1414_add__mult__distrib,axiom,
% 4.97/5.19 ! [M: nat,N: nat,K: nat] :
% 4.97/5.19 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 4.97/5.19 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mult_distrib
% 4.97/5.19 thf(fact_1415_add__mult__distrib2,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mult_distrib2
% 4.97/5.19 thf(fact_1416_diff__mult__distrib2,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.19 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_mult_distrib2
% 4.97/5.19 thf(fact_1417_diff__mult__distrib,axiom,
% 4.97/5.19 ! [M: nat,N: nat,K: nat] :
% 4.97/5.19 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 4.97/5.19 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_mult_distrib
% 4.97/5.19 thf(fact_1418_add__less__le__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_real @ C @ D )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_le_mono
% 4.97/5.19 thf(fact_1419_add__less__le__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_rat @ C @ D )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_le_mono
% 4.97/5.19 thf(fact_1420_add__less__le__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.97/5.19 ( ( ord_less_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_nat @ C @ D )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_le_mono
% 4.97/5.19 thf(fact_1421_add__less__le__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_int @ C @ D )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_less_le_mono
% 4.97/5.19 thf(fact_1422_add__le__less__mono,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real,D: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ B )
% 4.97/5.19 => ( ( ord_less_real @ C @ D )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_less_mono
% 4.97/5.19 thf(fact_1423_add__le__less__mono,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ B )
% 4.97/5.19 => ( ( ord_less_rat @ C @ D )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_less_mono
% 4.97/5.19 thf(fact_1424_add__le__less__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_nat @ C @ D )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_less_mono
% 4.97/5.19 thf(fact_1425_add__le__less__mono,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int,D: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ B )
% 4.97/5.19 => ( ( ord_less_int @ C @ D )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_le_less_mono
% 4.97/5.19 thf(fact_1426_add__mono__thms__linordered__field_I3_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_real @ I @ J )
% 4.97/5.19 & ( ord_less_eq_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(3)
% 4.97/5.19 thf(fact_1427_add__mono__thms__linordered__field_I3_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_rat @ I @ J )
% 4.97/5.19 & ( ord_less_eq_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(3)
% 4.97/5.19 thf(fact_1428_add__mono__thms__linordered__field_I3_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_nat @ I @ J )
% 4.97/5.19 & ( ord_less_eq_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(3)
% 4.97/5.19 thf(fact_1429_add__mono__thms__linordered__field_I3_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_int @ I @ J )
% 4.97/5.19 & ( ord_less_eq_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(3)
% 4.97/5.19 thf(fact_1430_add__mono__thms__linordered__field_I4_J,axiom,
% 4.97/5.19 ! [I: real,J: real,K: real,L: real] :
% 4.97/5.19 ( ( ( ord_less_eq_real @ I @ J )
% 4.97/5.19 & ( ord_less_real @ K @ L ) )
% 4.97/5.19 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(4)
% 4.97/5.19 thf(fact_1431_add__mono__thms__linordered__field_I4_J,axiom,
% 4.97/5.19 ! [I: rat,J: rat,K: rat,L: rat] :
% 4.97/5.19 ( ( ( ord_less_eq_rat @ I @ J )
% 4.97/5.19 & ( ord_less_rat @ K @ L ) )
% 4.97/5.19 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(4)
% 4.97/5.19 thf(fact_1432_add__mono__thms__linordered__field_I4_J,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat,L: nat] :
% 4.97/5.19 ( ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 & ( ord_less_nat @ K @ L ) )
% 4.97/5.19 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(4)
% 4.97/5.19 thf(fact_1433_add__mono__thms__linordered__field_I4_J,axiom,
% 4.97/5.19 ! [I: int,J: int,K: int,L: int] :
% 4.97/5.19 ( ( ( ord_less_eq_int @ I @ J )
% 4.97/5.19 & ( ord_less_int @ K @ L ) )
% 4.97/5.19 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_mono_thms_linordered_field(4)
% 4.97/5.19 thf(fact_1434_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( ( minus_minus_nat @ B @ A )
% 4.97/5.19 = C )
% 4.97/5.19 = ( B
% 4.97/5.19 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 4.97/5.19 thf(fact_1435_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 4.97/5.19 ! [A: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 4.97/5.19 = B ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 4.97/5.19 thf(fact_1436_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.97/5.19 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 4.97/5.19 thf(fact_1437_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 4.97/5.19 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 4.97/5.19 thf(fact_1438_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 4.97/5.19 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 4.97/5.19 thf(fact_1439_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 4.97/5.19 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 4.97/5.19 thf(fact_1440_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.97/5.19 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 4.97/5.19 thf(fact_1441_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.97/5.19 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 4.97/5.19 thf(fact_1442_le__add__diff,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_add_diff
% 4.97/5.19 thf(fact_1443_diff__add,axiom,
% 4.97/5.19 ! [A: nat,B: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ A @ B )
% 4.97/5.19 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 4.97/5.19 = B ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_add
% 4.97/5.19 thf(fact_1444_le__diff__eq,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.97/5.19 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_eq
% 4.97/5.19 thf(fact_1445_le__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.97/5.19 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_eq
% 4.97/5.19 thf(fact_1446_le__diff__eq,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.97/5.19 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_eq
% 4.97/5.19 thf(fact_1447_diff__le__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_eq
% 4.97/5.19 thf(fact_1448_diff__le__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_eq
% 4.97/5.19 thf(fact_1449_diff__le__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_le_eq
% 4.97/5.19 thf(fact_1450_less__diff__eq,axiom,
% 4.97/5.19 ! [A: real,C: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.97/5.19 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_eq
% 4.97/5.19 thf(fact_1451_less__diff__eq,axiom,
% 4.97/5.19 ! [A: rat,C: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.97/5.19 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_eq
% 4.97/5.19 thf(fact_1452_less__diff__eq,axiom,
% 4.97/5.19 ! [A: int,C: int,B: int] :
% 4.97/5.19 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.97/5.19 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_eq
% 4.97/5.19 thf(fact_1453_diff__less__eq,axiom,
% 4.97/5.19 ! [A: real,B: real,C: real] :
% 4.97/5.19 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_less_eq
% 4.97/5.19 thf(fact_1454_diff__less__eq,axiom,
% 4.97/5.19 ! [A: rat,B: rat,C: rat] :
% 4.97/5.19 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_less_eq
% 4.97/5.19 thf(fact_1455_diff__less__eq,axiom,
% 4.97/5.19 ! [A: int,B: int,C: int] :
% 4.97/5.19 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.97/5.19 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_less_eq
% 4.97/5.19 thf(fact_1456_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_real
% 4.97/5.19 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.97/5.19 thf(fact_1457_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_int
% 4.97/5.19 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.97/5.19 thf(fact_1458_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_complex
% 4.97/5.19 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.97/5.19 thf(fact_1459_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_8373710615458151222nteger
% 4.97/5.19 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.97/5.19 thf(fact_1460_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_rat
% 4.97/5.19 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.97/5.19 thf(fact_1461_diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_real
% 4.97/5.19 = ( ^ [A4: real,B3: real] : ( plus_plus_real @ A4 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_conv_add_uminus
% 4.97/5.19 thf(fact_1462_diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_int
% 4.97/5.19 = ( ^ [A4: int,B3: int] : ( plus_plus_int @ A4 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_conv_add_uminus
% 4.97/5.19 thf(fact_1463_diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_complex
% 4.97/5.19 = ( ^ [A4: complex,B3: complex] : ( plus_plus_complex @ A4 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_conv_add_uminus
% 4.97/5.19 thf(fact_1464_diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_8373710615458151222nteger
% 4.97/5.19 = ( ^ [A4: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A4 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_conv_add_uminus
% 4.97/5.19 thf(fact_1465_diff__conv__add__uminus,axiom,
% 4.97/5.19 ( minus_minus_rat
% 4.97/5.19 = ( ^ [A4: rat,B3: rat] : ( plus_plus_rat @ A4 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_conv_add_uminus
% 4.97/5.19 thf(fact_1466_group__cancel_Osub2,axiom,
% 4.97/5.19 ! [B4: real,K: real,B: real,A: real] :
% 4.97/5.19 ( ( B4
% 4.97/5.19 = ( plus_plus_real @ K @ B ) )
% 4.97/5.19 => ( ( minus_minus_real @ A @ B4 )
% 4.97/5.19 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub2
% 4.97/5.19 thf(fact_1467_group__cancel_Osub2,axiom,
% 4.97/5.19 ! [B4: int,K: int,B: int,A: int] :
% 4.97/5.19 ( ( B4
% 4.97/5.19 = ( plus_plus_int @ K @ B ) )
% 4.97/5.19 => ( ( minus_minus_int @ A @ B4 )
% 4.97/5.19 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub2
% 4.97/5.19 thf(fact_1468_group__cancel_Osub2,axiom,
% 4.97/5.19 ! [B4: complex,K: complex,B: complex,A: complex] :
% 4.97/5.19 ( ( B4
% 4.97/5.19 = ( plus_plus_complex @ K @ B ) )
% 4.97/5.19 => ( ( minus_minus_complex @ A @ B4 )
% 4.97/5.19 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub2
% 4.97/5.19 thf(fact_1469_group__cancel_Osub2,axiom,
% 4.97/5.19 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 4.97/5.19 ( ( B4
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 4.97/5.19 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub2
% 4.97/5.19 thf(fact_1470_group__cancel_Osub2,axiom,
% 4.97/5.19 ! [B4: rat,K: rat,B: rat,A: rat] :
% 4.97/5.19 ( ( B4
% 4.97/5.19 = ( plus_plus_rat @ K @ B ) )
% 4.97/5.19 => ( ( minus_minus_rat @ A @ B4 )
% 4.97/5.19 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % group_cancel.sub2
% 4.97/5.19 thf(fact_1471_mono__nat__linear__lb,axiom,
% 4.97/5.19 ! [F: nat > nat,M: nat,K: nat] :
% 4.97/5.19 ( ! [M4: nat,N3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M4 @ N3 )
% 4.97/5.19 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 4.97/5.19 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % mono_nat_linear_lb
% 4.97/5.19 thf(fact_1472_less__diff__iff,axiom,
% 4.97/5.19 ! [K: nat,M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ M )
% 4.97/5.19 => ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_iff
% 4.97/5.19 thf(fact_1473_diff__less__mono,axiom,
% 4.97/5.19 ! [A: nat,B: nat,C: nat] :
% 4.97/5.19 ( ( ord_less_nat @ A @ B )
% 4.97/5.19 => ( ( ord_less_eq_nat @ C @ A )
% 4.97/5.19 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_less_mono
% 4.97/5.19 thf(fact_1474_less__diff__conv,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.97/5.19 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_conv
% 4.97/5.19 thf(fact_1475_add__diff__inverse__nat,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ~ ( ord_less_nat @ M @ N )
% 4.97/5.19 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.19 = M ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_diff_inverse_nat
% 4.97/5.19 thf(fact_1476_le__diff__conv,axiom,
% 4.97/5.19 ! [J: nat,K: nat,I: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.97/5.19 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % le_diff_conv
% 4.97/5.19 thf(fact_1477_Nat_Ole__diff__conv2,axiom,
% 4.97/5.19 ! [K: nat,J: nat,I: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.19 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 4.97/5.19 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.le_diff_conv2
% 4.97/5.19 thf(fact_1478_Nat_Odiff__add__assoc,axiom,
% 4.97/5.19 ! [K: nat,J: nat,I: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.19 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 4.97/5.19 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.diff_add_assoc
% 4.97/5.19 thf(fact_1479_Nat_Odiff__add__assoc2,axiom,
% 4.97/5.19 ! [K: nat,J: nat,I: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.19 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 4.97/5.19 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.diff_add_assoc2
% 4.97/5.19 thf(fact_1480_Nat_Ole__imp__diff__is__add,axiom,
% 4.97/5.19 ! [I: nat,J: nat,K: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.19 => ( ( ( minus_minus_nat @ J @ I )
% 4.97/5.19 = K )
% 4.97/5.19 = ( J
% 4.97/5.19 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Nat.le_imp_diff_is_add
% 4.97/5.19 thf(fact_1481_div__mult2__numeral__eq,axiom,
% 4.97/5.19 ! [A: nat,K: num,L: num] :
% 4.97/5.19 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 4.97/5.19 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_mult2_numeral_eq
% 4.97/5.19 thf(fact_1482_div__mult2__numeral__eq,axiom,
% 4.97/5.19 ! [A: int,K: num,L: num] :
% 4.97/5.19 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 4.97/5.19 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % div_mult2_numeral_eq
% 4.97/5.19 thf(fact_1483_gt__half__sum,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % gt_half_sum
% 4.97/5.19 thf(fact_1484_gt__half__sum,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 4.97/5.19
% 4.97/5.19 % gt_half_sum
% 4.97/5.19 thf(fact_1485_less__half__sum,axiom,
% 4.97/5.19 ! [A: real,B: real] :
% 4.97/5.19 ( ( ord_less_real @ A @ B )
% 4.97/5.19 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_half_sum
% 4.97/5.19 thf(fact_1486_less__half__sum,axiom,
% 4.97/5.19 ! [A: rat,B: rat] :
% 4.97/5.19 ( ( ord_less_rat @ A @ B )
% 4.97/5.19 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_half_sum
% 4.97/5.19 thf(fact_1487_numeral__Bit0__div__2,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.19 = ( numeral_numeral_nat @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % numeral_Bit0_div_2
% 4.97/5.19 thf(fact_1488_numeral__Bit0__div__2,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.97/5.19 = ( numeral_numeral_int @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % numeral_Bit0_div_2
% 4.97/5.19 thf(fact_1489_less__diff__conv2,axiom,
% 4.97/5.19 ! [K: nat,J: nat,I: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.19 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 4.97/5.19 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % less_diff_conv2
% 4.97/5.19 thf(fact_1490_numeral__Bit1__div__2,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.19 = ( numeral_numeral_nat @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % numeral_Bit1_div_2
% 4.97/5.19 thf(fact_1491_numeral__Bit1__div__2,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.97/5.19 = ( numeral_numeral_int @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % numeral_Bit1_div_2
% 4.97/5.19 thf(fact_1492_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.97/5.19 ! [K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % neg_one_power_add_eq_neg_one_power_diff
% 4.97/5.19 thf(fact_1493_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.97/5.19 ! [K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % neg_one_power_add_eq_neg_one_power_diff
% 4.97/5.19 thf(fact_1494_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.97/5.19 ! [K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % neg_one_power_add_eq_neg_one_power_diff
% 4.97/5.19 thf(fact_1495_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.97/5.19 ! [K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % neg_one_power_add_eq_neg_one_power_diff
% 4.97/5.19 thf(fact_1496_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.97/5.19 ! [K: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ K @ N )
% 4.97/5.19 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 4.97/5.19 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % neg_one_power_add_eq_neg_one_power_diff
% 4.97/5.19 thf(fact_1497_in__children__def,axiom,
% 4.97/5.19 ( vEBT_V5917875025757280293ildren
% 4.97/5.19 = ( ^ [N4: nat,TreeList2: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X3 @ N4 ) ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % in_children_def
% 4.97/5.19 thf(fact_1498_invar__vebt_Ointros_I5_J,axiom,
% 4.97/5.19 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.97/5.19 ( ! [X4: vEBT_VEBT] :
% 4.97/5.19 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.19 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.97/5.19 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.97/5.19 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.97/5.19 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( M
% 4.97/5.19 = ( suc @ N ) )
% 4.97/5.19 => ( ( Deg
% 4.97/5.19 = ( plus_plus_nat @ N @ M ) )
% 4.97/5.19 => ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X5 ) )
% 4.97/5.19 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 4.97/5.19 => ( ( ( Mi = Ma )
% 4.97/5.19 => ! [X4: vEBT_VEBT] :
% 4.97/5.19 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.19 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 4.97/5.19 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.97/5.19 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.97/5.19 => ( ( ( Mi != Ma )
% 4.97/5.19 => ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.19 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 4.97/5.19 = I3 )
% 4.97/5.19 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 4.97/5.19 & ! [X4: nat] :
% 4.97/5.19 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 4.97/5.19 = I3 )
% 4.97/5.19 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 4.97/5.19 => ( ( ord_less_nat @ Mi @ X4 )
% 4.97/5.19 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 4.97/5.19 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % invar_vebt.intros(5)
% 4.97/5.19 thf(fact_1499_enat__ord__number_I1_J,axiom,
% 4.97/5.19 ! [M: num,N: num] :
% 4.97/5.19 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % enat_ord_number(1)
% 4.97/5.19 thf(fact_1500_enat__ord__number_I2_J,axiom,
% 4.97/5.19 ! [M: num,N: num] :
% 4.97/5.19 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 4.97/5.19 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % enat_ord_number(2)
% 4.97/5.19 thf(fact_1501_zdiv__numeral__Bit1,axiom,
% 4.97/5.19 ! [V: num,W: num] :
% 4.97/5.19 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.97/5.19 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % zdiv_numeral_Bit1
% 4.97/5.19 thf(fact_1502_compl__le__compl__iff,axiom,
% 4.97/5.19 ! [X2: set_int,Y: set_int] :
% 4.97/5.19 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 4.97/5.19 = ( ord_less_eq_set_int @ Y @ X2 ) ) ).
% 4.97/5.19
% 4.97/5.19 % compl_le_compl_iff
% 4.97/5.19 thf(fact_1503_divmod__step__eq,axiom,
% 4.97/5.19 ! [L: num,R: nat,Q2: nat] :
% 4.97/5.19 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R )
% 4.97/5.19 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 4.97/5.19 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L ) ) ) ) )
% 4.97/5.19 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R )
% 4.97/5.19 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 4.97/5.19 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divmod_step_eq
% 4.97/5.19 thf(fact_1504_divmod__step__eq,axiom,
% 4.97/5.19 ! [L: num,R: int,Q2: int] :
% 4.97/5.19 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R )
% 4.97/5.19 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 4.97/5.19 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L ) ) ) ) )
% 4.97/5.19 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R )
% 4.97/5.19 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 4.97/5.19 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divmod_step_eq
% 4.97/5.19 thf(fact_1505_divmod__step__eq,axiom,
% 4.97/5.19 ! [L: num,R: code_integer,Q2: code_integer] :
% 4.97/5.19 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R )
% 4.97/5.19 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 4.97/5.19 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 4.97/5.19 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R )
% 4.97/5.19 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 4.97/5.19 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % divmod_step_eq
% 4.97/5.19 thf(fact_1506_two__realpow__ge__two,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.19 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % two_realpow_ge_two
% 4.97/5.19 thf(fact_1507_all__set__conv__all__nth,axiom,
% 4.97/5.19 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.97/5.19 ( ( ! [X3: vEBT_VEBT] :
% 4.97/5.19 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.19 => ( P @ X3 ) ) )
% 4.97/5.19 = ( ! [I4: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_set_conv_all_nth
% 4.97/5.19 thf(fact_1508_all__set__conv__all__nth,axiom,
% 4.97/5.19 ! [Xs: list_o,P: $o > $o] :
% 4.97/5.19 ( ( ! [X3: $o] :
% 4.97/5.19 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 4.97/5.19 => ( P @ X3 ) ) )
% 4.97/5.19 = ( ! [I4: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_o @ Xs @ I4 ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_set_conv_all_nth
% 4.97/5.19 thf(fact_1509_all__set__conv__all__nth,axiom,
% 4.97/5.19 ! [Xs: list_nat,P: nat > $o] :
% 4.97/5.19 ( ( ! [X3: nat] :
% 4.97/5.19 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 4.97/5.19 => ( P @ X3 ) ) )
% 4.97/5.19 = ( ! [I4: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_set_conv_all_nth
% 4.97/5.19 thf(fact_1510_all__set__conv__all__nth,axiom,
% 4.97/5.19 ! [Xs: list_int,P: int > $o] :
% 4.97/5.19 ( ( ! [X3: int] :
% 4.97/5.19 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 4.97/5.19 => ( P @ X3 ) ) )
% 4.97/5.19 = ( ! [I4: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_int @ Xs @ I4 ) ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_set_conv_all_nth
% 4.97/5.19 thf(fact_1511_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_real,P: real > $o,X2: real] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_real @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1512_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_complex,P: complex > $o,X2: complex] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_complex @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1513_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_set_nat,P: set_nat > $o,X2: set_nat] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_set_nat @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1514_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1515_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_o,P: $o > $o,X2: $o] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_o @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1516_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_nat @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1517_all__nth__imp__all__set,axiom,
% 4.97/5.19 ! [Xs: list_int,P: int > $o,X2: int] :
% 4.97/5.19 ( ! [I3: nat] :
% 4.97/5.19 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.97/5.19 => ( P @ ( nth_int @ Xs @ I3 ) ) )
% 4.97/5.19 => ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 4.97/5.19 => ( P @ X2 ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % all_nth_imp_all_set
% 4.97/5.19 thf(fact_1518_even__odd__cases,axiom,
% 4.97/5.19 ! [X2: nat] :
% 4.97/5.19 ( ! [N3: nat] :
% 4.97/5.19 ( X2
% 4.97/5.19 != ( plus_plus_nat @ N3 @ N3 ) )
% 4.97/5.19 => ~ ! [N3: nat] :
% 4.97/5.19 ( X2
% 4.97/5.19 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % even_odd_cases
% 4.97/5.19 thf(fact_1519_nat_Oinject,axiom,
% 4.97/5.19 ! [X23: nat,Y22: nat] :
% 4.97/5.19 ( ( ( suc @ X23 )
% 4.97/5.19 = ( suc @ Y22 ) )
% 4.97/5.19 = ( X23 = Y22 ) ) ).
% 4.97/5.19
% 4.97/5.19 % nat.inject
% 4.97/5.19 thf(fact_1520_old_Onat_Oinject,axiom,
% 4.97/5.19 ! [Nat: nat,Nat2: nat] :
% 4.97/5.19 ( ( ( suc @ Nat )
% 4.97/5.19 = ( suc @ Nat2 ) )
% 4.97/5.19 = ( Nat = Nat2 ) ) ).
% 4.97/5.19
% 4.97/5.19 % old.nat.inject
% 4.97/5.19 thf(fact_1521_of__nat__eq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( semiri5074537144036343181t_real @ M )
% 4.97/5.19 = ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.19 = ( M = N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_iff
% 4.97/5.19 thf(fact_1522_of__nat__eq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( semiri1314217659103216013at_int @ M )
% 4.97/5.19 = ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.19 = ( M = N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_iff
% 4.97/5.19 thf(fact_1523_of__nat__eq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( semiri8010041392384452111omplex @ M )
% 4.97/5.19 = ( semiri8010041392384452111omplex @ N ) )
% 4.97/5.19 = ( M = N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_iff
% 4.97/5.19 thf(fact_1524_of__nat__eq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( semiri1316708129612266289at_nat @ M )
% 4.97/5.19 = ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.19 = ( M = N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_iff
% 4.97/5.19 thf(fact_1525_of__nat__eq__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ( semiri4939895301339042750nteger @ M )
% 4.97/5.19 = ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.19 = ( M = N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_iff
% 4.97/5.19 thf(fact_1526_Suc__less__eq,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % Suc_less_eq
% 4.97/5.19 thf(fact_1527_Suc__mono,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ M @ N )
% 4.97/5.19 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % Suc_mono
% 4.97/5.19 thf(fact_1528_lessI,axiom,
% 4.97/5.19 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % lessI
% 4.97/5.19 thf(fact_1529_Suc__le__mono,axiom,
% 4.97/5.19 ! [N: nat,M: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 4.97/5.19 = ( ord_less_eq_nat @ N @ M ) ) ).
% 4.97/5.19
% 4.97/5.19 % Suc_le_mono
% 4.97/5.19 thf(fact_1530_add__Suc__right,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 4.97/5.19 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % add_Suc_right
% 4.97/5.19 thf(fact_1531_diff__Suc__Suc,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 4.97/5.19 = ( minus_minus_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % diff_Suc_Suc
% 4.97/5.19 thf(fact_1532_Suc__diff__diff,axiom,
% 4.97/5.19 ! [M: nat,N: nat,K: nat] :
% 4.97/5.19 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 4.97/5.19 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 4.97/5.19
% 4.97/5.19 % Suc_diff_diff
% 4.97/5.19 thf(fact_1533_of__nat__less__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_less_iff
% 4.97/5.19 thf(fact_1534_of__nat__less__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_less_iff
% 4.97/5.19 thf(fact_1535_of__nat__less__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_less_iff
% 4.97/5.19 thf(fact_1536_of__nat__less__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_less_iff
% 4.97/5.19 thf(fact_1537_of__nat__less__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.19 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_less_iff
% 4.97/5.19 thf(fact_1538_of__nat__le__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_le_iff
% 4.97/5.19 thf(fact_1539_of__nat__le__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_le_iff
% 4.97/5.19 thf(fact_1540_of__nat__le__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_le_iff
% 4.97/5.19 thf(fact_1541_of__nat__le__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_le_iff
% 4.97/5.19 thf(fact_1542_of__nat__le__iff,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.19 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_le_iff
% 4.97/5.19 thf(fact_1543_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numeral_numeral_rat @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1544_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numeral_numeral_real @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1545_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numeral_numeral_int @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1546_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numera6690914467698888265omplex @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1547_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numeral_numeral_nat @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1548_of__nat__numeral,axiom,
% 4.97/5.19 ! [N: num] :
% 4.97/5.19 ( ( semiri4939895301339042750nteger @ ( numeral_numeral_nat @ N ) )
% 4.97/5.19 = ( numera6620942414471956472nteger @ N ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_numeral
% 4.97/5.19 thf(fact_1549_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1550_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1551_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1552_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1553_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1554_of__nat__add,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.19 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_add
% 4.97/5.19 thf(fact_1555_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1556_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1557_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1558_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1559_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1560_of__nat__mult,axiom,
% 4.97/5.19 ! [M: nat,N: nat] :
% 4.97/5.19 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 4.97/5.19 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_mult
% 4.97/5.19 thf(fact_1561_of__nat__eq__1__iff,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( ( semiri681578069525770553at_rat @ N )
% 4.97/5.19 = one_one_rat )
% 4.97/5.19 = ( N = one_one_nat ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_1_iff
% 4.97/5.19 thf(fact_1562_of__nat__eq__1__iff,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( ( semiri5074537144036343181t_real @ N )
% 4.97/5.19 = one_one_real )
% 4.97/5.19 = ( N = one_one_nat ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_1_iff
% 4.97/5.19 thf(fact_1563_of__nat__eq__1__iff,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( ( semiri1314217659103216013at_int @ N )
% 4.97/5.19 = one_one_int )
% 4.97/5.19 = ( N = one_one_nat ) ) ).
% 4.97/5.19
% 4.97/5.19 % of_nat_eq_1_iff
% 4.97/5.19 thf(fact_1564_of__nat__eq__1__iff,axiom,
% 4.97/5.19 ! [N: nat] :
% 4.97/5.19 ( ( ( semiri8010041392384452111omplex @ N )
% 4.97/5.19 = one_one_complex )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_1_iff
% 4.97/5.20 thf(fact_1565_of__nat__eq__1__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( ( semiri1316708129612266289at_nat @ N )
% 4.97/5.20 = one_one_nat )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_1_iff
% 4.97/5.20 thf(fact_1566_of__nat__eq__1__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( ( semiri4939895301339042750nteger @ N )
% 4.97/5.20 = one_one_Code_integer )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_1_iff
% 4.97/5.20 thf(fact_1567_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_rat
% 4.97/5.20 = ( semiri681578069525770553at_rat @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1568_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_real
% 4.97/5.20 = ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1569_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_int
% 4.97/5.20 = ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1570_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_complex
% 4.97/5.20 = ( semiri8010041392384452111omplex @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1571_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_nat
% 4.97/5.20 = ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1572_of__nat__1__eq__iff,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( one_one_Code_integer
% 4.97/5.20 = ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.20 = ( N = one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1_eq_iff
% 4.97/5.20 thf(fact_1573_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 4.97/5.20 = one_one_rat ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1574_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 4.97/5.20 = one_one_real ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1575_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 4.97/5.20 = one_one_int ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1576_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 4.97/5.20 = one_one_complex ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1577_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 4.97/5.20 = one_one_nat ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1578_of__nat__1,axiom,
% 4.97/5.20 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 4.97/5.20 = one_one_Code_integer ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_1
% 4.97/5.20 thf(fact_1579_mult__Suc__right,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( times_times_nat @ M @ ( suc @ N ) )
% 4.97/5.20 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_Suc_right
% 4.97/5.20 thf(fact_1580_of__nat__power,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 4.97/5.20 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power
% 4.97/5.20 thf(fact_1581_of__nat__power,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 4.97/5.20 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power
% 4.97/5.20 thf(fact_1582_of__nat__power,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 4.97/5.20 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power
% 4.97/5.20 thf(fact_1583_of__nat__power,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 4.97/5.20 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power
% 4.97/5.20 thf(fact_1584_of__nat__power,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N ) )
% 4.97/5.20 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power
% 4.97/5.20 thf(fact_1585_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 4.97/5.20 = ( semiri5074537144036343181t_real @ X2 ) )
% 4.97/5.20 = ( ( power_power_nat @ B @ W )
% 4.97/5.20 = X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1586_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 4.97/5.20 = ( semiri1314217659103216013at_int @ X2 ) )
% 4.97/5.20 = ( ( power_power_nat @ B @ W )
% 4.97/5.20 = X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1587_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 4.97/5.20 = ( semiri8010041392384452111omplex @ X2 ) )
% 4.97/5.20 = ( ( power_power_nat @ B @ W )
% 4.97/5.20 = X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1588_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 4.97/5.20 = ( semiri1316708129612266289at_nat @ X2 ) )
% 4.97/5.20 = ( ( power_power_nat @ B @ W )
% 4.97/5.20 = X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1589_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W )
% 4.97/5.20 = ( semiri4939895301339042750nteger @ X2 ) )
% 4.97/5.20 = ( ( power_power_nat @ B @ W )
% 4.97/5.20 = X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_eq_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1590_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ( semiri5074537144036343181t_real @ X2 )
% 4.97/5.20 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 4.97/5.20 = ( X2
% 4.97/5.20 = ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1591_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ( semiri1314217659103216013at_int @ X2 )
% 4.97/5.20 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 4.97/5.20 = ( X2
% 4.97/5.20 = ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1592_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ( semiri8010041392384452111omplex @ X2 )
% 4.97/5.20 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 4.97/5.20 = ( X2
% 4.97/5.20 = ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1593_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 4.97/5.20 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 4.97/5.20 = ( X2
% 4.97/5.20 = ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1594_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ( semiri4939895301339042750nteger @ X2 )
% 4.97/5.20 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 4.97/5.20 = ( X2
% 4.97/5.20 = ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1595_diff__Suc__1,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 4.97/5.20 = N ) ).
% 4.97/5.20
% 4.97/5.20 % diff_Suc_1
% 4.97/5.20 thf(fact_1596_zdiv__numeral__Bit0,axiom,
% 4.97/5.20 ! [V: num,W: num] :
% 4.97/5.20 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.97/5.20 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % zdiv_numeral_Bit0
% 4.97/5.20 thf(fact_1597_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 4.97/5.20 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1598_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 4.97/5.20 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1599_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 4.97/5.20 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1600_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 4.97/5.20 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1601_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 4.97/5.20 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1602_of__nat__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 4.97/5.20 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_Suc
% 4.97/5.20 thf(fact_1603_diff__Suc__diff__eq2,axiom,
% 4.97/5.20 ! [K: nat,J: nat,I: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.20 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 4.97/5.20 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % diff_Suc_diff_eq2
% 4.97/5.20 thf(fact_1604_diff__Suc__diff__eq1,axiom,
% 4.97/5.20 ! [K: nat,J: nat,I: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ K @ J )
% 4.97/5.20 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 4.97/5.20 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % diff_Suc_diff_eq1
% 4.97/5.20 thf(fact_1605_Suc__numeral,axiom,
% 4.97/5.20 ! [N: num] :
% 4.97/5.20 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 4.97/5.20 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_numeral
% 4.97/5.20 thf(fact_1606_add__2__eq__Suc,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 4.97/5.20 = ( suc @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_2_eq_Suc
% 4.97/5.20 thf(fact_1607_add__2__eq__Suc_H,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.20 = ( suc @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_2_eq_Suc'
% 4.97/5.20 thf(fact_1608_Suc__1,axiom,
% 4.97/5.20 ( ( suc @ one_one_nat )
% 4.97/5.20 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_1
% 4.97/5.20 thf(fact_1609_div2__Suc__Suc,axiom,
% 4.97/5.20 ! [M: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.97/5.20 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div2_Suc_Suc
% 4.97/5.20 thf(fact_1610_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1611_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1612_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1613_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1614_of__nat__less__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1615_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1616_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1617_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1618_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1619_of__nat__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1620_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1621_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1622_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1623_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1624_of__nat__le__of__nat__power__cancel__iff,axiom,
% 4.97/5.20 ! [B: nat,W: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_of_nat_power_cancel_iff
% 4.97/5.20 thf(fact_1625_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1626_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1627_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1628_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1629_of__nat__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,B: nat,W: nat] :
% 4.97/5.20 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1630_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 4.97/5.20 = ( semiri681578069525770553at_rat @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1631_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 4.97/5.20 = ( semiri5074537144036343181t_real @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1632_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 4.97/5.20 = ( semiri1314217659103216013at_int @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1633_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 4.97/5.20 = ( semiri8010041392384452111omplex @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1634_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = ( semiri1316708129612266289at_nat @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1635_numeral__power__eq__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [X2: num,N: nat,Y: nat] :
% 4.97/5.20 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N )
% 4.97/5.20 = ( semiri4939895301339042750nteger @ Y ) )
% 4.97/5.20 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 4.97/5.20 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_eq_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1636_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri681578069525770553at_rat @ Y )
% 4.97/5.20 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1637_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri5074537144036343181t_real @ Y )
% 4.97/5.20 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1638_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri1314217659103216013at_int @ Y )
% 4.97/5.20 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1639_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri8010041392384452111omplex @ Y )
% 4.97/5.20 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1640_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri1316708129612266289at_nat @ Y )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1641_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [Y: nat,X2: num,N: nat] :
% 4.97/5.20 ( ( ( semiri4939895301339042750nteger @ Y )
% 4.97/5.20 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X2 ) @ N ) )
% 4.97/5.20 = ( Y
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_eq_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1642_real__of__nat__less__numeral__iff,axiom,
% 4.97/5.20 ! [N: nat,W: num] :
% 4.97/5.20 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 4.97/5.20 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_less_numeral_iff
% 4.97/5.20 thf(fact_1643_numeral__less__real__of__nat__iff,axiom,
% 4.97/5.20 ! [W: num,N: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.20 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_less_real_of_nat_iff
% 4.97/5.20 thf(fact_1644_numeral__le__real__of__nat__iff,axiom,
% 4.97/5.20 ! [N: num,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_le_real_of_nat_iff
% 4.97/5.20 thf(fact_1645_Suc__div__eq__add3__div__numeral,axiom,
% 4.97/5.20 ! [M: nat,V: num] :
% 4.97/5.20 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 4.97/5.20 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_div_eq_add3_div_numeral
% 4.97/5.20 thf(fact_1646_div__Suc__eq__div__add3,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 4.97/5.20 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div_Suc_eq_div_add3
% 4.97/5.20 thf(fact_1647_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1648_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1649_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1650_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1651_numeral__power__less__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 4.97/5.20 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_less_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1652_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1653_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1654_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1655_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1656_of__nat__less__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1657_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1658_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1659_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1660_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1661_numeral__power__le__of__nat__cancel__iff,axiom,
% 4.97/5.20 ! [I: num,N: nat,X2: nat] :
% 4.97/5.20 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 4.97/5.20
% 4.97/5.20 % numeral_power_le_of_nat_cancel_iff
% 4.97/5.20 thf(fact_1662_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1663_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1664_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1665_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1666_of__nat__le__numeral__power__cancel__iff,axiom,
% 4.97/5.20 ! [X2: nat,I: num,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_le_numeral_power_cancel_iff
% 4.97/5.20 thf(fact_1667_enat__less__induct,axiom,
% 4.97/5.20 ! [P: extended_enat > $o,N: extended_enat] :
% 4.97/5.20 ( ! [N3: extended_enat] :
% 4.97/5.20 ( ! [M2: extended_enat] :
% 4.97/5.20 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 4.97/5.20 => ( P @ M2 ) )
% 4.97/5.20 => ( P @ N3 ) )
% 4.97/5.20 => ( P @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % enat_less_induct
% 4.97/5.20 thf(fact_1668_Suc__inject,axiom,
% 4.97/5.20 ! [X2: nat,Y: nat] :
% 4.97/5.20 ( ( ( suc @ X2 )
% 4.97/5.20 = ( suc @ Y ) )
% 4.97/5.20 => ( X2 = Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_inject
% 4.97/5.20 thf(fact_1669_n__not__Suc__n,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( N
% 4.97/5.20 != ( suc @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % n_not_Suc_n
% 4.97/5.20 thf(fact_1670_add__diff__assoc__enat,axiom,
% 4.97/5.20 ! [Z: extended_enat,Y: extended_enat,X2: extended_enat] :
% 4.97/5.20 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 4.97/5.20 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 4.97/5.20 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y ) @ Z ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_diff_assoc_enat
% 4.97/5.20 thf(fact_1671_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: rat] :
% 4.97/5.20 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y )
% 4.97/5.20 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1672_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: real] :
% 4.97/5.20 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y )
% 4.97/5.20 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1673_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: int] :
% 4.97/5.20 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y )
% 4.97/5.20 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1674_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: complex] :
% 4.97/5.20 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X2 ) @ Y )
% 4.97/5.20 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1675_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: nat] :
% 4.97/5.20 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y )
% 4.97/5.20 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1676_mult__of__nat__commute,axiom,
% 4.97/5.20 ! [X2: nat,Y: code_integer] :
% 4.97/5.20 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X2 ) @ Y )
% 4.97/5.20 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_of_nat_commute
% 4.97/5.20 thf(fact_1677_not__less__less__Suc__eq,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ~ ( ord_less_nat @ N @ M )
% 4.97/5.20 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 4.97/5.20 = ( N = M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % not_less_less_Suc_eq
% 4.97/5.20 thf(fact_1678_strict__inc__induct,axiom,
% 4.97/5.20 ! [I: nat,J: nat,P: nat > $o] :
% 4.97/5.20 ( ( ord_less_nat @ I @ J )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( J
% 4.97/5.20 = ( suc @ I3 ) )
% 4.97/5.20 => ( P @ I3 ) )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ J )
% 4.97/5.20 => ( ( P @ ( suc @ I3 ) )
% 4.97/5.20 => ( P @ I3 ) ) )
% 4.97/5.20 => ( P @ I ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % strict_inc_induct
% 4.97/5.20 thf(fact_1679_less__Suc__induct,axiom,
% 4.97/5.20 ! [I: nat,J: nat,P: nat > nat > $o] :
% 4.97/5.20 ( ( ord_less_nat @ I @ J )
% 4.97/5.20 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 4.97/5.20 => ( ! [I3: nat,J2: nat,K3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ J2 )
% 4.97/5.20 => ( ( ord_less_nat @ J2 @ K3 )
% 4.97/5.20 => ( ( P @ I3 @ J2 )
% 4.97/5.20 => ( ( P @ J2 @ K3 )
% 4.97/5.20 => ( P @ I3 @ K3 ) ) ) ) )
% 4.97/5.20 => ( P @ I @ J ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_Suc_induct
% 4.97/5.20 thf(fact_1680_less__trans__Suc,axiom,
% 4.97/5.20 ! [I: nat,J: nat,K: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I @ J )
% 4.97/5.20 => ( ( ord_less_nat @ J @ K )
% 4.97/5.20 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_trans_Suc
% 4.97/5.20 thf(fact_1681_Suc__less__SucD,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_less_SucD
% 4.97/5.20 thf(fact_1682_less__antisym,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ~ ( ord_less_nat @ N @ M )
% 4.97/5.20 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 4.97/5.20 => ( M = N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_antisym
% 4.97/5.20 thf(fact_1683_Suc__less__eq2,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 4.97/5.20 = ( ? [M5: nat] :
% 4.97/5.20 ( ( M
% 4.97/5.20 = ( suc @ M5 ) )
% 4.97/5.20 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_less_eq2
% 4.97/5.20 thf(fact_1684_All__less__Suc,axiom,
% 4.97/5.20 ! [N: nat,P: nat > $o] :
% 4.97/5.20 ( ( ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.97/5.20 => ( P @ I4 ) ) )
% 4.97/5.20 = ( ( P @ N )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ N )
% 4.97/5.20 => ( P @ I4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % All_less_Suc
% 4.97/5.20 thf(fact_1685_not__less__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ~ ( ord_less_nat @ M @ N ) )
% 4.97/5.20 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % not_less_eq
% 4.97/5.20 thf(fact_1686_less__Suc__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 4.97/5.20 = ( ( ord_less_nat @ M @ N )
% 4.97/5.20 | ( M = N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_Suc_eq
% 4.97/5.20 thf(fact_1687_Ex__less__Suc,axiom,
% 4.97/5.20 ! [N: nat,P: nat > $o] :
% 4.97/5.20 ( ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 4.97/5.20 & ( P @ I4 ) ) )
% 4.97/5.20 = ( ( P @ N )
% 4.97/5.20 | ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ N )
% 4.97/5.20 & ( P @ I4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Ex_less_Suc
% 4.97/5.20 thf(fact_1688_less__SucI,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_SucI
% 4.97/5.20 thf(fact_1689_less__SucE,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 4.97/5.20 => ( ~ ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( M = N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_SucE
% 4.97/5.20 thf(fact_1690_Suc__lessI,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ( ( suc @ M )
% 4.97/5.20 != N )
% 4.97/5.20 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_lessI
% 4.97/5.20 thf(fact_1691_Suc__lessE,axiom,
% 4.97/5.20 ! [I: nat,K: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 4.97/5.20 => ~ ! [J2: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I @ J2 )
% 4.97/5.20 => ( K
% 4.97/5.20 != ( suc @ J2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_lessE
% 4.97/5.20 thf(fact_1692_Suc__lessD,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_lessD
% 4.97/5.20 thf(fact_1693_Nat_OlessE,axiom,
% 4.97/5.20 ! [I: nat,K: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I @ K )
% 4.97/5.20 => ( ( K
% 4.97/5.20 != ( suc @ I ) )
% 4.97/5.20 => ~ ! [J2: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I @ J2 )
% 4.97/5.20 => ( K
% 4.97/5.20 != ( suc @ J2 ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Nat.lessE
% 4.97/5.20 thf(fact_1694_transitive__stepwise__le,axiom,
% 4.97/5.20 ! [M: nat,N: nat,R2: nat > nat > $o] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( ! [X4: nat] : ( R2 @ X4 @ X4 )
% 4.97/5.20 => ( ! [X4: nat,Y3: nat,Z3: nat] :
% 4.97/5.20 ( ( R2 @ X4 @ Y3 )
% 4.97/5.20 => ( ( R2 @ Y3 @ Z3 )
% 4.97/5.20 => ( R2 @ X4 @ Z3 ) ) )
% 4.97/5.20 => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 4.97/5.20 => ( R2 @ M @ N ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % transitive_stepwise_le
% 4.97/5.20 thf(fact_1695_nat__induct__at__least,axiom,
% 4.97/5.20 ! [M: nat,N: nat,P: nat > $o] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( ( P @ M )
% 4.97/5.20 => ( ! [N3: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N3 )
% 4.97/5.20 => ( ( P @ N3 )
% 4.97/5.20 => ( P @ ( suc @ N3 ) ) ) )
% 4.97/5.20 => ( P @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nat_induct_at_least
% 4.97/5.20 thf(fact_1696_full__nat__induct,axiom,
% 4.97/5.20 ! [P: nat > $o,N: nat] :
% 4.97/5.20 ( ! [N3: nat] :
% 4.97/5.20 ( ! [M2: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 4.97/5.20 => ( P @ M2 ) )
% 4.97/5.20 => ( P @ N3 ) )
% 4.97/5.20 => ( P @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % full_nat_induct
% 4.97/5.20 thf(fact_1697_not__less__eq__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 4.97/5.20
% 4.97/5.20 % not_less_eq_eq
% 4.97/5.20 thf(fact_1698_Suc__n__not__le__n,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_n_not_le_n
% 4.97/5.20 thf(fact_1699_le__Suc__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 4.97/5.20 = ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 | ( M
% 4.97/5.20 = ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_Suc_eq
% 4.97/5.20 thf(fact_1700_Suc__le__D,axiom,
% 4.97/5.20 ! [N: nat,M6: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 4.97/5.20 => ? [M4: nat] :
% 4.97/5.20 ( M6
% 4.97/5.20 = ( suc @ M4 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_le_D
% 4.97/5.20 thf(fact_1701_le__SucI,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_SucI
% 4.97/5.20 thf(fact_1702_le__SucE,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 4.97/5.20 => ( ~ ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( M
% 4.97/5.20 = ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_SucE
% 4.97/5.20 thf(fact_1703_Suc__leD,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 4.97/5.20 => ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_leD
% 4.97/5.20 thf(fact_1704_add__Suc__shift,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 4.97/5.20 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_Suc_shift
% 4.97/5.20 thf(fact_1705_add__Suc,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 4.97/5.20 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_Suc
% 4.97/5.20 thf(fact_1706_nat__arith_Osuc1,axiom,
% 4.97/5.20 ! [A2: nat,K: nat,A: nat] :
% 4.97/5.20 ( ( A2
% 4.97/5.20 = ( plus_plus_nat @ K @ A ) )
% 4.97/5.20 => ( ( suc @ A2 )
% 4.97/5.20 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nat_arith.suc1
% 4.97/5.20 thf(fact_1707_zero__induct__lemma,axiom,
% 4.97/5.20 ! [P: nat > $o,K: nat,I: nat] :
% 4.97/5.20 ( ( P @ K )
% 4.97/5.20 => ( ! [N3: nat] :
% 4.97/5.20 ( ( P @ ( suc @ N3 ) )
% 4.97/5.20 => ( P @ N3 ) )
% 4.97/5.20 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % zero_induct_lemma
% 4.97/5.20 thf(fact_1708_Suc__mult__cancel1,axiom,
% 4.97/5.20 ! [K: nat,M: nat,N: nat] :
% 4.97/5.20 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 4.97/5.20 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.97/5.20 = ( M = N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_mult_cancel1
% 4.97/5.20 thf(fact_1709_div__mult2__eq_H,axiom,
% 4.97/5.20 ! [A: int,M: nat,N: nat] :
% 4.97/5.20 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 4.97/5.20 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div_mult2_eq'
% 4.97/5.20 thf(fact_1710_div__mult2__eq_H,axiom,
% 4.97/5.20 ! [A: nat,M: nat,N: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 4.97/5.20 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div_mult2_eq'
% 4.97/5.20 thf(fact_1711_div__mult2__eq_H,axiom,
% 4.97/5.20 ! [A: code_integer,M: nat,N: nat] :
% 4.97/5.20 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 4.97/5.20 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div_mult2_eq'
% 4.97/5.20 thf(fact_1712_of__nat__less__imp__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_imp_less
% 4.97/5.20 thf(fact_1713_of__nat__less__imp__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_imp_less
% 4.97/5.20 thf(fact_1714_of__nat__less__imp__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_imp_less
% 4.97/5.20 thf(fact_1715_of__nat__less__imp__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_imp_less
% 4.97/5.20 thf(fact_1716_of__nat__less__imp__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_imp_less
% 4.97/5.20 thf(fact_1717_less__imp__of__nat__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_of_nat_less
% 4.97/5.20 thf(fact_1718_less__imp__of__nat__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_of_nat_less
% 4.97/5.20 thf(fact_1719_less__imp__of__nat__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_of_nat_less
% 4.97/5.20 thf(fact_1720_less__imp__of__nat__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_of_nat_less
% 4.97/5.20 thf(fact_1721_less__imp__of__nat__less,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_of_nat_less
% 4.97/5.20 thf(fact_1722_of__nat__mono,axiom,
% 4.97/5.20 ! [I: nat,J: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_mono
% 4.97/5.20 thf(fact_1723_of__nat__mono,axiom,
% 4.97/5.20 ! [I: nat,J: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_mono
% 4.97/5.20 thf(fact_1724_of__nat__mono,axiom,
% 4.97/5.20 ! [I: nat,J: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_mono
% 4.97/5.20 thf(fact_1725_of__nat__mono,axiom,
% 4.97/5.20 ! [I: nat,J: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_mono
% 4.97/5.20 thf(fact_1726_of__nat__mono,axiom,
% 4.97/5.20 ! [I: nat,J: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_mono
% 4.97/5.20 thf(fact_1727_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 4.97/5.20 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 4.97/5.20 thf(fact_1728_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 4.97/5.20 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 4.97/5.20 thf(fact_1729_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N ) )
% 4.97/5.20 = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 4.97/5.20 thf(fact_1730_power__Suc,axiom,
% 4.97/5.20 ! [A: real,N: nat] :
% 4.97/5.20 ( ( power_power_real @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc
% 4.97/5.20 thf(fact_1731_power__Suc,axiom,
% 4.97/5.20 ! [A: rat,N: nat] :
% 4.97/5.20 ( ( power_power_rat @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc
% 4.97/5.20 thf(fact_1732_power__Suc,axiom,
% 4.97/5.20 ! [A: nat,N: nat] :
% 4.97/5.20 ( ( power_power_nat @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc
% 4.97/5.20 thf(fact_1733_power__Suc,axiom,
% 4.97/5.20 ! [A: int,N: nat] :
% 4.97/5.20 ( ( power_power_int @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc
% 4.97/5.20 thf(fact_1734_power__Suc,axiom,
% 4.97/5.20 ! [A: complex,N: nat] :
% 4.97/5.20 ( ( power_power_complex @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc
% 4.97/5.20 thf(fact_1735_power__Suc2,axiom,
% 4.97/5.20 ! [A: real,N: nat] :
% 4.97/5.20 ( ( power_power_real @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc2
% 4.97/5.20 thf(fact_1736_power__Suc2,axiom,
% 4.97/5.20 ! [A: rat,N: nat] :
% 4.97/5.20 ( ( power_power_rat @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc2
% 4.97/5.20 thf(fact_1737_power__Suc2,axiom,
% 4.97/5.20 ! [A: nat,N: nat] :
% 4.97/5.20 ( ( power_power_nat @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc2
% 4.97/5.20 thf(fact_1738_power__Suc2,axiom,
% 4.97/5.20 ! [A: int,N: nat] :
% 4.97/5.20 ( ( power_power_int @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc2
% 4.97/5.20 thf(fact_1739_power__Suc2,axiom,
% 4.97/5.20 ! [A: complex,N: nat] :
% 4.97/5.20 ( ( power_power_complex @ A @ ( suc @ N ) )
% 4.97/5.20 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_Suc2
% 4.97/5.20 thf(fact_1740_lift__Suc__mono__less__iff,axiom,
% 4.97/5.20 ! [F: nat > real,N: nat,M: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 4.97/5.20 = ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less_iff
% 4.97/5.20 thf(fact_1741_lift__Suc__mono__less__iff,axiom,
% 4.97/5.20 ! [F: nat > rat,N: nat,M: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 4.97/5.20 = ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less_iff
% 4.97/5.20 thf(fact_1742_lift__Suc__mono__less__iff,axiom,
% 4.97/5.20 ! [F: nat > num,N: nat,M: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 4.97/5.20 = ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less_iff
% 4.97/5.20 thf(fact_1743_lift__Suc__mono__less__iff,axiom,
% 4.97/5.20 ! [F: nat > nat,N: nat,M: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 4.97/5.20 = ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less_iff
% 4.97/5.20 thf(fact_1744_lift__Suc__mono__less__iff,axiom,
% 4.97/5.20 ! [F: nat > int,N: nat,M: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 4.97/5.20 = ( ord_less_nat @ N @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less_iff
% 4.97/5.20 thf(fact_1745_lift__Suc__mono__less,axiom,
% 4.97/5.20 ! [F: nat > real,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less
% 4.97/5.20 thf(fact_1746_lift__Suc__mono__less,axiom,
% 4.97/5.20 ! [F: nat > rat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less
% 4.97/5.20 thf(fact_1747_lift__Suc__mono__less,axiom,
% 4.97/5.20 ! [F: nat > num,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less
% 4.97/5.20 thf(fact_1748_lift__Suc__mono__less,axiom,
% 4.97/5.20 ! [F: nat > nat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less
% 4.97/5.20 thf(fact_1749_lift__Suc__mono__less,axiom,
% 4.97/5.20 ! [F: nat > int,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_less
% 4.97/5.20 thf(fact_1750_lift__Suc__mono__le,axiom,
% 4.97/5.20 ! [F: nat > set_int,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_le
% 4.97/5.20 thf(fact_1751_lift__Suc__mono__le,axiom,
% 4.97/5.20 ! [F: nat > rat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_le
% 4.97/5.20 thf(fact_1752_lift__Suc__mono__le,axiom,
% 4.97/5.20 ! [F: nat > num,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_le
% 4.97/5.20 thf(fact_1753_lift__Suc__mono__le,axiom,
% 4.97/5.20 ! [F: nat > nat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_le
% 4.97/5.20 thf(fact_1754_lift__Suc__mono__le,axiom,
% 4.97/5.20 ! [F: nat > int,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_mono_le
% 4.97/5.20 thf(fact_1755_lift__Suc__antimono__le,axiom,
% 4.97/5.20 ! [F: nat > set_int,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_antimono_le
% 4.97/5.20 thf(fact_1756_lift__Suc__antimono__le,axiom,
% 4.97/5.20 ! [F: nat > rat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_antimono_le
% 4.97/5.20 thf(fact_1757_lift__Suc__antimono__le,axiom,
% 4.97/5.20 ! [F: nat > num,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_antimono_le
% 4.97/5.20 thf(fact_1758_lift__Suc__antimono__le,axiom,
% 4.97/5.20 ! [F: nat > nat,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_antimono_le
% 4.97/5.20 thf(fact_1759_lift__Suc__antimono__le,axiom,
% 4.97/5.20 ! [F: nat > int,N: nat,N5: nat] :
% 4.97/5.20 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 4.97/5.20 => ( ( ord_less_eq_nat @ N @ N5 )
% 4.97/5.20 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % lift_Suc_antimono_le
% 4.97/5.20 thf(fact_1760_Suc__leI,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_leI
% 4.97/5.20 thf(fact_1761_Suc__le__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 4.97/5.20 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_le_eq
% 4.97/5.20 thf(fact_1762_dec__induct,axiom,
% 4.97/5.20 ! [I: nat,J: nat,P: nat > $o] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ( P @ I )
% 4.97/5.20 => ( ! [N3: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ N3 )
% 4.97/5.20 => ( ( ord_less_nat @ N3 @ J )
% 4.97/5.20 => ( ( P @ N3 )
% 4.97/5.20 => ( P @ ( suc @ N3 ) ) ) ) )
% 4.97/5.20 => ( P @ J ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dec_induct
% 4.97/5.20 thf(fact_1763_inc__induct,axiom,
% 4.97/5.20 ! [I: nat,J: nat,P: nat > $o] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ J )
% 4.97/5.20 => ( ( P @ J )
% 4.97/5.20 => ( ! [N3: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ I @ N3 )
% 4.97/5.20 => ( ( ord_less_nat @ N3 @ J )
% 4.97/5.20 => ( ( P @ ( suc @ N3 ) )
% 4.97/5.20 => ( P @ N3 ) ) ) )
% 4.97/5.20 => ( P @ I ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % inc_induct
% 4.97/5.20 thf(fact_1764_Suc__le__lessD,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 4.97/5.20 => ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_le_lessD
% 4.97/5.20 thf(fact_1765_le__less__Suc__eq,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 4.97/5.20 = ( N = M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_less_Suc_eq
% 4.97/5.20 thf(fact_1766_less__Suc__eq__le,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_Suc_eq_le
% 4.97/5.20 thf(fact_1767_less__eq__Suc__le,axiom,
% 4.97/5.20 ( ord_less_nat
% 4.97/5.20 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_eq_Suc_le
% 4.97/5.20 thf(fact_1768_le__imp__less__Suc,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.20 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_imp_less_Suc
% 4.97/5.20 thf(fact_1769_less__natE,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ~ ! [Q3: nat] :
% 4.97/5.20 ( N
% 4.97/5.20 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_natE
% 4.97/5.20 thf(fact_1770_less__add__Suc1,axiom,
% 4.97/5.20 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_add_Suc1
% 4.97/5.20 thf(fact_1771_less__add__Suc2,axiom,
% 4.97/5.20 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_add_Suc2
% 4.97/5.20 thf(fact_1772_less__iff__Suc__add,axiom,
% 4.97/5.20 ( ord_less_nat
% 4.97/5.20 = ( ^ [M3: nat,N4: nat] :
% 4.97/5.20 ? [K2: nat] :
% 4.97/5.20 ( N4
% 4.97/5.20 = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_iff_Suc_add
% 4.97/5.20 thf(fact_1773_less__imp__Suc__add,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ M @ N )
% 4.97/5.20 => ? [K3: nat] :
% 4.97/5.20 ( N
% 4.97/5.20 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % less_imp_Suc_add
% 4.97/5.20 thf(fact_1774_Suc__diff__Suc,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_nat @ N @ M )
% 4.97/5.20 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 4.97/5.20 = ( minus_minus_nat @ M @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_diff_Suc
% 4.97/5.20 thf(fact_1775_diff__less__Suc,axiom,
% 4.97/5.20 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 4.97/5.20
% 4.97/5.20 % diff_less_Suc
% 4.97/5.20 thf(fact_1776_Suc__mult__less__cancel1,axiom,
% 4.97/5.20 ! [K: nat,M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.97/5.20 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_mult_less_cancel1
% 4.97/5.20 thf(fact_1777_Suc__diff__le,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 4.97/5.20 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_diff_le
% 4.97/5.20 thf(fact_1778_Suc__mult__le__cancel1,axiom,
% 4.97/5.20 ! [K: nat,M: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 4.97/5.20 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_mult_le_cancel1
% 4.97/5.20 thf(fact_1779_mult__Suc,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( times_times_nat @ ( suc @ M ) @ N )
% 4.97/5.20 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_Suc
% 4.97/5.20 thf(fact_1780_Suc__eq__plus1,axiom,
% 4.97/5.20 ( suc
% 4.97/5.20 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_eq_plus1
% 4.97/5.20 thf(fact_1781_plus__1__eq__Suc,axiom,
% 4.97/5.20 ( ( plus_plus_nat @ one_one_nat )
% 4.97/5.20 = suc ) ).
% 4.97/5.20
% 4.97/5.20 % plus_1_eq_Suc
% 4.97/5.20 thf(fact_1782_Suc__eq__plus1__left,axiom,
% 4.97/5.20 ( suc
% 4.97/5.20 = ( plus_plus_nat @ one_one_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_eq_plus1_left
% 4.97/5.20 thf(fact_1783_Suc__div__le__mono,axiom,
% 4.97/5.20 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_div_le_mono
% 4.97/5.20 thf(fact_1784_diff__Suc__eq__diff__pred,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 4.97/5.20 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % diff_Suc_eq_diff_pred
% 4.97/5.20 thf(fact_1785_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1786_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1787_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1788_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1789_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1790_of__nat__diff,axiom,
% 4.97/5.20 ! [N: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ M )
% 4.97/5.20 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N ) )
% 4.97/5.20 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_diff
% 4.97/5.20 thf(fact_1791_power__gt1,axiom,
% 4.97/5.20 ! [A: real,N: nat] :
% 4.97/5.20 ( ( ord_less_real @ one_one_real @ A )
% 4.97/5.20 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_gt1
% 4.97/5.20 thf(fact_1792_power__gt1,axiom,
% 4.97/5.20 ! [A: rat,N: nat] :
% 4.97/5.20 ( ( ord_less_rat @ one_one_rat @ A )
% 4.97/5.20 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_gt1
% 4.97/5.20 thf(fact_1793_power__gt1,axiom,
% 4.97/5.20 ! [A: nat,N: nat] :
% 4.97/5.20 ( ( ord_less_nat @ one_one_nat @ A )
% 4.97/5.20 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_gt1
% 4.97/5.20 thf(fact_1794_power__gt1,axiom,
% 4.97/5.20 ! [A: int,N: nat] :
% 4.97/5.20 ( ( ord_less_int @ one_one_int @ A )
% 4.97/5.20 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_gt1
% 4.97/5.20 thf(fact_1795_xor__num_Ocases,axiom,
% 4.97/5.20 ! [X2: product_prod_num_num] :
% 4.97/5.20 ( ( X2
% 4.97/5.20 != ( product_Pair_num_num @ one @ one ) )
% 4.97/5.20 => ( ! [N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 4.97/5.20 => ( ! [N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 4.97/5.20 => ( ! [M4: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 4.97/5.20 => ( ! [M4: num,N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 4.97/5.20 => ( ! [M4: num,N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 4.97/5.20 => ( ! [M4: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 4.97/5.20 => ( ! [M4: num,N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 4.97/5.20 => ~ ! [M4: num,N3: num] :
% 4.97/5.20 ( X2
% 4.97/5.20 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % xor_num.cases
% 4.97/5.20 thf(fact_1796_nat__le__real__less,axiom,
% 4.97/5.20 ( ord_less_eq_nat
% 4.97/5.20 = ( ^ [N4: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nat_le_real_less
% 4.97/5.20 thf(fact_1797_real__of__nat__div4,axiom,
% 4.97/5.20 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_div4
% 4.97/5.20 thf(fact_1798_eval__nat__numeral_I3_J,axiom,
% 4.97/5.20 ! [N: num] :
% 4.97/5.20 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 4.97/5.20 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % eval_nat_numeral(3)
% 4.97/5.20 thf(fact_1799_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_real,B4: set_real] :
% 4.97/5.20 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: real] :
% 4.97/5.20 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 4.97/5.20 => ( member_real @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1800_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_complex,B4: set_complex] :
% 4.97/5.20 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: complex] :
% 4.97/5.20 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 4.97/5.20 => ( member_complex @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1801_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_set_nat,B4: set_set_nat] :
% 4.97/5.20 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: set_nat] :
% 4.97/5.20 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 4.97/5.20 => ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1802_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 4.97/5.20 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.20 => ( member_VEBT_VEBT @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1803_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_nat,B4: set_nat] :
% 4.97/5.20 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: nat] :
% 4.97/5.20 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 4.97/5.20 => ( member_nat @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1804_subset__code_I1_J,axiom,
% 4.97/5.20 ! [Xs: list_int,B4: set_int] :
% 4.97/5.20 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B4 )
% 4.97/5.20 = ( ! [X3: int] :
% 4.97/5.20 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 4.97/5.20 => ( member_int @ X3 @ B4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % subset_code(1)
% 4.97/5.20 thf(fact_1805_neq__if__length__neq,axiom,
% 4.97/5.20 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 4.97/5.20 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 4.97/5.20 => ( Xs != Ys ) ) ).
% 4.97/5.20
% 4.97/5.20 % neq_if_length_neq
% 4.97/5.20 thf(fact_1806_neq__if__length__neq,axiom,
% 4.97/5.20 ! [Xs: list_o,Ys: list_o] :
% 4.97/5.20 ( ( ( size_size_list_o @ Xs )
% 4.97/5.20 != ( size_size_list_o @ Ys ) )
% 4.97/5.20 => ( Xs != Ys ) ) ).
% 4.97/5.20
% 4.97/5.20 % neq_if_length_neq
% 4.97/5.20 thf(fact_1807_neq__if__length__neq,axiom,
% 4.97/5.20 ! [Xs: list_nat,Ys: list_nat] :
% 4.97/5.20 ( ( ( size_size_list_nat @ Xs )
% 4.97/5.20 != ( size_size_list_nat @ Ys ) )
% 4.97/5.20 => ( Xs != Ys ) ) ).
% 4.97/5.20
% 4.97/5.20 % neq_if_length_neq
% 4.97/5.20 thf(fact_1808_neq__if__length__neq,axiom,
% 4.97/5.20 ! [Xs: list_int,Ys: list_int] :
% 4.97/5.20 ( ( ( size_size_list_int @ Xs )
% 4.97/5.20 != ( size_size_list_int @ Ys ) )
% 4.97/5.20 => ( Xs != Ys ) ) ).
% 4.97/5.20
% 4.97/5.20 % neq_if_length_neq
% 4.97/5.20 thf(fact_1809_Ex__list__of__length,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ? [Xs2: list_VEBT_VEBT] :
% 4.97/5.20 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.97/5.20 = N ) ).
% 4.97/5.20
% 4.97/5.20 % Ex_list_of_length
% 4.97/5.20 thf(fact_1810_Ex__list__of__length,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ? [Xs2: list_o] :
% 4.97/5.20 ( ( size_size_list_o @ Xs2 )
% 4.97/5.20 = N ) ).
% 4.97/5.20
% 4.97/5.20 % Ex_list_of_length
% 4.97/5.20 thf(fact_1811_Ex__list__of__length,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ? [Xs2: list_nat] :
% 4.97/5.20 ( ( size_size_list_nat @ Xs2 )
% 4.97/5.20 = N ) ).
% 4.97/5.20
% 4.97/5.20 % Ex_list_of_length
% 4.97/5.20 thf(fact_1812_Ex__list__of__length,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ? [Xs2: list_int] :
% 4.97/5.20 ( ( size_size_list_int @ Xs2 )
% 4.97/5.20 = N ) ).
% 4.97/5.20
% 4.97/5.20 % Ex_list_of_length
% 4.97/5.20 thf(fact_1813_nat__less__real__le,axiom,
% 4.97/5.20 ( ord_less_nat
% 4.97/5.20 = ( ^ [N4: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N4 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nat_less_real_le
% 4.97/5.20 thf(fact_1814_Suc__double__not__eq__double,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.20 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_double_not_eq_double
% 4.97/5.20 thf(fact_1815_double__not__eq__Suc__double,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 4.97/5.20 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % double_not_eq_Suc_double
% 4.97/5.20 thf(fact_1816_Suc3__eq__add__3,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 4.97/5.20 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc3_eq_add_3
% 4.97/5.20 thf(fact_1817_div__nat__eqI,axiom,
% 4.97/5.20 ! [N: nat,Q2: nat,M: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 4.97/5.20 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 4.97/5.20 => ( ( divide_divide_nat @ M @ N )
% 4.97/5.20 = Q2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % div_nat_eqI
% 4.97/5.20 thf(fact_1818_Suc__nat__number__of__add,axiom,
% 4.97/5.20 ! [V: num,N: nat] :
% 4.97/5.20 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 4.97/5.20 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_nat_number_of_add
% 4.97/5.20 thf(fact_1819_of__nat__less__two__power,axiom,
% 4.97/5.20 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_two_power
% 4.97/5.20 thf(fact_1820_of__nat__less__two__power,axiom,
% 4.97/5.20 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_two_power
% 4.97/5.20 thf(fact_1821_of__nat__less__two__power,axiom,
% 4.97/5.20 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_two_power
% 4.97/5.20 thf(fact_1822_of__nat__less__two__power,axiom,
% 4.97/5.20 ! [N: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % of_nat_less_two_power
% 4.97/5.20 thf(fact_1823_real__of__nat__div3,axiom,
% 4.97/5.20 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) @ one_one_real ) ).
% 4.97/5.20
% 4.97/5.20 % real_of_nat_div3
% 4.97/5.20 thf(fact_1824_Suc__div__eq__add3__div,axiom,
% 4.97/5.20 ! [M: nat,N: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 4.97/5.20 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % Suc_div_eq_add3_div
% 4.97/5.20 thf(fact_1825_power__odd__eq,axiom,
% 4.97/5.20 ! [A: real,N: nat] :
% 4.97/5.20 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_odd_eq
% 4.97/5.20 thf(fact_1826_power__odd__eq,axiom,
% 4.97/5.20 ! [A: rat,N: nat] :
% 4.97/5.20 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_odd_eq
% 4.97/5.20 thf(fact_1827_power__odd__eq,axiom,
% 4.97/5.20 ! [A: nat,N: nat] :
% 4.97/5.20 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_odd_eq
% 4.97/5.20 thf(fact_1828_power__odd__eq,axiom,
% 4.97/5.20 ! [A: int,N: nat] :
% 4.97/5.20 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_odd_eq
% 4.97/5.20 thf(fact_1829_power__odd__eq,axiom,
% 4.97/5.20 ! [A: complex,N: nat] :
% 4.97/5.20 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_odd_eq
% 4.97/5.20 thf(fact_1830_Bernoulli__inequality,axiom,
% 4.97/5.20 ! [X2: real,N: nat] :
% 4.97/5.20 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 4.97/5.20 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Bernoulli_inequality
% 4.97/5.20 thf(fact_1831_compl__mono,axiom,
% 4.97/5.20 ! [X2: set_int,Y: set_int] :
% 4.97/5.20 ( ( ord_less_eq_set_int @ X2 @ Y )
% 4.97/5.20 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X2 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % compl_mono
% 4.97/5.20 thf(fact_1832_compl__le__swap1,axiom,
% 4.97/5.20 ! [Y: set_int,X2: set_int] :
% 4.97/5.20 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X2 ) )
% 4.97/5.20 => ( ord_less_eq_set_int @ X2 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % compl_le_swap1
% 4.97/5.20 thf(fact_1833_compl__le__swap2,axiom,
% 4.97/5.20 ! [Y: set_int,X2: set_int] :
% 4.97/5.20 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X2 )
% 4.97/5.20 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X2 ) @ Y ) ) ).
% 4.97/5.20
% 4.97/5.20 % compl_le_swap2
% 4.97/5.20 thf(fact_1834_length__induct,axiom,
% 4.97/5.20 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 4.97/5.20 ( ! [Xs2: list_VEBT_VEBT] :
% 4.97/5.20 ( ! [Ys2: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 4.97/5.20 => ( P @ Ys2 ) )
% 4.97/5.20 => ( P @ Xs2 ) )
% 4.97/5.20 => ( P @ Xs ) ) ).
% 4.97/5.20
% 4.97/5.20 % length_induct
% 4.97/5.20 thf(fact_1835_length__induct,axiom,
% 4.97/5.20 ! [P: list_o > $o,Xs: list_o] :
% 4.97/5.20 ( ! [Xs2: list_o] :
% 4.97/5.20 ( ! [Ys2: list_o] :
% 4.97/5.20 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 4.97/5.20 => ( P @ Ys2 ) )
% 4.97/5.20 => ( P @ Xs2 ) )
% 4.97/5.20 => ( P @ Xs ) ) ).
% 4.97/5.20
% 4.97/5.20 % length_induct
% 4.97/5.20 thf(fact_1836_length__induct,axiom,
% 4.97/5.20 ! [P: list_nat > $o,Xs: list_nat] :
% 4.97/5.20 ( ! [Xs2: list_nat] :
% 4.97/5.20 ( ! [Ys2: list_nat] :
% 4.97/5.20 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 4.97/5.20 => ( P @ Ys2 ) )
% 4.97/5.20 => ( P @ Xs2 ) )
% 4.97/5.20 => ( P @ Xs ) ) ).
% 4.97/5.20
% 4.97/5.20 % length_induct
% 4.97/5.20 thf(fact_1837_length__induct,axiom,
% 4.97/5.20 ! [P: list_int > $o,Xs: list_int] :
% 4.97/5.20 ( ! [Xs2: list_int] :
% 4.97/5.20 ( ! [Ys2: list_int] :
% 4.97/5.20 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 4.97/5.20 => ( P @ Ys2 ) )
% 4.97/5.20 => ( P @ Xs2 ) )
% 4.97/5.20 => ( P @ Xs ) ) ).
% 4.97/5.20
% 4.97/5.20 % length_induct
% 4.97/5.20 thf(fact_1838_power__minus1__odd,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_minus1_odd
% 4.97/5.20 thf(fact_1839_power__minus1__odd,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_minus1_odd
% 4.97/5.20 thf(fact_1840_power__minus1__odd,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_minus1_odd
% 4.97/5.20 thf(fact_1841_power__minus1__odd,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_minus1_odd
% 4.97/5.20 thf(fact_1842_power__minus1__odd,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 4.97/5.20 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % power_minus1_odd
% 4.97/5.20 thf(fact_1843_list__eq__iff__nth__eq,axiom,
% 4.97/5.20 ( ( ^ [Y5: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y5 = Z4 ) )
% 4.97/5.20 = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 4.97/5.20 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 4.97/5.20 => ( ( nth_VEBT_VEBT @ Xs3 @ I4 )
% 4.97/5.20 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_eq_iff_nth_eq
% 4.97/5.20 thf(fact_1844_list__eq__iff__nth__eq,axiom,
% 4.97/5.20 ( ( ^ [Y5: list_o,Z4: list_o] : ( Y5 = Z4 ) )
% 4.97/5.20 = ( ^ [Xs3: list_o,Ys3: list_o] :
% 4.97/5.20 ( ( ( size_size_list_o @ Xs3 )
% 4.97/5.20 = ( size_size_list_o @ Ys3 ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs3 ) )
% 4.97/5.20 => ( ( nth_o @ Xs3 @ I4 )
% 4.97/5.20 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_eq_iff_nth_eq
% 4.97/5.20 thf(fact_1845_list__eq__iff__nth__eq,axiom,
% 4.97/5.20 ( ( ^ [Y5: list_nat,Z4: list_nat] : ( Y5 = Z4 ) )
% 4.97/5.20 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 4.97/5.20 ( ( ( size_size_list_nat @ Xs3 )
% 4.97/5.20 = ( size_size_list_nat @ Ys3 ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs3 ) )
% 4.97/5.20 => ( ( nth_nat @ Xs3 @ I4 )
% 4.97/5.20 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_eq_iff_nth_eq
% 4.97/5.20 thf(fact_1846_list__eq__iff__nth__eq,axiom,
% 4.97/5.20 ( ( ^ [Y5: list_int,Z4: list_int] : ( Y5 = Z4 ) )
% 4.97/5.20 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 4.97/5.20 ( ( ( size_size_list_int @ Xs3 )
% 4.97/5.20 = ( size_size_list_int @ Ys3 ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs3 ) )
% 4.97/5.20 => ( ( nth_int @ Xs3 @ I4 )
% 4.97/5.20 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_eq_iff_nth_eq
% 4.97/5.20 thf(fact_1847_Skolem__list__nth,axiom,
% 4.97/5.20 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 4.97/5.20 ( ( ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ? [X5: vEBT_VEBT] : ( P @ I4 @ X5 ) ) )
% 4.97/5.20 = ( ? [Xs3: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 4.97/5.20 = K )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Skolem_list_nth
% 4.97/5.20 thf(fact_1848_Skolem__list__nth,axiom,
% 4.97/5.20 ! [K: nat,P: nat > $o > $o] :
% 4.97/5.20 ( ( ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ? [X5: $o] : ( P @ I4 @ X5 ) ) )
% 4.97/5.20 = ( ? [Xs3: list_o] :
% 4.97/5.20 ( ( ( size_size_list_o @ Xs3 )
% 4.97/5.20 = K )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ( P @ I4 @ ( nth_o @ Xs3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Skolem_list_nth
% 4.97/5.20 thf(fact_1849_Skolem__list__nth,axiom,
% 4.97/5.20 ! [K: nat,P: nat > nat > $o] :
% 4.97/5.20 ( ( ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ? [X5: nat] : ( P @ I4 @ X5 ) ) )
% 4.97/5.20 = ( ? [Xs3: list_nat] :
% 4.97/5.20 ( ( ( size_size_list_nat @ Xs3 )
% 4.97/5.20 = K )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ( P @ I4 @ ( nth_nat @ Xs3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Skolem_list_nth
% 4.97/5.20 thf(fact_1850_Skolem__list__nth,axiom,
% 4.97/5.20 ! [K: nat,P: nat > int > $o] :
% 4.97/5.20 ( ( ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ? [X5: int] : ( P @ I4 @ X5 ) ) )
% 4.97/5.20 = ( ? [Xs3: list_int] :
% 4.97/5.20 ( ( ( size_size_list_int @ Xs3 )
% 4.97/5.20 = K )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ K )
% 4.97/5.20 => ( P @ I4 @ ( nth_int @ Xs3 @ I4 ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % Skolem_list_nth
% 4.97/5.20 thf(fact_1851_nth__equalityI,axiom,
% 4.97/5.20 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 4.97/5.20 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.20 => ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 4.97/5.20 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 4.97/5.20 => ( Xs = Ys ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_equalityI
% 4.97/5.20 thf(fact_1852_nth__equalityI,axiom,
% 4.97/5.20 ! [Xs: list_o,Ys: list_o] :
% 4.97/5.20 ( ( ( size_size_list_o @ Xs )
% 4.97/5.20 = ( size_size_list_o @ Ys ) )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.97/5.20 => ( ( nth_o @ Xs @ I3 )
% 4.97/5.20 = ( nth_o @ Ys @ I3 ) ) )
% 4.97/5.20 => ( Xs = Ys ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_equalityI
% 4.97/5.20 thf(fact_1853_nth__equalityI,axiom,
% 4.97/5.20 ! [Xs: list_nat,Ys: list_nat] :
% 4.97/5.20 ( ( ( size_size_list_nat @ Xs )
% 4.97/5.20 = ( size_size_list_nat @ Ys ) )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.97/5.20 => ( ( nth_nat @ Xs @ I3 )
% 4.97/5.20 = ( nth_nat @ Ys @ I3 ) ) )
% 4.97/5.20 => ( Xs = Ys ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_equalityI
% 4.97/5.20 thf(fact_1854_nth__equalityI,axiom,
% 4.97/5.20 ! [Xs: list_int,Ys: list_int] :
% 4.97/5.20 ( ( ( size_size_list_int @ Xs )
% 4.97/5.20 = ( size_size_list_int @ Ys ) )
% 4.97/5.20 => ( ! [I3: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.97/5.20 => ( ( nth_int @ Xs @ I3 )
% 4.97/5.20 = ( nth_int @ Ys @ I3 ) ) )
% 4.97/5.20 => ( Xs = Ys ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_equalityI
% 4.97/5.20 thf(fact_1855_invar__vebt_Ointros_I3_J,axiom,
% 4.97/5.20 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 4.97/5.20 ( ! [X4: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ X4 @ N ) )
% 4.97/5.20 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.97/5.20 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.97/5.20 => ( ( M
% 4.97/5.20 = ( suc @ N ) )
% 4.97/5.20 => ( ( Deg
% 4.97/5.20 = ( plus_plus_nat @ N @ M ) )
% 4.97/5.20 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 4.97/5.20 => ( ! [X4: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.97/5.20 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % invar_vebt.intros(3)
% 4.97/5.20 thf(fact_1856_discrete,axiom,
% 4.97/5.20 ( ord_less_nat
% 4.97/5.20 = ( ^ [A4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A4 @ one_one_nat ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % discrete
% 4.97/5.20 thf(fact_1857_discrete,axiom,
% 4.97/5.20 ( ord_less_int
% 4.97/5.20 = ( ^ [A4: int] : ( ord_less_eq_int @ ( plus_plus_int @ A4 @ one_one_int ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % discrete
% 4.97/5.20 thf(fact_1858_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_real] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 4.97/5.20 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1859_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_complex] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.97/5.20 => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1860_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_set_nat] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.97/5.20 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1861_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_VEBT_VEBT] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.20 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1862_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_o] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.97/5.20 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1863_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_nat] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.97/5.20 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1864_nth__mem,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_int] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.97/5.20 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % nth_mem
% 4.97/5.20 thf(fact_1865_list__ball__nth,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.20 => ( ! [X4: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.20 => ( P @ X4 ) )
% 4.97/5.20 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_ball_nth
% 4.97/5.20 thf(fact_1866_list__ball__nth,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_o,P: $o > $o] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 4.97/5.20 => ( ! [X4: $o] :
% 4.97/5.20 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 4.97/5.20 => ( P @ X4 ) )
% 4.97/5.20 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_ball_nth
% 4.97/5.20 thf(fact_1867_list__ball__nth,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 4.97/5.20 => ( ! [X4: nat] :
% 4.97/5.20 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 4.97/5.20 => ( P @ X4 ) )
% 4.97/5.20 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_ball_nth
% 4.97/5.20 thf(fact_1868_list__ball__nth,axiom,
% 4.97/5.20 ! [N: nat,Xs: list_int,P: int > $o] :
% 4.97/5.20 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 4.97/5.20 => ( ! [X4: int] :
% 4.97/5.20 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 4.97/5.20 => ( P @ X4 ) )
% 4.97/5.20 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % list_ball_nth
% 4.97/5.20 thf(fact_1869_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: real,Xs: list_real] :
% 4.97/5.20 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 4.97/5.20 & ( ( nth_real @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1870_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: complex,Xs: list_complex] :
% 4.97/5.20 ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.97/5.20 & ( ( nth_complex @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1871_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: set_nat,Xs: list_set_nat] :
% 4.97/5.20 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.97/5.20 & ( ( nth_set_nat @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1872_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.97/5.20 & ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1873_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: $o,Xs: list_o] :
% 4.97/5.20 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 4.97/5.20 & ( ( nth_o @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1874_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: nat,Xs: list_nat] :
% 4.97/5.20 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 4.97/5.20 & ( ( nth_nat @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1875_in__set__conv__nth,axiom,
% 4.97/5.20 ! [X2: int,Xs: list_int] :
% 4.97/5.20 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 4.97/5.20 = ( ? [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 4.97/5.20 & ( ( nth_int @ Xs @ I4 )
% 4.97/5.20 = X2 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % in_set_conv_nth
% 4.97/5.20 thf(fact_1876_dbl__dec__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.20 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_dec_simps(4)
% 4.97/5.20 thf(fact_1877_dbl__dec__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_dec_simps(4)
% 4.97/5.20 thf(fact_1878_dbl__dec__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.20 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_dec_simps(4)
% 4.97/5.20 thf(fact_1879_dbl__dec__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.20 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_dec_simps(4)
% 4.97/5.20 thf(fact_1880_dbl__dec__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.20 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_dec_simps(4)
% 4.97/5.20 thf(fact_1881_dbl__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.20 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(4)
% 4.97/5.20 thf(fact_1882_dbl__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.20 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(4)
% 4.97/5.20 thf(fact_1883_dbl__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.20 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(4)
% 4.97/5.20 thf(fact_1884_dbl__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.20 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(4)
% 4.97/5.20 thf(fact_1885_dbl__simps_I4_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.20 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(4)
% 4.97/5.20 thf(fact_1886_low__def,axiom,
% 4.97/5.20 ( vEBT_VEBT_low
% 4.97/5.20 = ( ^ [X3: nat,N4: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % low_def
% 4.97/5.20 thf(fact_1887_dbl__inc__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 4.97/5.20 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_inc_simps(3)
% 4.97/5.20 thf(fact_1888_dbl__inc__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 4.97/5.20 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_inc_simps(3)
% 4.97/5.20 thf(fact_1889_dbl__inc__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 4.97/5.20 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_inc_simps(3)
% 4.97/5.20 thf(fact_1890_dbl__inc__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 4.97/5.20 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_inc_simps(3)
% 4.97/5.20 thf(fact_1891_dbl__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 4.97/5.20 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(3)
% 4.97/5.20 thf(fact_1892_dbl__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_real @ one_one_real )
% 4.97/5.20 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(3)
% 4.97/5.20 thf(fact_1893_dbl__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 4.97/5.20 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(3)
% 4.97/5.20 thf(fact_1894_dbl__simps_I3_J,axiom,
% 4.97/5.20 ( ( neg_numeral_dbl_int @ one_one_int )
% 4.97/5.20 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % dbl_simps(3)
% 4.97/5.20 thf(fact_1895_invar__vebt_Osimps,axiom,
% 4.97/5.20 ( vEBT_invar_vebt
% 4.97/5.20 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 4.97/5.20 ( ( ? [A4: $o,B3: $o] :
% 4.97/5.20 ( A1
% 4.97/5.20 = ( vEBT_Leaf @ A4 @ B3 ) )
% 4.97/5.20 & ( A22
% 4.97/5.20 = ( suc @ zero_zero_nat ) ) )
% 4.97/5.20 | ? [TreeList2: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT] :
% 4.97/5.20 ( ( A1
% 4.97/5.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary2 ) )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.97/5.20 & ( vEBT_invar_vebt @ Summary2 @ N4 )
% 4.97/5.20 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.97/5.20 & ( A22
% 4.97/5.20 = ( plus_plus_nat @ N4 @ N4 ) )
% 4.97/5.20 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X5 ) ) )
% 4.97/5.20 | ? [TreeList2: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT] :
% 4.97/5.20 ( ( A1
% 4.97/5.20 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList2 @ Summary2 ) )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.97/5.20 & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N4 ) )
% 4.97/5.20 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.97/5.20 & ( A22
% 4.97/5.20 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 4.97/5.20 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X5 ) ) )
% 4.97/5.20 | ? [TreeList2: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 4.97/5.20 ( ( A1
% 4.97/5.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList2 @ Summary2 ) )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.97/5.20 & ( vEBT_invar_vebt @ Summary2 @ N4 )
% 4.97/5.20 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.97/5.20 & ( A22
% 4.97/5.20 = ( plus_plus_nat @ N4 @ N4 ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.97/5.20 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 4.97/5.20 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.97/5.20 & ( ( Mi2 = Ma2 )
% 4.97/5.20 => ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X5 ) ) )
% 4.97/5.20 & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.97/5.20 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 4.97/5.20 & ( ( Mi2 != Ma2 )
% 4.97/5.20 => ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 4.97/5.20 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 4.97/5.20 = I4 )
% 4.97/5.20 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 4.97/5.20 & ! [X3: nat] :
% 4.97/5.20 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 4.97/5.20 = I4 )
% 4.97/5.20 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ Mi2 @ X3 )
% 4.97/5.20 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) )
% 4.97/5.20 | ? [TreeList2: list_VEBT_VEBT,N4: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 4.97/5.20 ( ( A1
% 4.97/5.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList2 @ Summary2 ) )
% 4.97/5.20 & ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 4.97/5.20 & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N4 ) )
% 4.97/5.20 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.97/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.97/5.20 & ( A22
% 4.97/5.20 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 4.97/5.20 & ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.97/5.20 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 4.97/5.20 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 4.97/5.20 & ( ( Mi2 = Ma2 )
% 4.97/5.20 => ! [X3: vEBT_VEBT] :
% 4.97/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.97/5.20 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X5 ) ) )
% 4.97/5.20 & ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.97/5.20 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 4.97/5.20 & ( ( Mi2 != Ma2 )
% 4.97/5.20 => ! [I4: nat] :
% 4.97/5.20 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 4.97/5.20 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N4 )
% 4.97/5.20 = I4 )
% 4.97/5.20 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N4 ) ) )
% 4.97/5.20 & ! [X3: nat] :
% 4.97/5.20 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 4.97/5.20 = I4 )
% 4.97/5.20 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 4.97/5.20 => ( ( ord_less_nat @ Mi2 @ X3 )
% 4.97/5.20 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % invar_vebt.simps
% 4.97/5.20 thf(fact_1896_deg__not__0,axiom,
% 4.97/5.20 ! [T: vEBT_VEBT,N: nat] :
% 4.97/5.20 ( ( vEBT_invar_vebt @ T @ N )
% 4.97/5.20 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.97/5.20
% 4.97/5.20 % deg_not_0
% 4.97/5.20 thf(fact_1897_mod__mod__trivial,axiom,
% 4.97/5.20 ! [A: nat,B: nat] :
% 4.97/5.20 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.97/5.20 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.20
% 4.97/5.20 % mod_mod_trivial
% 4.97/5.20 thf(fact_1898_mod__mod__trivial,axiom,
% 4.97/5.20 ! [A: int,B: int] :
% 4.97/5.20 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.97/5.20 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.20
% 4.97/5.20 % mod_mod_trivial
% 4.97/5.20 thf(fact_1899_mod__mod__trivial,axiom,
% 4.97/5.20 ! [A: code_integer,B: code_integer] :
% 4.97/5.20 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 4.97/5.20 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.20
% 4.97/5.20 % mod_mod_trivial
% 4.97/5.20 thf(fact_1900_VEBT_Oinject_I2_J,axiom,
% 4.97/5.20 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 4.97/5.20 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 4.97/5.20 = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 4.97/5.20 = ( ( X21 = Y21 )
% 4.97/5.20 & ( X222 = Y222 ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % VEBT.inject(2)
% 4.97/5.20 thf(fact_1901_le__zero__eq,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 4.97/5.20 = ( N = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % le_zero_eq
% 4.97/5.20 thf(fact_1902_not__gr__zero,axiom,
% 4.97/5.20 ! [N: nat] :
% 4.97/5.20 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 4.97/5.20 = ( N = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % not_gr_zero
% 4.97/5.20 thf(fact_1903_mult__cancel__right,axiom,
% 4.97/5.20 ! [A: real,C: real,B: real] :
% 4.97/5.20 ( ( ( times_times_real @ A @ C )
% 4.97/5.20 = ( times_times_real @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_real )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_right
% 4.97/5.20 thf(fact_1904_mult__cancel__right,axiom,
% 4.97/5.20 ! [A: rat,C: rat,B: rat] :
% 4.97/5.20 ( ( ( times_times_rat @ A @ C )
% 4.97/5.20 = ( times_times_rat @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_rat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_right
% 4.97/5.20 thf(fact_1905_mult__cancel__right,axiom,
% 4.97/5.20 ! [A: nat,C: nat,B: nat] :
% 4.97/5.20 ( ( ( times_times_nat @ A @ C )
% 4.97/5.20 = ( times_times_nat @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_nat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_right
% 4.97/5.20 thf(fact_1906_mult__cancel__right,axiom,
% 4.97/5.20 ! [A: int,C: int,B: int] :
% 4.97/5.20 ( ( ( times_times_int @ A @ C )
% 4.97/5.20 = ( times_times_int @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_int )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_right
% 4.97/5.20 thf(fact_1907_mult__cancel__right,axiom,
% 4.97/5.20 ! [A: complex,C: complex,B: complex] :
% 4.97/5.20 ( ( ( times_times_complex @ A @ C )
% 4.97/5.20 = ( times_times_complex @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_complex )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_right
% 4.97/5.20 thf(fact_1908_mult__cancel__left,axiom,
% 4.97/5.20 ! [C: real,A: real,B: real] :
% 4.97/5.20 ( ( ( times_times_real @ C @ A )
% 4.97/5.20 = ( times_times_real @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_real )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_left
% 4.97/5.20 thf(fact_1909_mult__cancel__left,axiom,
% 4.97/5.20 ! [C: rat,A: rat,B: rat] :
% 4.97/5.20 ( ( ( times_times_rat @ C @ A )
% 4.97/5.20 = ( times_times_rat @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_rat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_left
% 4.97/5.20 thf(fact_1910_mult__cancel__left,axiom,
% 4.97/5.20 ! [C: nat,A: nat,B: nat] :
% 4.97/5.20 ( ( ( times_times_nat @ C @ A )
% 4.97/5.20 = ( times_times_nat @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_nat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_left
% 4.97/5.20 thf(fact_1911_mult__cancel__left,axiom,
% 4.97/5.20 ! [C: int,A: int,B: int] :
% 4.97/5.20 ( ( ( times_times_int @ C @ A )
% 4.97/5.20 = ( times_times_int @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_int )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_left
% 4.97/5.20 thf(fact_1912_mult__cancel__left,axiom,
% 4.97/5.20 ! [C: complex,A: complex,B: complex] :
% 4.97/5.20 ( ( ( times_times_complex @ C @ A )
% 4.97/5.20 = ( times_times_complex @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_complex )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_cancel_left
% 4.97/5.20 thf(fact_1913_mult__eq__0__iff,axiom,
% 4.97/5.20 ! [A: real,B: real] :
% 4.97/5.20 ( ( ( times_times_real @ A @ B )
% 4.97/5.20 = zero_zero_real )
% 4.97/5.20 = ( ( A = zero_zero_real )
% 4.97/5.20 | ( B = zero_zero_real ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_eq_0_iff
% 4.97/5.20 thf(fact_1914_mult__eq__0__iff,axiom,
% 4.97/5.20 ! [A: rat,B: rat] :
% 4.97/5.20 ( ( ( times_times_rat @ A @ B )
% 4.97/5.20 = zero_zero_rat )
% 4.97/5.20 = ( ( A = zero_zero_rat )
% 4.97/5.20 | ( B = zero_zero_rat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_eq_0_iff
% 4.97/5.20 thf(fact_1915_mult__eq__0__iff,axiom,
% 4.97/5.20 ! [A: nat,B: nat] :
% 4.97/5.20 ( ( ( times_times_nat @ A @ B )
% 4.97/5.20 = zero_zero_nat )
% 4.97/5.20 = ( ( A = zero_zero_nat )
% 4.97/5.20 | ( B = zero_zero_nat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_eq_0_iff
% 4.97/5.20 thf(fact_1916_mult__eq__0__iff,axiom,
% 4.97/5.20 ! [A: int,B: int] :
% 4.97/5.20 ( ( ( times_times_int @ A @ B )
% 4.97/5.20 = zero_zero_int )
% 4.97/5.20 = ( ( A = zero_zero_int )
% 4.97/5.20 | ( B = zero_zero_int ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_eq_0_iff
% 4.97/5.20 thf(fact_1917_mult__eq__0__iff,axiom,
% 4.97/5.20 ! [A: complex,B: complex] :
% 4.97/5.20 ( ( ( times_times_complex @ A @ B )
% 4.97/5.20 = zero_zero_complex )
% 4.97/5.20 = ( ( A = zero_zero_complex )
% 4.97/5.20 | ( B = zero_zero_complex ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % mult_eq_0_iff
% 4.97/5.20 thf(fact_1918_mult__zero__right,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( times_times_real @ A @ zero_zero_real )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_right
% 4.97/5.20 thf(fact_1919_mult__zero__right,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( times_times_rat @ A @ zero_zero_rat )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_right
% 4.97/5.20 thf(fact_1920_mult__zero__right,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( times_times_nat @ A @ zero_zero_nat )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_right
% 4.97/5.20 thf(fact_1921_mult__zero__right,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( times_times_int @ A @ zero_zero_int )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_right
% 4.97/5.20 thf(fact_1922_mult__zero__right,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( times_times_complex @ A @ zero_zero_complex )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_right
% 4.97/5.20 thf(fact_1923_mult__zero__left,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( times_times_real @ zero_zero_real @ A )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_left
% 4.97/5.20 thf(fact_1924_mult__zero__left,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( times_times_rat @ zero_zero_rat @ A )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_left
% 4.97/5.20 thf(fact_1925_mult__zero__left,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( times_times_nat @ zero_zero_nat @ A )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_left
% 4.97/5.20 thf(fact_1926_mult__zero__left,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( times_times_int @ zero_zero_int @ A )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_left
% 4.97/5.20 thf(fact_1927_mult__zero__left,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( times_times_complex @ zero_zero_complex @ A )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % mult_zero_left
% 4.97/5.20 thf(fact_1928_add_Oright__neutral,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add.right_neutral
% 4.97/5.20 thf(fact_1929_add_Oright__neutral,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add.right_neutral
% 4.97/5.20 thf(fact_1930_add_Oright__neutral,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add.right_neutral
% 4.97/5.20 thf(fact_1931_add_Oright__neutral,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add.right_neutral
% 4.97/5.20 thf(fact_1932_add_Oright__neutral,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add.right_neutral
% 4.97/5.20 thf(fact_1933_double__zero__sym,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( zero_zero_real
% 4.97/5.20 = ( plus_plus_real @ A @ A ) )
% 4.97/5.20 = ( A = zero_zero_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % double_zero_sym
% 4.97/5.20 thf(fact_1934_double__zero__sym,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( zero_zero_rat
% 4.97/5.20 = ( plus_plus_rat @ A @ A ) )
% 4.97/5.20 = ( A = zero_zero_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % double_zero_sym
% 4.97/5.20 thf(fact_1935_double__zero__sym,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( zero_zero_int
% 4.97/5.20 = ( plus_plus_int @ A @ A ) )
% 4.97/5.20 = ( A = zero_zero_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % double_zero_sym
% 4.97/5.20 thf(fact_1936_add__cancel__left__left,axiom,
% 4.97/5.20 ! [B: complex,A: complex] :
% 4.97/5.20 ( ( ( plus_plus_complex @ B @ A )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_complex ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_left
% 4.97/5.20 thf(fact_1937_add__cancel__left__left,axiom,
% 4.97/5.20 ! [B: real,A: real] :
% 4.97/5.20 ( ( ( plus_plus_real @ B @ A )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_left
% 4.97/5.20 thf(fact_1938_add__cancel__left__left,axiom,
% 4.97/5.20 ! [B: rat,A: rat] :
% 4.97/5.20 ( ( ( plus_plus_rat @ B @ A )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_left
% 4.97/5.20 thf(fact_1939_add__cancel__left__left,axiom,
% 4.97/5.20 ! [B: nat,A: nat] :
% 4.97/5.20 ( ( ( plus_plus_nat @ B @ A )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_left
% 4.97/5.20 thf(fact_1940_add__cancel__left__left,axiom,
% 4.97/5.20 ! [B: int,A: int] :
% 4.97/5.20 ( ( ( plus_plus_int @ B @ A )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_left
% 4.97/5.20 thf(fact_1941_add__cancel__left__right,axiom,
% 4.97/5.20 ! [A: complex,B: complex] :
% 4.97/5.20 ( ( ( plus_plus_complex @ A @ B )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_complex ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_right
% 4.97/5.20 thf(fact_1942_add__cancel__left__right,axiom,
% 4.97/5.20 ! [A: real,B: real] :
% 4.97/5.20 ( ( ( plus_plus_real @ A @ B )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_right
% 4.97/5.20 thf(fact_1943_add__cancel__left__right,axiom,
% 4.97/5.20 ! [A: rat,B: rat] :
% 4.97/5.20 ( ( ( plus_plus_rat @ A @ B )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_right
% 4.97/5.20 thf(fact_1944_add__cancel__left__right,axiom,
% 4.97/5.20 ! [A: nat,B: nat] :
% 4.97/5.20 ( ( ( plus_plus_nat @ A @ B )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_right
% 4.97/5.20 thf(fact_1945_add__cancel__left__right,axiom,
% 4.97/5.20 ! [A: int,B: int] :
% 4.97/5.20 ( ( ( plus_plus_int @ A @ B )
% 4.97/5.20 = A )
% 4.97/5.20 = ( B = zero_zero_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_left_right
% 4.97/5.20 thf(fact_1946_add__cancel__right__left,axiom,
% 4.97/5.20 ! [A: complex,B: complex] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_complex @ B @ A ) )
% 4.97/5.20 = ( B = zero_zero_complex ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_left
% 4.97/5.20 thf(fact_1947_add__cancel__right__left,axiom,
% 4.97/5.20 ! [A: real,B: real] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_real @ B @ A ) )
% 4.97/5.20 = ( B = zero_zero_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_left
% 4.97/5.20 thf(fact_1948_add__cancel__right__left,axiom,
% 4.97/5.20 ! [A: rat,B: rat] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_rat @ B @ A ) )
% 4.97/5.20 = ( B = zero_zero_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_left
% 4.97/5.20 thf(fact_1949_add__cancel__right__left,axiom,
% 4.97/5.20 ! [A: nat,B: nat] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_nat @ B @ A ) )
% 4.97/5.20 = ( B = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_left
% 4.97/5.20 thf(fact_1950_add__cancel__right__left,axiom,
% 4.97/5.20 ! [A: int,B: int] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_int @ B @ A ) )
% 4.97/5.20 = ( B = zero_zero_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_left
% 4.97/5.20 thf(fact_1951_add__cancel__right__right,axiom,
% 4.97/5.20 ! [A: complex,B: complex] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_complex @ A @ B ) )
% 4.97/5.20 = ( B = zero_zero_complex ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_right
% 4.97/5.20 thf(fact_1952_add__cancel__right__right,axiom,
% 4.97/5.20 ! [A: real,B: real] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_real @ A @ B ) )
% 4.97/5.20 = ( B = zero_zero_real ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_right
% 4.97/5.20 thf(fact_1953_add__cancel__right__right,axiom,
% 4.97/5.20 ! [A: rat,B: rat] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_rat @ A @ B ) )
% 4.97/5.20 = ( B = zero_zero_rat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_right
% 4.97/5.20 thf(fact_1954_add__cancel__right__right,axiom,
% 4.97/5.20 ! [A: nat,B: nat] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_nat @ A @ B ) )
% 4.97/5.20 = ( B = zero_zero_nat ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_right
% 4.97/5.20 thf(fact_1955_add__cancel__right__right,axiom,
% 4.97/5.20 ! [A: int,B: int] :
% 4.97/5.20 ( ( A
% 4.97/5.20 = ( plus_plus_int @ A @ B ) )
% 4.97/5.20 = ( B = zero_zero_int ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_cancel_right_right
% 4.97/5.20 thf(fact_1956_add__eq__0__iff__both__eq__0,axiom,
% 4.97/5.20 ! [X2: nat,Y: nat] :
% 4.97/5.20 ( ( ( plus_plus_nat @ X2 @ Y )
% 4.97/5.20 = zero_zero_nat )
% 4.97/5.20 = ( ( X2 = zero_zero_nat )
% 4.97/5.20 & ( Y = zero_zero_nat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % add_eq_0_iff_both_eq_0
% 4.97/5.20 thf(fact_1957_zero__eq__add__iff__both__eq__0,axiom,
% 4.97/5.20 ! [X2: nat,Y: nat] :
% 4.97/5.20 ( ( zero_zero_nat
% 4.97/5.20 = ( plus_plus_nat @ X2 @ Y ) )
% 4.97/5.20 = ( ( X2 = zero_zero_nat )
% 4.97/5.20 & ( Y = zero_zero_nat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % zero_eq_add_iff_both_eq_0
% 4.97/5.20 thf(fact_1958_add__0,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add_0
% 4.97/5.20 thf(fact_1959_add__0,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add_0
% 4.97/5.20 thf(fact_1960_add__0,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add_0
% 4.97/5.20 thf(fact_1961_add__0,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add_0
% 4.97/5.20 thf(fact_1962_add__0,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % add_0
% 4.97/5.20 thf(fact_1963_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( minus_minus_real @ A @ A )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % cancel_comm_monoid_add_class.diff_cancel
% 4.97/5.20 thf(fact_1964_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( minus_minus_rat @ A @ A )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % cancel_comm_monoid_add_class.diff_cancel
% 4.97/5.20 thf(fact_1965_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( minus_minus_nat @ A @ A )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % cancel_comm_monoid_add_class.diff_cancel
% 4.97/5.20 thf(fact_1966_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( minus_minus_int @ A @ A )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % cancel_comm_monoid_add_class.diff_cancel
% 4.97/5.20 thf(fact_1967_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( minus_minus_complex @ A @ A )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % cancel_comm_monoid_add_class.diff_cancel
% 4.97/5.20 thf(fact_1968_diff__zero,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_zero
% 4.97/5.20 thf(fact_1969_diff__zero,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_zero
% 4.97/5.20 thf(fact_1970_diff__zero,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_zero
% 4.97/5.20 thf(fact_1971_diff__zero,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_zero
% 4.97/5.20 thf(fact_1972_diff__zero,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_zero
% 4.97/5.20 thf(fact_1973_zero__diff,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % zero_diff
% 4.97/5.20 thf(fact_1974_diff__0__right,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_0_right
% 4.97/5.20 thf(fact_1975_diff__0__right,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_0_right
% 4.97/5.20 thf(fact_1976_diff__0__right,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_0_right
% 4.97/5.20 thf(fact_1977_diff__0__right,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 4.97/5.20 = A ) ).
% 4.97/5.20
% 4.97/5.20 % diff_0_right
% 4.97/5.20 thf(fact_1978_diff__self,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( minus_minus_real @ A @ A )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % diff_self
% 4.97/5.20 thf(fact_1979_diff__self,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( minus_minus_rat @ A @ A )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % diff_self
% 4.97/5.20 thf(fact_1980_diff__self,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( minus_minus_int @ A @ A )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % diff_self
% 4.97/5.20 thf(fact_1981_diff__self,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( minus_minus_complex @ A @ A )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % diff_self
% 4.97/5.20 thf(fact_1982_divide__eq__0__iff,axiom,
% 4.97/5.20 ! [A: complex,B: complex] :
% 4.97/5.20 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.97/5.20 = zero_zero_complex )
% 4.97/5.20 = ( ( A = zero_zero_complex )
% 4.97/5.20 | ( B = zero_zero_complex ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_eq_0_iff
% 4.97/5.20 thf(fact_1983_divide__eq__0__iff,axiom,
% 4.97/5.20 ! [A: real,B: real] :
% 4.97/5.20 ( ( ( divide_divide_real @ A @ B )
% 4.97/5.20 = zero_zero_real )
% 4.97/5.20 = ( ( A = zero_zero_real )
% 4.97/5.20 | ( B = zero_zero_real ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_eq_0_iff
% 4.97/5.20 thf(fact_1984_divide__eq__0__iff,axiom,
% 4.97/5.20 ! [A: rat,B: rat] :
% 4.97/5.20 ( ( ( divide_divide_rat @ A @ B )
% 4.97/5.20 = zero_zero_rat )
% 4.97/5.20 = ( ( A = zero_zero_rat )
% 4.97/5.20 | ( B = zero_zero_rat ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_eq_0_iff
% 4.97/5.20 thf(fact_1985_divide__cancel__left,axiom,
% 4.97/5.20 ! [C: complex,A: complex,B: complex] :
% 4.97/5.20 ( ( ( divide1717551699836669952omplex @ C @ A )
% 4.97/5.20 = ( divide1717551699836669952omplex @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_complex )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_left
% 4.97/5.20 thf(fact_1986_divide__cancel__left,axiom,
% 4.97/5.20 ! [C: real,A: real,B: real] :
% 4.97/5.20 ( ( ( divide_divide_real @ C @ A )
% 4.97/5.20 = ( divide_divide_real @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_real )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_left
% 4.97/5.20 thf(fact_1987_divide__cancel__left,axiom,
% 4.97/5.20 ! [C: rat,A: rat,B: rat] :
% 4.97/5.20 ( ( ( divide_divide_rat @ C @ A )
% 4.97/5.20 = ( divide_divide_rat @ C @ B ) )
% 4.97/5.20 = ( ( C = zero_zero_rat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_left
% 4.97/5.20 thf(fact_1988_divide__cancel__right,axiom,
% 4.97/5.20 ! [A: complex,C: complex,B: complex] :
% 4.97/5.20 ( ( ( divide1717551699836669952omplex @ A @ C )
% 4.97/5.20 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_complex )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_right
% 4.97/5.20 thf(fact_1989_divide__cancel__right,axiom,
% 4.97/5.20 ! [A: real,C: real,B: real] :
% 4.97/5.20 ( ( ( divide_divide_real @ A @ C )
% 4.97/5.20 = ( divide_divide_real @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_real )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_right
% 4.97/5.20 thf(fact_1990_divide__cancel__right,axiom,
% 4.97/5.20 ! [A: rat,C: rat,B: rat] :
% 4.97/5.20 ( ( ( divide_divide_rat @ A @ C )
% 4.97/5.20 = ( divide_divide_rat @ B @ C ) )
% 4.97/5.20 = ( ( C = zero_zero_rat )
% 4.97/5.20 | ( A = B ) ) ) ).
% 4.97/5.20
% 4.97/5.20 % divide_cancel_right
% 4.97/5.20 thf(fact_1991_division__ring__divide__zero,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % division_ring_divide_zero
% 4.97/5.20 thf(fact_1992_division__ring__divide__zero,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % division_ring_divide_zero
% 4.97/5.20 thf(fact_1993_division__ring__divide__zero,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % division_ring_divide_zero
% 4.97/5.20 thf(fact_1994_div__0,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % div_0
% 4.97/5.20 thf(fact_1995_div__0,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( divide_divide_real @ zero_zero_real @ A )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % div_0
% 4.97/5.20 thf(fact_1996_div__0,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % div_0
% 4.97/5.20 thf(fact_1997_div__0,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % div_0
% 4.97/5.20 thf(fact_1998_div__0,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % div_0
% 4.97/5.20 thf(fact_1999_div__by__0,axiom,
% 4.97/5.20 ! [A: complex] :
% 4.97/5.20 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 4.97/5.20 = zero_zero_complex ) ).
% 4.97/5.20
% 4.97/5.20 % div_by_0
% 4.97/5.20 thf(fact_2000_div__by__0,axiom,
% 4.97/5.20 ! [A: real] :
% 4.97/5.20 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.97/5.20 = zero_zero_real ) ).
% 4.97/5.20
% 4.97/5.20 % div_by_0
% 4.97/5.20 thf(fact_2001_div__by__0,axiom,
% 4.97/5.20 ! [A: rat] :
% 4.97/5.20 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.97/5.20 = zero_zero_rat ) ).
% 4.97/5.20
% 4.97/5.20 % div_by_0
% 4.97/5.20 thf(fact_2002_div__by__0,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % div_by_0
% 4.97/5.20 thf(fact_2003_div__by__0,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % div_by_0
% 4.97/5.20 thf(fact_2004_bits__div__0,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % bits_div_0
% 4.97/5.20 thf(fact_2005_bits__div__0,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.97/5.20 = zero_zero_int ) ).
% 4.97/5.20
% 4.97/5.20 % bits_div_0
% 4.97/5.20 thf(fact_2006_bits__div__by__0,axiom,
% 4.97/5.20 ! [A: nat] :
% 4.97/5.20 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.97/5.20 = zero_zero_nat ) ).
% 4.97/5.20
% 4.97/5.20 % bits_div_by_0
% 4.97/5.20 thf(fact_2007_bits__div__by__0,axiom,
% 4.97/5.20 ! [A: int] :
% 4.97/5.20 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % bits_div_by_0
% 4.97/5.21 thf(fact_2008_add_Oinverse__neutral,axiom,
% 4.97/5.21 ( ( uminus_uminus_real @ zero_zero_real )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % add.inverse_neutral
% 4.97/5.21 thf(fact_2009_add_Oinverse__neutral,axiom,
% 4.97/5.21 ( ( uminus_uminus_int @ zero_zero_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % add.inverse_neutral
% 4.97/5.21 thf(fact_2010_add_Oinverse__neutral,axiom,
% 4.97/5.21 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % add.inverse_neutral
% 4.97/5.21 thf(fact_2011_add_Oinverse__neutral,axiom,
% 4.97/5.21 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % add.inverse_neutral
% 4.97/5.21 thf(fact_2012_add_Oinverse__neutral,axiom,
% 4.97/5.21 ( ( uminus_uminus_rat @ zero_zero_rat )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % add.inverse_neutral
% 4.97/5.21 thf(fact_2013_neg__0__equal__iff__equal,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( zero_zero_real
% 4.97/5.21 = ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( zero_zero_real = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_equal_iff_equal
% 4.97/5.21 thf(fact_2014_neg__0__equal__iff__equal,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( zero_zero_int
% 4.97/5.21 = ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( zero_zero_int = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_equal_iff_equal
% 4.97/5.21 thf(fact_2015_neg__0__equal__iff__equal,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( zero_zero_complex
% 4.97/5.21 = ( uminus1482373934393186551omplex @ A ) )
% 4.97/5.21 = ( zero_zero_complex = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_equal_iff_equal
% 4.97/5.21 thf(fact_2016_neg__0__equal__iff__equal,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( zero_z3403309356797280102nteger
% 4.97/5.21 = ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( zero_z3403309356797280102nteger = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_equal_iff_equal
% 4.97/5.21 thf(fact_2017_neg__0__equal__iff__equal,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( zero_zero_rat
% 4.97/5.21 = ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( zero_zero_rat = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_equal_iff_equal
% 4.97/5.21 thf(fact_2018_neg__equal__0__iff__equal,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ( uminus_uminus_real @ A )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 = ( A = zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_0_iff_equal
% 4.97/5.21 thf(fact_2019_neg__equal__0__iff__equal,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ( uminus_uminus_int @ A )
% 4.97/5.21 = zero_zero_int )
% 4.97/5.21 = ( A = zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_0_iff_equal
% 4.97/5.21 thf(fact_2020_neg__equal__0__iff__equal,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( ( uminus1482373934393186551omplex @ A )
% 4.97/5.21 = zero_zero_complex )
% 4.97/5.21 = ( A = zero_zero_complex ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_0_iff_equal
% 4.97/5.21 thf(fact_2021_neg__equal__0__iff__equal,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ( uminus1351360451143612070nteger @ A )
% 4.97/5.21 = zero_z3403309356797280102nteger )
% 4.97/5.21 = ( A = zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_0_iff_equal
% 4.97/5.21 thf(fact_2022_neg__equal__0__iff__equal,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ( uminus_uminus_rat @ A )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 = ( A = zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_0_iff_equal
% 4.97/5.21 thf(fact_2023_equal__neg__zero,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( A = zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % equal_neg_zero
% 4.97/5.21 thf(fact_2024_equal__neg__zero,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( A = zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % equal_neg_zero
% 4.97/5.21 thf(fact_2025_equal__neg__zero,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( A = zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % equal_neg_zero
% 4.97/5.21 thf(fact_2026_equal__neg__zero,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( A = zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % equal_neg_zero
% 4.97/5.21 thf(fact_2027_neg__equal__zero,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ( uminus_uminus_real @ A )
% 4.97/5.21 = A )
% 4.97/5.21 = ( A = zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_zero
% 4.97/5.21 thf(fact_2028_neg__equal__zero,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ( uminus_uminus_int @ A )
% 4.97/5.21 = A )
% 4.97/5.21 = ( A = zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_zero
% 4.97/5.21 thf(fact_2029_neg__equal__zero,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ( uminus1351360451143612070nteger @ A )
% 4.97/5.21 = A )
% 4.97/5.21 = ( A = zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_zero
% 4.97/5.21 thf(fact_2030_neg__equal__zero,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ( uminus_uminus_rat @ A )
% 4.97/5.21 = A )
% 4.97/5.21 = ( A = zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_equal_zero
% 4.97/5.21 thf(fact_2031_bits__mod__0,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_0
% 4.97/5.21 thf(fact_2032_bits__mod__0,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_0
% 4.97/5.21 thf(fact_2033_bits__mod__0,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_0
% 4.97/5.21 thf(fact_2034_mod__self,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ A @ A )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_self
% 4.97/5.21 thf(fact_2035_mod__self,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ A @ A )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_self
% 4.97/5.21 thf(fact_2036_mod__self,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ A @ A )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_self
% 4.97/5.21 thf(fact_2037_mod__by__0,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_0
% 4.97/5.21 thf(fact_2038_mod__by__0,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_0
% 4.97/5.21 thf(fact_2039_mod__by__0,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_0
% 4.97/5.21 thf(fact_2040_mod__0,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_0
% 4.97/5.21 thf(fact_2041_mod__0,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_0
% 4.97/5.21 thf(fact_2042_mod__0,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_0
% 4.97/5.21 thf(fact_2043_bot__nat__0_Onot__eq__extremum,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( A != zero_zero_nat )
% 4.97/5.21 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % bot_nat_0.not_eq_extremum
% 4.97/5.21 thf(fact_2044_neq0__conv,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( N != zero_zero_nat )
% 4.97/5.21 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 4.97/5.21
% 4.97/5.21 % neq0_conv
% 4.97/5.21 thf(fact_2045_less__nat__zero__code,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % less_nat_zero_code
% 4.97/5.21 thf(fact_2046_mod__add__self1,axiom,
% 4.97/5.21 ! [B: nat,A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self1
% 4.97/5.21 thf(fact_2047_mod__add__self1,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self1
% 4.97/5.21 thf(fact_2048_mod__add__self1,axiom,
% 4.97/5.21 ! [B: code_integer,A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self1
% 4.97/5.21 thf(fact_2049_mod__add__self2,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self2
% 4.97/5.21 thf(fact_2050_mod__add__self2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self2
% 4.97/5.21 thf(fact_2051_mod__add__self2,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_add_self2
% 4.97/5.21 thf(fact_2052_bot__nat__0_Oextremum,axiom,
% 4.97/5.21 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 4.97/5.21
% 4.97/5.21 % bot_nat_0.extremum
% 4.97/5.21 thf(fact_2053_le0,axiom,
% 4.97/5.21 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 4.97/5.21
% 4.97/5.21 % le0
% 4.97/5.21 thf(fact_2054_minus__mod__self2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % minus_mod_self2
% 4.97/5.21 thf(fact_2055_minus__mod__self2,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % minus_mod_self2
% 4.97/5.21 thf(fact_2056_add__is__0,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ( plus_plus_nat @ M @ N )
% 4.97/5.21 = zero_zero_nat )
% 4.97/5.21 = ( ( M = zero_zero_nat )
% 4.97/5.21 & ( N = zero_zero_nat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_is_0
% 4.97/5.21 thf(fact_2057_Nat_Oadd__0__right,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 4.97/5.21 = M ) ).
% 4.97/5.21
% 4.97/5.21 % Nat.add_0_right
% 4.97/5.21 thf(fact_2058_mod__minus__minus,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 4.97/5.21 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_minus_minus
% 4.97/5.21 thf(fact_2059_mod__minus__minus,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 4.97/5.21 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_minus_minus
% 4.97/5.21 thf(fact_2060_diff__self__eq__0,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( minus_minus_nat @ M @ M )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % diff_self_eq_0
% 4.97/5.21 thf(fact_2061_diff__0__eq__0,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0_eq_0
% 4.97/5.21 thf(fact_2062_mult__cancel2,axiom,
% 4.97/5.21 ! [M: nat,K: nat,N: nat] :
% 4.97/5.21 ( ( ( times_times_nat @ M @ K )
% 4.97/5.21 = ( times_times_nat @ N @ K ) )
% 4.97/5.21 = ( ( M = N )
% 4.97/5.21 | ( K = zero_zero_nat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel2
% 4.97/5.21 thf(fact_2063_mult__cancel1,axiom,
% 4.97/5.21 ! [K: nat,M: nat,N: nat] :
% 4.97/5.21 ( ( ( times_times_nat @ K @ M )
% 4.97/5.21 = ( times_times_nat @ K @ N ) )
% 4.97/5.21 = ( ( M = N )
% 4.97/5.21 | ( K = zero_zero_nat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel1
% 4.97/5.21 thf(fact_2064_mult__0__right,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( times_times_nat @ M @ zero_zero_nat )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mult_0_right
% 4.97/5.21 thf(fact_2065_mult__is__0,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ( times_times_nat @ M @ N )
% 4.97/5.21 = zero_zero_nat )
% 4.97/5.21 = ( ( M = zero_zero_nat )
% 4.97/5.21 | ( N = zero_zero_nat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_is_0
% 4.97/5.21 thf(fact_2066_mod__less,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ M @ N )
% 4.97/5.21 => ( ( modulo_modulo_nat @ M @ N )
% 4.97/5.21 = M ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_less
% 4.97/5.21 thf(fact_2067_dbl__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(2)
% 4.97/5.21 thf(fact_2068_dbl__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(2)
% 4.97/5.21 thf(fact_2069_dbl__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(2)
% 4.97/5.21 thf(fact_2070_dbl__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(2)
% 4.97/5.21 thf(fact_2071_dbl__dec__simps_I3_J,axiom,
% 4.97/5.21 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 4.97/5.21 = one_one_complex ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_dec_simps(3)
% 4.97/5.21 thf(fact_2072_dbl__dec__simps_I3_J,axiom,
% 4.97/5.21 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 4.97/5.21 = one_one_real ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_dec_simps(3)
% 4.97/5.21 thf(fact_2073_dbl__dec__simps_I3_J,axiom,
% 4.97/5.21 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 4.97/5.21 = one_one_rat ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_dec_simps(3)
% 4.97/5.21 thf(fact_2074_dbl__dec__simps_I3_J,axiom,
% 4.97/5.21 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 4.97/5.21 = one_one_int ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_dec_simps(3)
% 4.97/5.21 thf(fact_2075_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_le_double_add_iff_zero_le_single_add
% 4.97/5.21 thf(fact_2076_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_le_double_add_iff_zero_le_single_add
% 4.97/5.21 thf(fact_2077_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.97/5.21 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_le_double_add_iff_zero_le_single_add
% 4.97/5.21 thf(fact_2078_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_le_zero_iff_single_add_le_zero
% 4.97/5.21 thf(fact_2079_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_le_zero_iff_single_add_le_zero
% 4.97/5.21 thf(fact_2080_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.97/5.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_le_zero_iff_single_add_le_zero
% 4.97/5.21 thf(fact_2081_le__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel2
% 4.97/5.21 thf(fact_2082_le__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel2
% 4.97/5.21 thf(fact_2083_le__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.97/5.21 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel2
% 4.97/5.21 thf(fact_2084_le__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.97/5.21 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel2
% 4.97/5.21 thf(fact_2085_le__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel1
% 4.97/5.21 thf(fact_2086_le__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel1
% 4.97/5.21 thf(fact_2087_le__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel1
% 4.97/5.21 thf(fact_2088_le__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % le_add_same_cancel1
% 4.97/5.21 thf(fact_2089_add__le__same__cancel2,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel2
% 4.97/5.21 thf(fact_2090_add__le__same__cancel2,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel2
% 4.97/5.21 thf(fact_2091_add__le__same__cancel2,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel2
% 4.97/5.21 thf(fact_2092_add__le__same__cancel2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel2
% 4.97/5.21 thf(fact_2093_add__le__same__cancel1,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel1
% 4.97/5.21 thf(fact_2094_add__le__same__cancel1,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel1
% 4.97/5.21 thf(fact_2095_add__le__same__cancel1,axiom,
% 4.97/5.21 ! [B: nat,A: nat] :
% 4.97/5.21 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel1
% 4.97/5.21 thf(fact_2096_add__le__same__cancel1,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_le_same_cancel1
% 4.97/5.21 thf(fact_2097_diff__ge__0__iff__ge,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_real @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_ge_0_iff_ge
% 4.97/5.21 thf(fact_2098_diff__ge__0__iff__ge,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_rat @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_ge_0_iff_ge
% 4.97/5.21 thf(fact_2099_diff__ge__0__iff__ge,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.97/5.21 = ( ord_less_eq_int @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_ge_0_iff_ge
% 4.97/5.21 thf(fact_2100_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_double_add_iff_zero_less_single_add
% 4.97/5.21 thf(fact_2101_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_double_add_iff_zero_less_single_add
% 4.97/5.21 thf(fact_2102_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.97/5.21 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_double_add_iff_zero_less_single_add
% 4.97/5.21 thf(fact_2103_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_less_zero_iff_single_add_less_zero
% 4.97/5.21 thf(fact_2104_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_less_zero_iff_single_add_less_zero
% 4.97/5.21 thf(fact_2105_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.97/5.21 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % double_add_less_zero_iff_single_add_less_zero
% 4.97/5.21 thf(fact_2106_less__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel2
% 4.97/5.21 thf(fact_2107_less__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel2
% 4.97/5.21 thf(fact_2108_less__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.97/5.21 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel2
% 4.97/5.21 thf(fact_2109_less__add__same__cancel2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.97/5.21 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel2
% 4.97/5.21 thf(fact_2110_less__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel1
% 4.97/5.21 thf(fact_2111_less__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel1
% 4.97/5.21 thf(fact_2112_less__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.97/5.21 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel1
% 4.97/5.21 thf(fact_2113_less__add__same__cancel1,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.97/5.21 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_add_same_cancel1
% 4.97/5.21 thf(fact_2114_add__less__same__cancel2,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel2
% 4.97/5.21 thf(fact_2115_add__less__same__cancel2,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel2
% 4.97/5.21 thf(fact_2116_add__less__same__cancel2,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel2
% 4.97/5.21 thf(fact_2117_add__less__same__cancel2,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.97/5.21 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel2
% 4.97/5.21 thf(fact_2118_add__less__same__cancel1,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel1
% 4.97/5.21 thf(fact_2119_add__less__same__cancel1,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel1
% 4.97/5.21 thf(fact_2120_add__less__same__cancel1,axiom,
% 4.97/5.21 ! [B: nat,A: nat] :
% 4.97/5.21 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel1
% 4.97/5.21 thf(fact_2121_add__less__same__cancel1,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.97/5.21 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_less_same_cancel1
% 4.97/5.21 thf(fact_2122_neg__less__eq__nonneg,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_eq_nonneg
% 4.97/5.21 thf(fact_2123_neg__less__eq__nonneg,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 4.97/5.21 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_eq_nonneg
% 4.97/5.21 thf(fact_2124_neg__less__eq__nonneg,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_eq_nonneg
% 4.97/5.21 thf(fact_2125_neg__less__eq__nonneg,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 4.97/5.21 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_eq_nonneg
% 4.97/5.21 thf(fact_2126_less__eq__neg__nonpos,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_eq_neg_nonpos
% 4.97/5.21 thf(fact_2127_less__eq__neg__nonpos,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_eq_neg_nonpos
% 4.97/5.21 thf(fact_2128_less__eq__neg__nonpos,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_eq_neg_nonpos
% 4.97/5.21 thf(fact_2129_less__eq__neg__nonpos,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_eq_neg_nonpos
% 4.97/5.21 thf(fact_2130_neg__le__0__iff__le,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_le_0_iff_le
% 4.97/5.21 thf(fact_2131_neg__le__0__iff__le,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 4.97/5.21 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_le_0_iff_le
% 4.97/5.21 thf(fact_2132_neg__le__0__iff__le,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_le_0_iff_le
% 4.97/5.21 thf(fact_2133_neg__le__0__iff__le,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 4.97/5.21 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_le_0_iff_le
% 4.97/5.21 thf(fact_2134_neg__0__le__iff__le,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_le_iff_le
% 4.97/5.21 thf(fact_2135_neg__0__le__iff__le,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_le_iff_le
% 4.97/5.21 thf(fact_2136_neg__0__le__iff__le,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_le_iff_le
% 4.97/5.21 thf(fact_2137_neg__0__le__iff__le,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_le_iff_le
% 4.97/5.21 thf(fact_2138_diff__gt__0__iff__gt,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.97/5.21 = ( ord_less_real @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_gt_0_iff_gt
% 4.97/5.21 thf(fact_2139_diff__gt__0__iff__gt,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.97/5.21 = ( ord_less_rat @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_gt_0_iff_gt
% 4.97/5.21 thf(fact_2140_diff__gt__0__iff__gt,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.97/5.21 = ( ord_less_int @ B @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_gt_0_iff_gt
% 4.97/5.21 thf(fact_2141_sum__squares__eq__zero__iff,axiom,
% 4.97/5.21 ! [X2: real,Y: real] :
% 4.97/5.21 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 = ( ( X2 = zero_zero_real )
% 4.97/5.21 & ( Y = zero_zero_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % sum_squares_eq_zero_iff
% 4.97/5.21 thf(fact_2142_sum__squares__eq__zero__iff,axiom,
% 4.97/5.21 ! [X2: rat,Y: rat] :
% 4.97/5.21 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 = ( ( X2 = zero_zero_rat )
% 4.97/5.21 & ( Y = zero_zero_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % sum_squares_eq_zero_iff
% 4.97/5.21 thf(fact_2143_sum__squares__eq__zero__iff,axiom,
% 4.97/5.21 ! [X2: int,Y: int] :
% 4.97/5.21 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 4.97/5.21 = zero_zero_int )
% 4.97/5.21 = ( ( X2 = zero_zero_int )
% 4.97/5.21 & ( Y = zero_zero_int ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % sum_squares_eq_zero_iff
% 4.97/5.21 thf(fact_2144_mult__cancel__left1,axiom,
% 4.97/5.21 ! [C: real,B: real] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_real @ C @ B ) )
% 4.97/5.21 = ( ( C = zero_zero_real )
% 4.97/5.21 | ( B = one_one_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left1
% 4.97/5.21 thf(fact_2145_mult__cancel__left1,axiom,
% 4.97/5.21 ! [C: rat,B: rat] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_rat @ C @ B ) )
% 4.97/5.21 = ( ( C = zero_zero_rat )
% 4.97/5.21 | ( B = one_one_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left1
% 4.97/5.21 thf(fact_2146_mult__cancel__left1,axiom,
% 4.97/5.21 ! [C: int,B: int] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_int @ C @ B ) )
% 4.97/5.21 = ( ( C = zero_zero_int )
% 4.97/5.21 | ( B = one_one_int ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left1
% 4.97/5.21 thf(fact_2147_mult__cancel__left1,axiom,
% 4.97/5.21 ! [C: complex,B: complex] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_complex @ C @ B ) )
% 4.97/5.21 = ( ( C = zero_zero_complex )
% 4.97/5.21 | ( B = one_one_complex ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left1
% 4.97/5.21 thf(fact_2148_mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: real,A: real] :
% 4.97/5.21 ( ( ( times_times_real @ C @ A )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_real )
% 4.97/5.21 | ( A = one_one_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left2
% 4.97/5.21 thf(fact_2149_mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: rat,A: rat] :
% 4.97/5.21 ( ( ( times_times_rat @ C @ A )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_rat )
% 4.97/5.21 | ( A = one_one_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left2
% 4.97/5.21 thf(fact_2150_mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: int,A: int] :
% 4.97/5.21 ( ( ( times_times_int @ C @ A )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_int )
% 4.97/5.21 | ( A = one_one_int ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left2
% 4.97/5.21 thf(fact_2151_mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: complex,A: complex] :
% 4.97/5.21 ( ( ( times_times_complex @ C @ A )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_complex )
% 4.97/5.21 | ( A = one_one_complex ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_left2
% 4.97/5.21 thf(fact_2152_mult__cancel__right1,axiom,
% 4.97/5.21 ! [C: real,B: real] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_real @ B @ C ) )
% 4.97/5.21 = ( ( C = zero_zero_real )
% 4.97/5.21 | ( B = one_one_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right1
% 4.97/5.21 thf(fact_2153_mult__cancel__right1,axiom,
% 4.97/5.21 ! [C: rat,B: rat] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_rat @ B @ C ) )
% 4.97/5.21 = ( ( C = zero_zero_rat )
% 4.97/5.21 | ( B = one_one_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right1
% 4.97/5.21 thf(fact_2154_mult__cancel__right1,axiom,
% 4.97/5.21 ! [C: int,B: int] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_int @ B @ C ) )
% 4.97/5.21 = ( ( C = zero_zero_int )
% 4.97/5.21 | ( B = one_one_int ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right1
% 4.97/5.21 thf(fact_2155_mult__cancel__right1,axiom,
% 4.97/5.21 ! [C: complex,B: complex] :
% 4.97/5.21 ( ( C
% 4.97/5.21 = ( times_times_complex @ B @ C ) )
% 4.97/5.21 = ( ( C = zero_zero_complex )
% 4.97/5.21 | ( B = one_one_complex ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right1
% 4.97/5.21 thf(fact_2156_mult__cancel__right2,axiom,
% 4.97/5.21 ! [A: real,C: real] :
% 4.97/5.21 ( ( ( times_times_real @ A @ C )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_real )
% 4.97/5.21 | ( A = one_one_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right2
% 4.97/5.21 thf(fact_2157_mult__cancel__right2,axiom,
% 4.97/5.21 ! [A: rat,C: rat] :
% 4.97/5.21 ( ( ( times_times_rat @ A @ C )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_rat )
% 4.97/5.21 | ( A = one_one_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right2
% 4.97/5.21 thf(fact_2158_mult__cancel__right2,axiom,
% 4.97/5.21 ! [A: int,C: int] :
% 4.97/5.21 ( ( ( times_times_int @ A @ C )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_int )
% 4.97/5.21 | ( A = one_one_int ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right2
% 4.97/5.21 thf(fact_2159_mult__cancel__right2,axiom,
% 4.97/5.21 ! [A: complex,C: complex] :
% 4.97/5.21 ( ( ( times_times_complex @ A @ C )
% 4.97/5.21 = C )
% 4.97/5.21 = ( ( C = zero_zero_complex )
% 4.97/5.21 | ( A = one_one_complex ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_cancel_right2
% 4.97/5.21 thf(fact_2160_less__neg__neg,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_neg_neg
% 4.97/5.21 thf(fact_2161_less__neg__neg,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_neg_neg
% 4.97/5.21 thf(fact_2162_less__neg__neg,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_neg_neg
% 4.97/5.21 thf(fact_2163_less__neg__neg,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_neg_neg
% 4.97/5.21 thf(fact_2164_neg__less__pos,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_pos
% 4.97/5.21 thf(fact_2165_neg__less__pos,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 4.97/5.21 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_pos
% 4.97/5.21 thf(fact_2166_neg__less__pos,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 4.97/5.21 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_pos
% 4.97/5.21 thf(fact_2167_neg__less__pos,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_pos
% 4.97/5.21 thf(fact_2168_neg__0__less__iff__less,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_less_iff_less
% 4.97/5.21 thf(fact_2169_neg__0__less__iff__less,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 4.97/5.21 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_less_iff_less
% 4.97/5.21 thf(fact_2170_neg__0__less__iff__less,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_less_iff_less
% 4.97/5.21 thf(fact_2171_neg__0__less__iff__less,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_0_less_iff_less
% 4.97/5.21 thf(fact_2172_neg__less__0__iff__less,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_0_iff_less
% 4.97/5.21 thf(fact_2173_neg__less__0__iff__less,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 4.97/5.21 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_0_iff_less
% 4.97/5.21 thf(fact_2174_neg__less__0__iff__less,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 4.97/5.21 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_0_iff_less
% 4.97/5.21 thf(fact_2175_neg__less__0__iff__less,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % neg_less_0_iff_less
% 4.97/5.21 thf(fact_2176_diff__add__zero,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % diff_add_zero
% 4.97/5.21 thf(fact_2177_diff__numeral__special_I9_J,axiom,
% 4.97/5.21 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(9)
% 4.97/5.21 thf(fact_2178_diff__numeral__special_I9_J,axiom,
% 4.97/5.21 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(9)
% 4.97/5.21 thf(fact_2179_diff__numeral__special_I9_J,axiom,
% 4.97/5.21 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(9)
% 4.97/5.21 thf(fact_2180_diff__numeral__special_I9_J,axiom,
% 4.97/5.21 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(9)
% 4.97/5.21 thf(fact_2181_div__mult__mult1__if,axiom,
% 4.97/5.21 ! [C: nat,A: nat,B: nat] :
% 4.97/5.21 ( ( ( C = zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.97/5.21 = zero_zero_nat ) )
% 4.97/5.21 & ( ( C != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.97/5.21 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult1_if
% 4.97/5.21 thf(fact_2182_div__mult__mult1__if,axiom,
% 4.97/5.21 ! [C: int,A: int,B: int] :
% 4.97/5.21 ( ( ( C = zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.97/5.21 = zero_zero_int ) )
% 4.97/5.21 & ( ( C != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.97/5.21 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult1_if
% 4.97/5.21 thf(fact_2183_div__mult__mult2,axiom,
% 4.97/5.21 ! [C: nat,A: nat,B: nat] :
% 4.97/5.21 ( ( C != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.97/5.21 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult2
% 4.97/5.21 thf(fact_2184_div__mult__mult2,axiom,
% 4.97/5.21 ! [C: int,A: int,B: int] :
% 4.97/5.21 ( ( C != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.97/5.21 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult2
% 4.97/5.21 thf(fact_2185_div__mult__mult1,axiom,
% 4.97/5.21 ! [C: nat,A: nat,B: nat] :
% 4.97/5.21 ( ( C != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.97/5.21 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult1
% 4.97/5.21 thf(fact_2186_div__mult__mult1,axiom,
% 4.97/5.21 ! [C: int,A: int,B: int] :
% 4.97/5.21 ( ( C != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.97/5.21 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_mult1
% 4.97/5.21 thf(fact_2187_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.97/5.21 ! [C: complex,A: complex,B: complex] :
% 4.97/5.21 ( ( C != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right2
% 4.97/5.21 thf(fact_2188_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.97/5.21 ! [C: real,A: real,B: real] :
% 4.97/5.21 ( ( C != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 4.97/5.21 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right2
% 4.97/5.21 thf(fact_2189_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.97/5.21 ! [C: rat,A: rat,B: rat] :
% 4.97/5.21 ( ( C != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right2
% 4.97/5.21 thf(fact_2190_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [C: complex,A: complex,B: complex] :
% 4.97/5.21 ( ( C != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2191_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [C: real,A: real,B: real] :
% 4.97/5.21 ( ( C != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.97/5.21 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2192_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [C: rat,A: rat,B: rat] :
% 4.97/5.21 ( ( C != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2193_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: complex,A: complex,B: complex] :
% 4.97/5.21 ( ( C != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left2
% 4.97/5.21 thf(fact_2194_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: real,A: real,B: real] :
% 4.97/5.21 ( ( C != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 4.97/5.21 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left2
% 4.97/5.21 thf(fact_2195_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.97/5.21 ! [C: rat,A: rat,B: rat] :
% 4.97/5.21 ( ( C != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left2
% 4.97/5.21 thf(fact_2196_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [C: complex,A: complex,B: complex] :
% 4.97/5.21 ( ( C != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2197_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [C: real,A: real,B: real] :
% 4.97/5.21 ( ( C != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.97/5.21 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2198_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [C: rat,A: rat,B: rat] :
% 4.97/5.21 ( ( C != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2199_mult__divide__mult__cancel__left__if,axiom,
% 4.97/5.21 ! [C: complex,A: complex,B: complex] :
% 4.97/5.21 ( ( ( C = zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.97/5.21 = zero_zero_complex ) )
% 4.97/5.21 & ( ( C != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_divide_mult_cancel_left_if
% 4.97/5.21 thf(fact_2200_mult__divide__mult__cancel__left__if,axiom,
% 4.97/5.21 ! [C: real,A: real,B: real] :
% 4.97/5.21 ( ( ( C = zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.97/5.21 = zero_zero_real ) )
% 4.97/5.21 & ( ( C != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.97/5.21 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_divide_mult_cancel_left_if
% 4.97/5.21 thf(fact_2201_mult__divide__mult__cancel__left__if,axiom,
% 4.97/5.21 ! [C: rat,A: rat,B: rat] :
% 4.97/5.21 ( ( ( C = zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.97/5.21 = zero_zero_rat ) )
% 4.97/5.21 & ( ( C != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_divide_mult_cancel_left_if
% 4.97/5.21 thf(fact_2202_nonzero__mult__div__cancel__right,axiom,
% 4.97/5.21 ! [B: complex,A: complex] :
% 4.97/5.21 ( ( B != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 4.97/5.21 = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_right
% 4.97/5.21 thf(fact_2203_nonzero__mult__div__cancel__right,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( B != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 4.97/5.21 = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_right
% 4.97/5.21 thf(fact_2204_nonzero__mult__div__cancel__right,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( B != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 4.97/5.21 = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_right
% 4.97/5.21 thf(fact_2205_nonzero__mult__div__cancel__right,axiom,
% 4.97/5.21 ! [B: nat,A: nat] :
% 4.97/5.21 ( ( B != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.97/5.21 = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_right
% 4.97/5.21 thf(fact_2206_nonzero__mult__div__cancel__right,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( B != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 4.97/5.21 = A ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_right
% 4.97/5.21 thf(fact_2207_nonzero__mult__div__cancel__left,axiom,
% 4.97/5.21 ! [A: complex,B: complex] :
% 4.97/5.21 ( ( A != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 4.97/5.21 = B ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_left
% 4.97/5.21 thf(fact_2208_nonzero__mult__div__cancel__left,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( A != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 4.97/5.21 = B ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_left
% 4.97/5.21 thf(fact_2209_nonzero__mult__div__cancel__left,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( A != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 4.97/5.21 = B ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_left
% 4.97/5.21 thf(fact_2210_nonzero__mult__div__cancel__left,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( A != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 4.97/5.21 = B ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_left
% 4.97/5.21 thf(fact_2211_nonzero__mult__div__cancel__left,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( A != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 4.97/5.21 = B ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_mult_div_cancel_left
% 4.97/5.21 thf(fact_2212_divide__eq__1__iff,axiom,
% 4.97/5.21 ! [A: complex,B: complex] :
% 4.97/5.21 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.97/5.21 = one_one_complex )
% 4.97/5.21 = ( ( B != zero_zero_complex )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_1_iff
% 4.97/5.21 thf(fact_2213_divide__eq__1__iff,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ( divide_divide_real @ A @ B )
% 4.97/5.21 = one_one_real )
% 4.97/5.21 = ( ( B != zero_zero_real )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_1_iff
% 4.97/5.21 thf(fact_2214_divide__eq__1__iff,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ( divide_divide_rat @ A @ B )
% 4.97/5.21 = one_one_rat )
% 4.97/5.21 = ( ( B != zero_zero_rat )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_1_iff
% 4.97/5.21 thf(fact_2215_one__eq__divide__iff,axiom,
% 4.97/5.21 ! [A: complex,B: complex] :
% 4.97/5.21 ( ( one_one_complex
% 4.97/5.21 = ( divide1717551699836669952omplex @ A @ B ) )
% 4.97/5.21 = ( ( B != zero_zero_complex )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_eq_divide_iff
% 4.97/5.21 thf(fact_2216_one__eq__divide__iff,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( one_one_real
% 4.97/5.21 = ( divide_divide_real @ A @ B ) )
% 4.97/5.21 = ( ( B != zero_zero_real )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_eq_divide_iff
% 4.97/5.21 thf(fact_2217_one__eq__divide__iff,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( one_one_rat
% 4.97/5.21 = ( divide_divide_rat @ A @ B ) )
% 4.97/5.21 = ( ( B != zero_zero_rat )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_eq_divide_iff
% 4.97/5.21 thf(fact_2218_divide__self,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( A != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.97/5.21 = one_one_complex ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self
% 4.97/5.21 thf(fact_2219_divide__self,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( A != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ A @ A )
% 4.97/5.21 = one_one_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self
% 4.97/5.21 thf(fact_2220_divide__self,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( A != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ A @ A )
% 4.97/5.21 = one_one_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self
% 4.97/5.21 thf(fact_2221_divide__self__if,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( ( A = zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.97/5.21 = zero_zero_complex ) )
% 4.97/5.21 & ( ( A != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.97/5.21 = one_one_complex ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self_if
% 4.97/5.21 thf(fact_2222_divide__self__if,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ( A = zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ A @ A )
% 4.97/5.21 = zero_zero_real ) )
% 4.97/5.21 & ( ( A != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ A @ A )
% 4.97/5.21 = one_one_real ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self_if
% 4.97/5.21 thf(fact_2223_divide__self__if,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ( A = zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ A @ A )
% 4.97/5.21 = zero_zero_rat ) )
% 4.97/5.21 & ( ( A != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ A @ A )
% 4.97/5.21 = one_one_rat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_self_if
% 4.97/5.21 thf(fact_2224_divide__eq__eq__1,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( ( divide_divide_real @ B @ A )
% 4.97/5.21 = one_one_real )
% 4.97/5.21 = ( ( A != zero_zero_real )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_eq_1
% 4.97/5.21 thf(fact_2225_divide__eq__eq__1,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( ( divide_divide_rat @ B @ A )
% 4.97/5.21 = one_one_rat )
% 4.97/5.21 = ( ( A != zero_zero_rat )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_eq_1
% 4.97/5.21 thf(fact_2226_eq__divide__eq__1,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( one_one_real
% 4.97/5.21 = ( divide_divide_real @ B @ A ) )
% 4.97/5.21 = ( ( A != zero_zero_real )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % eq_divide_eq_1
% 4.97/5.21 thf(fact_2227_eq__divide__eq__1,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( one_one_rat
% 4.97/5.21 = ( divide_divide_rat @ B @ A ) )
% 4.97/5.21 = ( ( A != zero_zero_rat )
% 4.97/5.21 & ( A = B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % eq_divide_eq_1
% 4.97/5.21 thf(fact_2228_one__divide__eq__0__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ( divide_divide_real @ one_one_real @ A )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 = ( A = zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_divide_eq_0_iff
% 4.97/5.21 thf(fact_2229_one__divide__eq__0__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 = ( A = zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_divide_eq_0_iff
% 4.97/5.21 thf(fact_2230_zero__eq__1__divide__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( zero_zero_real
% 4.97/5.21 = ( divide_divide_real @ one_one_real @ A ) )
% 4.97/5.21 = ( A = zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_eq_1_divide_iff
% 4.97/5.21 thf(fact_2231_zero__eq__1__divide__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( zero_zero_rat
% 4.97/5.21 = ( divide_divide_rat @ one_one_rat @ A ) )
% 4.97/5.21 = ( A = zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_eq_1_divide_iff
% 4.97/5.21 thf(fact_2232_div__self,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( A != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.97/5.21 = one_one_complex ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_self
% 4.97/5.21 thf(fact_2233_div__self,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( A != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ A @ A )
% 4.97/5.21 = one_one_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_self
% 4.97/5.21 thf(fact_2234_div__self,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( A != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ A @ A )
% 4.97/5.21 = one_one_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_self
% 4.97/5.21 thf(fact_2235_div__self,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( A != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ A @ A )
% 4.97/5.21 = one_one_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_self
% 4.97/5.21 thf(fact_2236_div__self,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( A != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ A @ A )
% 4.97/5.21 = one_one_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_self
% 4.97/5.21 thf(fact_2237_ab__left__minus,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % ab_left_minus
% 4.97/5.21 thf(fact_2238_ab__left__minus,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % ab_left_minus
% 4.97/5.21 thf(fact_2239_ab__left__minus,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % ab_left_minus
% 4.97/5.21 thf(fact_2240_ab__left__minus,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % ab_left_minus
% 4.97/5.21 thf(fact_2241_ab__left__minus,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % ab_left_minus
% 4.97/5.21 thf(fact_2242_add_Oright__inverse,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % add.right_inverse
% 4.97/5.21 thf(fact_2243_add_Oright__inverse,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % add.right_inverse
% 4.97/5.21 thf(fact_2244_add_Oright__inverse,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % add.right_inverse
% 4.97/5.21 thf(fact_2245_add_Oright__inverse,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % add.right_inverse
% 4.97/5.21 thf(fact_2246_add_Oright__inverse,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % add.right_inverse
% 4.97/5.21 thf(fact_2247_diff__0,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( minus_minus_real @ zero_zero_real @ A )
% 4.97/5.21 = ( uminus_uminus_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0
% 4.97/5.21 thf(fact_2248_diff__0,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( minus_minus_int @ zero_zero_int @ A )
% 4.97/5.21 = ( uminus_uminus_int @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0
% 4.97/5.21 thf(fact_2249_diff__0,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 4.97/5.21 = ( uminus1482373934393186551omplex @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0
% 4.97/5.21 thf(fact_2250_diff__0,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 4.97/5.21 = ( uminus1351360451143612070nteger @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0
% 4.97/5.21 thf(fact_2251_diff__0,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 4.97/5.21 = ( uminus_uminus_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_0
% 4.97/5.21 thf(fact_2252_power__0__Suc,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % power_0_Suc
% 4.97/5.21 thf(fact_2253_power__0__Suc,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % power_0_Suc
% 4.97/5.21 thf(fact_2254_power__0__Suc,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % power_0_Suc
% 4.97/5.21 thf(fact_2255_power__0__Suc,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % power_0_Suc
% 4.97/5.21 thf(fact_2256_power__0__Suc,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % power_0_Suc
% 4.97/5.21 thf(fact_2257_power__zero__numeral,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % power_zero_numeral
% 4.97/5.21 thf(fact_2258_power__zero__numeral,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % power_zero_numeral
% 4.97/5.21 thf(fact_2259_power__zero__numeral,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % power_zero_numeral
% 4.97/5.21 thf(fact_2260_power__zero__numeral,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % power_zero_numeral
% 4.97/5.21 thf(fact_2261_power__zero__numeral,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % power_zero_numeral
% 4.97/5.21 thf(fact_2262_mod__mult__self1__is__0,axiom,
% 4.97/5.21 ! [B: nat,A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1_is_0
% 4.97/5.21 thf(fact_2263_mod__mult__self1__is__0,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1_is_0
% 4.97/5.21 thf(fact_2264_mod__mult__self1__is__0,axiom,
% 4.97/5.21 ! [B: code_integer,A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1_is_0
% 4.97/5.21 thf(fact_2265_mod__mult__self2__is__0,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2_is_0
% 4.97/5.21 thf(fact_2266_mod__mult__self2__is__0,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2_is_0
% 4.97/5.21 thf(fact_2267_mod__mult__self2__is__0,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2_is_0
% 4.97/5.21 thf(fact_2268_bits__mod__by__1,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_by_1
% 4.97/5.21 thf(fact_2269_bits__mod__by__1,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_by_1
% 4.97/5.21 thf(fact_2270_bits__mod__by__1,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_by_1
% 4.97/5.21 thf(fact_2271_mod__by__1,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_1
% 4.97/5.21 thf(fact_2272_mod__by__1,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_1
% 4.97/5.21 thf(fact_2273_mod__by__1,axiom,
% 4.97/5.21 ! [A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_1
% 4.97/5.21 thf(fact_2274_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri681578069525770553at_rat @ M )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2275_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri5074537144036343181t_real @ M )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2276_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri1314217659103216013at_int @ M )
% 4.97/5.21 = zero_zero_int )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2277_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri8010041392384452111omplex @ M )
% 4.97/5.21 = zero_zero_complex )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2278_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri1316708129612266289at_nat @ M )
% 4.97/5.21 = zero_zero_nat )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2279_of__nat__eq__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ( semiri4939895301339042750nteger @ M )
% 4.97/5.21 = zero_z3403309356797280102nteger )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_eq_0_iff
% 4.97/5.21 thf(fact_2280_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_zero_rat
% 4.97/5.21 = ( semiri681578069525770553at_rat @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2281_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_zero_real
% 4.97/5.21 = ( semiri5074537144036343181t_real @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2282_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_zero_int
% 4.97/5.21 = ( semiri1314217659103216013at_int @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2283_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_zero_complex
% 4.97/5.21 = ( semiri8010041392384452111omplex @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2284_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_zero_nat
% 4.97/5.21 = ( semiri1316708129612266289at_nat @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2285_of__nat__0__eq__iff,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( zero_z3403309356797280102nteger
% 4.97/5.21 = ( semiri4939895301339042750nteger @ N ) )
% 4.97/5.21 = ( zero_zero_nat = N ) ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0_eq_iff
% 4.97/5.21 thf(fact_2286_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2287_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2288_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2289_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2290_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2291_of__nat__0,axiom,
% 4.97/5.21 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % of_nat_0
% 4.97/5.21 thf(fact_2292_mod__div__trivial,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_div_trivial
% 4.97/5.21 thf(fact_2293_mod__div__trivial,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % mod_div_trivial
% 4.97/5.21 thf(fact_2294_mod__div__trivial,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % mod_div_trivial
% 4.97/5.21 thf(fact_2295_bits__mod__div__trivial,axiom,
% 4.97/5.21 ! [A: nat,B: nat] :
% 4.97/5.21 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_div_trivial
% 4.97/5.21 thf(fact_2296_bits__mod__div__trivial,axiom,
% 4.97/5.21 ! [A: int,B: int] :
% 4.97/5.21 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_div_trivial
% 4.97/5.21 thf(fact_2297_bits__mod__div__trivial,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer] :
% 4.97/5.21 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % bits_mod_div_trivial
% 4.97/5.21 thf(fact_2298_mod__mult__self4,axiom,
% 4.97/5.21 ! [B: nat,C: nat,A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self4
% 4.97/5.21 thf(fact_2299_mod__mult__self4,axiom,
% 4.97/5.21 ! [B: int,C: int,A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self4
% 4.97/5.21 thf(fact_2300_mod__mult__self4,axiom,
% 4.97/5.21 ! [B: code_integer,C: code_integer,A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self4
% 4.97/5.21 thf(fact_2301_mod__mult__self3,axiom,
% 4.97/5.21 ! [C: nat,B: nat,A: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self3
% 4.97/5.21 thf(fact_2302_mod__mult__self3,axiom,
% 4.97/5.21 ! [C: int,B: int,A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self3
% 4.97/5.21 thf(fact_2303_mod__mult__self3,axiom,
% 4.97/5.21 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self3
% 4.97/5.21 thf(fact_2304_mod__mult__self2,axiom,
% 4.97/5.21 ! [A: nat,B: nat,C: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2
% 4.97/5.21 thf(fact_2305_mod__mult__self2,axiom,
% 4.97/5.21 ! [A: int,B: int,C: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2
% 4.97/5.21 thf(fact_2306_mod__mult__self2,axiom,
% 4.97/5.21 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self2
% 4.97/5.21 thf(fact_2307_mod__mult__self1,axiom,
% 4.97/5.21 ! [A: nat,C: nat,B: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 4.97/5.21 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1
% 4.97/5.21 thf(fact_2308_mod__mult__self1,axiom,
% 4.97/5.21 ! [A: int,C: int,B: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1
% 4.97/5.21 thf(fact_2309_mod__mult__self1,axiom,
% 4.97/5.21 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % mod_mult_self1
% 4.97/5.21 thf(fact_2310_power__Suc0__right,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % power_Suc0_right
% 4.97/5.21 thf(fact_2311_power__Suc0__right,axiom,
% 4.97/5.21 ! [A: nat] :
% 4.97/5.21 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % power_Suc0_right
% 4.97/5.21 thf(fact_2312_power__Suc0__right,axiom,
% 4.97/5.21 ! [A: int] :
% 4.97/5.21 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % power_Suc0_right
% 4.97/5.21 thf(fact_2313_power__Suc0__right,axiom,
% 4.97/5.21 ! [A: complex] :
% 4.97/5.21 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = A ) ).
% 4.97/5.21
% 4.97/5.21 % power_Suc0_right
% 4.97/5.21 thf(fact_2314_zero__less__Suc,axiom,
% 4.97/5.21 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_Suc
% 4.97/5.21 thf(fact_2315_less__Suc0,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = ( N = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_Suc0
% 4.97/5.21 thf(fact_2316_minus__mod__self1,axiom,
% 4.97/5.21 ! [B: int,A: int] :
% 4.97/5.21 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 4.97/5.21 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % minus_mod_self1
% 4.97/5.21 thf(fact_2317_minus__mod__self1,axiom,
% 4.97/5.21 ! [B: code_integer,A: code_integer] :
% 4.97/5.21 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 4.97/5.21 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 4.97/5.21
% 4.97/5.21 % minus_mod_self1
% 4.97/5.21 thf(fact_2318_add__gr__0,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 4.97/5.21 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.97/5.21 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % add_gr_0
% 4.97/5.21 thf(fact_2319_mult__eq__1__iff,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ( times_times_nat @ M @ N )
% 4.97/5.21 = ( suc @ zero_zero_nat ) )
% 4.97/5.21 = ( ( M
% 4.97/5.21 = ( suc @ zero_zero_nat ) )
% 4.97/5.21 & ( N
% 4.97/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_eq_1_iff
% 4.97/5.21 thf(fact_2320_one__eq__mult__iff,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ( suc @ zero_zero_nat )
% 4.97/5.21 = ( times_times_nat @ M @ N ) )
% 4.97/5.21 = ( ( M
% 4.97/5.21 = ( suc @ zero_zero_nat ) )
% 4.97/5.21 & ( N
% 4.97/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % one_eq_mult_iff
% 4.97/5.21 thf(fact_2321_zero__less__diff,axiom,
% 4.97/5.21 ! [N: nat,M: nat] :
% 4.97/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 4.97/5.21 = ( ord_less_nat @ M @ N ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_diff
% 4.97/5.21 thf(fact_2322_nat__0__less__mult__iff,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 4.97/5.21 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.97/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nat_0_less_mult_iff
% 4.97/5.21 thf(fact_2323_mult__less__cancel2,axiom,
% 4.97/5.21 ! [M: nat,K: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 4.97/5.21 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.97/5.21 & ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % mult_less_cancel2
% 4.97/5.21 thf(fact_2324_nat__mult__less__cancel__disj,axiom,
% 4.97/5.21 ! [K: nat,M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 4.97/5.21 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.97/5.21 & ( ord_less_nat @ M @ N ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nat_mult_less_cancel_disj
% 4.97/5.21 thf(fact_2325_diff__is__0__eq,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ( minus_minus_nat @ M @ N )
% 4.97/5.21 = zero_zero_nat )
% 4.97/5.21 = ( ord_less_eq_nat @ M @ N ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_is_0_eq
% 4.97/5.21 thf(fact_2326_diff__is__0__eq_H,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_eq_nat @ M @ N )
% 4.97/5.21 => ( ( minus_minus_nat @ M @ N )
% 4.97/5.21 = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % diff_is_0_eq'
% 4.97/5.21 thf(fact_2327_less__one,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ N @ one_one_nat )
% 4.97/5.21 = ( N = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_one
% 4.97/5.21 thf(fact_2328_div__by__Suc__0,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = M ) ).
% 4.97/5.21
% 4.97/5.21 % div_by_Suc_0
% 4.97/5.21 thf(fact_2329_nat__power__eq__Suc__0__iff,axiom,
% 4.97/5.21 ! [X2: nat,M: nat] :
% 4.97/5.21 ( ( ( power_power_nat @ X2 @ M )
% 4.97/5.21 = ( suc @ zero_zero_nat ) )
% 4.97/5.21 = ( ( M = zero_zero_nat )
% 4.97/5.21 | ( X2
% 4.97/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nat_power_eq_Suc_0_iff
% 4.97/5.21 thf(fact_2330_power__Suc__0,axiom,
% 4.97/5.21 ! [N: nat] :
% 4.97/5.21 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 4.97/5.21 = ( suc @ zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % power_Suc_0
% 4.97/5.21 thf(fact_2331_div__less,axiom,
% 4.97/5.21 ! [M: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ M @ N )
% 4.97/5.21 => ( ( divide_divide_nat @ M @ N )
% 4.97/5.21 = zero_zero_nat ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_less
% 4.97/5.21 thf(fact_2332_nat__zero__less__power__iff,axiom,
% 4.97/5.21 ! [X2: nat,N: nat] :
% 4.97/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 4.97/5.21 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 4.97/5.21 | ( N = zero_zero_nat ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nat_zero_less_power_iff
% 4.97/5.21 thf(fact_2333_mod__by__Suc__0,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 4.97/5.21 = zero_zero_nat ) ).
% 4.97/5.21
% 4.97/5.21 % mod_by_Suc_0
% 4.97/5.21 thf(fact_2334_nat__mult__div__cancel__disj,axiom,
% 4.97/5.21 ! [K: nat,M: nat,N: nat] :
% 4.97/5.21 ( ( ( K = zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 4.97/5.21 = zero_zero_nat ) )
% 4.97/5.21 & ( ( K != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 4.97/5.21 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nat_mult_div_cancel_disj
% 4.97/5.21 thf(fact_2335_dbl__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 4.97/5.21 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(5)
% 4.97/5.21 thf(fact_2336_dbl__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 4.97/5.21 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(5)
% 4.97/5.21 thf(fact_2337_dbl__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 4.97/5.21 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(5)
% 4.97/5.21 thf(fact_2338_dbl__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 4.97/5.21 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(5)
% 4.97/5.21 thf(fact_2339_dbl__simps_I1_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 4.97/5.21 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(1)
% 4.97/5.21 thf(fact_2340_dbl__simps_I1_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 4.97/5.21 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(1)
% 4.97/5.21 thf(fact_2341_dbl__simps_I1_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 4.97/5.21 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(1)
% 4.97/5.21 thf(fact_2342_dbl__simps_I1_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 4.97/5.21 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(1)
% 4.97/5.21 thf(fact_2343_dbl__simps_I1_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 4.97/5.21 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_simps(1)
% 4.97/5.21 thf(fact_2344_dbl__inc__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 4.97/5.21 = one_one_complex ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(2)
% 4.97/5.21 thf(fact_2345_dbl__inc__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 4.97/5.21 = one_one_real ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(2)
% 4.97/5.21 thf(fact_2346_dbl__inc__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 4.97/5.21 = one_one_rat ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(2)
% 4.97/5.21 thf(fact_2347_dbl__inc__simps_I2_J,axiom,
% 4.97/5.21 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 4.97/5.21 = one_one_int ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(2)
% 4.97/5.21 thf(fact_2348_dbl__inc__simps_I4_J,axiom,
% 4.97/5.21 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.21 = ( uminus_uminus_real @ one_one_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(4)
% 4.97/5.21 thf(fact_2349_dbl__inc__simps_I4_J,axiom,
% 4.97/5.21 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.21 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(4)
% 4.97/5.21 thf(fact_2350_dbl__inc__simps_I4_J,axiom,
% 4.97/5.21 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.21 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(4)
% 4.97/5.21 thf(fact_2351_dbl__inc__simps_I4_J,axiom,
% 4.97/5.21 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.21 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(4)
% 4.97/5.21 thf(fact_2352_dbl__inc__simps_I4_J,axiom,
% 4.97/5.21 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.21 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(4)
% 4.97/5.21 thf(fact_2353_dbl__inc__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 4.97/5.21 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(5)
% 4.97/5.21 thf(fact_2354_dbl__inc__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 4.97/5.21 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(5)
% 4.97/5.21 thf(fact_2355_dbl__inc__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 4.97/5.21 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(5)
% 4.97/5.21 thf(fact_2356_dbl__inc__simps_I5_J,axiom,
% 4.97/5.21 ! [K: num] :
% 4.97/5.21 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 4.97/5.21 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % dbl_inc_simps(5)
% 4.97/5.21 thf(fact_2357_divide__le__0__1__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_le_0_1_iff
% 4.97/5.21 thf(fact_2358_divide__le__0__1__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_le_0_1_iff
% 4.97/5.21 thf(fact_2359_zero__le__divide__1__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.97/5.21 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_le_divide_1_iff
% 4.97/5.21 thf(fact_2360_zero__le__divide__1__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.97/5.21 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_le_divide_1_iff
% 4.97/5.21 thf(fact_2361_divide__less__0__1__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.97/5.21 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_0_1_iff
% 4.97/5.21 thf(fact_2362_divide__less__0__1__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.97/5.21 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_0_1_iff
% 4.97/5.21 thf(fact_2363_divide__less__eq__1__neg,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ A @ zero_zero_real )
% 4.97/5.21 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.97/5.21 = ( ord_less_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_eq_1_neg
% 4.97/5.21 thf(fact_2364_divide__less__eq__1__neg,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.97/5.21 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.97/5.21 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_eq_1_neg
% 4.97/5.21 thf(fact_2365_divide__less__eq__1__pos,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.97/5.21 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.97/5.21 = ( ord_less_real @ B @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_eq_1_pos
% 4.97/5.21 thf(fact_2366_divide__less__eq__1__pos,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.97/5.21 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.97/5.21 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_less_eq_1_pos
% 4.97/5.21 thf(fact_2367_less__divide__eq__1__neg,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ A @ zero_zero_real )
% 4.97/5.21 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.97/5.21 = ( ord_less_real @ B @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_divide_eq_1_neg
% 4.97/5.21 thf(fact_2368_less__divide__eq__1__neg,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.97/5.21 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.97/5.21 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_divide_eq_1_neg
% 4.97/5.21 thf(fact_2369_less__divide__eq__1__pos,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.97/5.21 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.97/5.21 = ( ord_less_real @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_divide_eq_1_pos
% 4.97/5.21 thf(fact_2370_less__divide__eq__1__pos,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.97/5.21 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.97/5.21 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % less_divide_eq_1_pos
% 4.97/5.21 thf(fact_2371_zero__less__divide__1__iff,axiom,
% 4.97/5.21 ! [A: real] :
% 4.97/5.21 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.97/5.21 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_divide_1_iff
% 4.97/5.21 thf(fact_2372_zero__less__divide__1__iff,axiom,
% 4.97/5.21 ! [A: rat] :
% 4.97/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.97/5.21 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.97/5.21
% 4.97/5.21 % zero_less_divide_1_iff
% 4.97/5.21 thf(fact_2373_eq__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [A: complex,B: complex,W: num] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 4.97/5.21 = ( ( ( ( numera6690914467698888265omplex @ W )
% 4.97/5.21 != zero_zero_complex )
% 4.97/5.21 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 4.97/5.21 = B ) )
% 4.97/5.21 & ( ( ( numera6690914467698888265omplex @ W )
% 4.97/5.21 = zero_zero_complex )
% 4.97/5.21 => ( A = zero_zero_complex ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % eq_divide_eq_numeral1(1)
% 4.97/5.21 thf(fact_2374_eq__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [A: real,B: real,W: num] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.97/5.21 = ( ( ( ( numeral_numeral_real @ W )
% 4.97/5.21 != zero_zero_real )
% 4.97/5.21 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 4.97/5.21 = B ) )
% 4.97/5.21 & ( ( ( numeral_numeral_real @ W )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 => ( A = zero_zero_real ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % eq_divide_eq_numeral1(1)
% 4.97/5.21 thf(fact_2375_eq__divide__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [A: rat,B: rat,W: num] :
% 4.97/5.21 ( ( A
% 4.97/5.21 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.97/5.21 = ( ( ( ( numeral_numeral_rat @ W )
% 4.97/5.21 != zero_zero_rat )
% 4.97/5.21 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 4.97/5.21 = B ) )
% 4.97/5.21 & ( ( ( numeral_numeral_rat @ W )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 => ( A = zero_zero_rat ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % eq_divide_eq_numeral1(1)
% 4.97/5.21 thf(fact_2376_divide__eq__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [B: complex,W: num,A: complex] :
% 4.97/5.21 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 4.97/5.21 = A )
% 4.97/5.21 = ( ( ( ( numera6690914467698888265omplex @ W )
% 4.97/5.21 != zero_zero_complex )
% 4.97/5.21 => ( B
% 4.97/5.21 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 4.97/5.21 & ( ( ( numera6690914467698888265omplex @ W )
% 4.97/5.21 = zero_zero_complex )
% 4.97/5.21 => ( A = zero_zero_complex ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_eq_numeral1(1)
% 4.97/5.21 thf(fact_2377_divide__eq__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [B: real,W: num,A: real] :
% 4.97/5.21 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 4.97/5.21 = A )
% 4.97/5.21 = ( ( ( ( numeral_numeral_real @ W )
% 4.97/5.21 != zero_zero_real )
% 4.97/5.21 => ( B
% 4.97/5.21 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 4.97/5.21 & ( ( ( numeral_numeral_real @ W )
% 4.97/5.21 = zero_zero_real )
% 4.97/5.21 => ( A = zero_zero_real ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_eq_numeral1(1)
% 4.97/5.21 thf(fact_2378_divide__eq__eq__numeral1_I1_J,axiom,
% 4.97/5.21 ! [B: rat,W: num,A: rat] :
% 4.97/5.21 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 4.97/5.21 = A )
% 4.97/5.21 = ( ( ( ( numeral_numeral_rat @ W )
% 4.97/5.21 != zero_zero_rat )
% 4.97/5.21 => ( B
% 4.97/5.21 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 4.97/5.21 & ( ( ( numeral_numeral_rat @ W )
% 4.97/5.21 = zero_zero_rat )
% 4.97/5.21 => ( A = zero_zero_rat ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % divide_eq_eq_numeral1(1)
% 4.97/5.21 thf(fact_2379_div__mult__self4,axiom,
% 4.97/5.21 ! [B: nat,C: nat,A: nat] :
% 4.97/5.21 ( ( B != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 4.97/5.21 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self4
% 4.97/5.21 thf(fact_2380_div__mult__self4,axiom,
% 4.97/5.21 ! [B: int,C: int,A: int] :
% 4.97/5.21 ( ( B != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 4.97/5.21 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self4
% 4.97/5.21 thf(fact_2381_div__mult__self3,axiom,
% 4.97/5.21 ! [B: nat,C: nat,A: nat] :
% 4.97/5.21 ( ( B != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 4.97/5.21 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self3
% 4.97/5.21 thf(fact_2382_div__mult__self3,axiom,
% 4.97/5.21 ! [B: int,C: int,A: int] :
% 4.97/5.21 ( ( B != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 4.97/5.21 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self3
% 4.97/5.21 thf(fact_2383_div__mult__self2,axiom,
% 4.97/5.21 ! [B: nat,A: nat,C: nat] :
% 4.97/5.21 ( ( B != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 4.97/5.21 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self2
% 4.97/5.21 thf(fact_2384_div__mult__self2,axiom,
% 4.97/5.21 ! [B: int,A: int,C: int] :
% 4.97/5.21 ( ( B != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 4.97/5.21 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self2
% 4.97/5.21 thf(fact_2385_div__mult__self1,axiom,
% 4.97/5.21 ! [B: nat,A: nat,C: nat] :
% 4.97/5.21 ( ( B != zero_zero_nat )
% 4.97/5.21 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 4.97/5.21 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self1
% 4.97/5.21 thf(fact_2386_div__mult__self1,axiom,
% 4.97/5.21 ! [B: int,A: int,C: int] :
% 4.97/5.21 ( ( B != zero_zero_int )
% 4.97/5.21 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 4.97/5.21 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % div_mult_self1
% 4.97/5.21 thf(fact_2387_nonzero__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [A: complex,B: complex] :
% 4.97/5.21 ( ( A != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2388_nonzero__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [A: real,B: real] :
% 4.97/5.21 ( ( A != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 4.97/5.21 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2389_nonzero__divide__mult__cancel__left,axiom,
% 4.97/5.21 ! [A: rat,B: rat] :
% 4.97/5.21 ( ( A != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 4.97/5.21 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_left
% 4.97/5.21 thf(fact_2390_nonzero__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [B: complex,A: complex] :
% 4.97/5.21 ( ( B != zero_zero_complex )
% 4.97/5.21 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 4.97/5.21 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2391_nonzero__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [B: real,A: real] :
% 4.97/5.21 ( ( B != zero_zero_real )
% 4.97/5.21 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 4.97/5.21 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2392_nonzero__divide__mult__cancel__right,axiom,
% 4.97/5.21 ! [B: rat,A: rat] :
% 4.97/5.21 ( ( B != zero_zero_rat )
% 4.97/5.21 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 4.97/5.21 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 4.97/5.21
% 4.97/5.21 % nonzero_divide_mult_cancel_right
% 4.97/5.21 thf(fact_2393_add__neg__numeral__special_I8_J,axiom,
% 4.97/5.21 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(8)
% 4.97/5.21 thf(fact_2394_add__neg__numeral__special_I8_J,axiom,
% 4.97/5.21 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(8)
% 4.97/5.21 thf(fact_2395_add__neg__numeral__special_I8_J,axiom,
% 4.97/5.21 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(8)
% 4.97/5.21 thf(fact_2396_add__neg__numeral__special_I8_J,axiom,
% 4.97/5.21 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(8)
% 4.97/5.21 thf(fact_2397_add__neg__numeral__special_I8_J,axiom,
% 4.97/5.21 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(8)
% 4.97/5.21 thf(fact_2398_add__neg__numeral__special_I7_J,axiom,
% 4.97/5.21 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(7)
% 4.97/5.21 thf(fact_2399_add__neg__numeral__special_I7_J,axiom,
% 4.97/5.21 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(7)
% 4.97/5.21 thf(fact_2400_add__neg__numeral__special_I7_J,axiom,
% 4.97/5.21 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(7)
% 4.97/5.21 thf(fact_2401_add__neg__numeral__special_I7_J,axiom,
% 4.97/5.21 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(7)
% 4.97/5.21 thf(fact_2402_add__neg__numeral__special_I7_J,axiom,
% 4.97/5.21 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % add_neg_numeral_special(7)
% 4.97/5.21 thf(fact_2403_diff__numeral__special_I12_J,axiom,
% 4.97/5.21 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 4.97/5.21 = zero_zero_real ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(12)
% 4.97/5.21 thf(fact_2404_diff__numeral__special_I12_J,axiom,
% 4.97/5.21 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.97/5.21 = zero_zero_int ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(12)
% 4.97/5.21 thf(fact_2405_diff__numeral__special_I12_J,axiom,
% 4.97/5.21 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 4.97/5.21 = zero_zero_complex ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(12)
% 4.97/5.21 thf(fact_2406_diff__numeral__special_I12_J,axiom,
% 4.97/5.21 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.97/5.21 = zero_z3403309356797280102nteger ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(12)
% 4.97/5.21 thf(fact_2407_diff__numeral__special_I12_J,axiom,
% 4.97/5.21 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.97/5.21 = zero_zero_rat ) ).
% 4.97/5.21
% 4.97/5.21 % diff_numeral_special(12)
% 4.97/5.21 thf(fact_2408_of__nat__le__0__iff,axiom,
% 4.97/5.21 ! [M: nat] :
% 4.97/5.21 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 4.97/5.21 = ( M = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_le_0_iff
% 5.01/5.21 thf(fact_2409_of__nat__le__0__iff,axiom,
% 5.01/5.21 ! [M: nat] :
% 5.01/5.21 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 5.01/5.21 = ( M = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_le_0_iff
% 5.01/5.21 thf(fact_2410_of__nat__le__0__iff,axiom,
% 5.01/5.21 ! [M: nat] :
% 5.01/5.21 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.01/5.21 = ( M = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_le_0_iff
% 5.01/5.21 thf(fact_2411_of__nat__le__0__iff,axiom,
% 5.01/5.21 ! [M: nat] :
% 5.01/5.21 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.01/5.21 = ( M = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_le_0_iff
% 5.01/5.21 thf(fact_2412_of__nat__le__0__iff,axiom,
% 5.01/5.21 ! [M: nat] :
% 5.01/5.21 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.01/5.21 = ( M = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_le_0_iff
% 5.01/5.21 thf(fact_2413_power__eq__0__iff,axiom,
% 5.01/5.21 ! [A: rat,N: nat] :
% 5.01/5.21 ( ( ( power_power_rat @ A @ N )
% 5.01/5.21 = zero_zero_rat )
% 5.01/5.21 = ( ( A = zero_zero_rat )
% 5.01/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_eq_0_iff
% 5.01/5.21 thf(fact_2414_power__eq__0__iff,axiom,
% 5.01/5.21 ! [A: real,N: nat] :
% 5.01/5.21 ( ( ( power_power_real @ A @ N )
% 5.01/5.21 = zero_zero_real )
% 5.01/5.21 = ( ( A = zero_zero_real )
% 5.01/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_eq_0_iff
% 5.01/5.21 thf(fact_2415_power__eq__0__iff,axiom,
% 5.01/5.21 ! [A: nat,N: nat] :
% 5.01/5.21 ( ( ( power_power_nat @ A @ N )
% 5.01/5.21 = zero_zero_nat )
% 5.01/5.21 = ( ( A = zero_zero_nat )
% 5.01/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_eq_0_iff
% 5.01/5.21 thf(fact_2416_power__eq__0__iff,axiom,
% 5.01/5.21 ! [A: int,N: nat] :
% 5.01/5.21 ( ( ( power_power_int @ A @ N )
% 5.01/5.21 = zero_zero_int )
% 5.01/5.21 = ( ( A = zero_zero_int )
% 5.01/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_eq_0_iff
% 5.01/5.21 thf(fact_2417_power__eq__0__iff,axiom,
% 5.01/5.21 ! [A: complex,N: nat] :
% 5.01/5.21 ( ( ( power_power_complex @ A @ N )
% 5.01/5.21 = zero_zero_complex )
% 5.01/5.21 = ( ( A = zero_zero_complex )
% 5.01/5.21 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_eq_0_iff
% 5.01/5.21 thf(fact_2418_mod__minus1__right,axiom,
% 5.01/5.21 ! [A: int] :
% 5.01/5.21 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.21 = zero_zero_int ) ).
% 5.01/5.21
% 5.01/5.21 % mod_minus1_right
% 5.01/5.21 thf(fact_2419_mod__minus1__right,axiom,
% 5.01/5.21 ! [A: code_integer] :
% 5.01/5.21 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.21 = zero_z3403309356797280102nteger ) ).
% 5.01/5.21
% 5.01/5.21 % mod_minus1_right
% 5.01/5.21 thf(fact_2420_Suc__pred,axiom,
% 5.01/5.21 ! [N: nat] :
% 5.01/5.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.01/5.21 = N ) ) ).
% 5.01/5.21
% 5.01/5.21 % Suc_pred
% 5.01/5.21 thf(fact_2421_one__le__mult__iff,axiom,
% 5.01/5.21 ! [M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.01/5.21 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.01/5.21 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % one_le_mult_iff
% 5.01/5.21 thf(fact_2422_mult__le__cancel2,axiom,
% 5.01/5.21 ! [M: nat,K: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.01/5.21 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.21 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % mult_le_cancel2
% 5.01/5.21 thf(fact_2423_nat__mult__le__cancel__disj,axiom,
% 5.01/5.21 ! [K: nat,M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.21 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.21 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % nat_mult_le_cancel_disj
% 5.01/5.21 thf(fact_2424_div__mult__self1__is__m,axiom,
% 5.01/5.21 ! [N: nat,M: nat] :
% 5.01/5.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.01/5.21 = M ) ) ).
% 5.01/5.21
% 5.01/5.21 % div_mult_self1_is_m
% 5.01/5.21 thf(fact_2425_div__mult__self__is__m,axiom,
% 5.01/5.21 ! [N: nat,M: nat] :
% 5.01/5.21 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.01/5.21 = M ) ) ).
% 5.01/5.21
% 5.01/5.21 % div_mult_self_is_m
% 5.01/5.21 thf(fact_2426_Suc__mod__mult__self4,axiom,
% 5.01/5.21 ! [N: nat,K: nat,M: nat] :
% 5.01/5.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.01/5.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % Suc_mod_mult_self4
% 5.01/5.21 thf(fact_2427_Suc__mod__mult__self3,axiom,
% 5.01/5.21 ! [K: nat,N: nat,M: nat] :
% 5.01/5.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.01/5.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % Suc_mod_mult_self3
% 5.01/5.21 thf(fact_2428_Suc__mod__mult__self2,axiom,
% 5.01/5.21 ! [M: nat,N: nat,K: nat] :
% 5.01/5.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.01/5.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % Suc_mod_mult_self2
% 5.01/5.21 thf(fact_2429_Suc__mod__mult__self1,axiom,
% 5.01/5.21 ! [M: nat,K: nat,N: nat] :
% 5.01/5.21 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.01/5.21 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % Suc_mod_mult_self1
% 5.01/5.21 thf(fact_2430_dbl__dec__simps_I2_J,axiom,
% 5.01/5.21 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.01/5.21 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(2)
% 5.01/5.21 thf(fact_2431_dbl__dec__simps_I2_J,axiom,
% 5.01/5.21 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.01/5.21 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(2)
% 5.01/5.21 thf(fact_2432_dbl__dec__simps_I2_J,axiom,
% 5.01/5.21 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.01/5.21 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(2)
% 5.01/5.21 thf(fact_2433_dbl__dec__simps_I2_J,axiom,
% 5.01/5.21 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.01/5.21 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(2)
% 5.01/5.21 thf(fact_2434_dbl__dec__simps_I2_J,axiom,
% 5.01/5.21 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.01/5.21 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(2)
% 5.01/5.21 thf(fact_2435_divide__le__eq__1__neg,axiom,
% 5.01/5.21 ! [A: real,B: real] :
% 5.01/5.21 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.21 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.01/5.21 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_le_eq_1_neg
% 5.01/5.21 thf(fact_2436_divide__le__eq__1__neg,axiom,
% 5.01/5.21 ! [A: rat,B: rat] :
% 5.01/5.21 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.21 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.01/5.21 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_le_eq_1_neg
% 5.01/5.21 thf(fact_2437_divide__le__eq__1__pos,axiom,
% 5.01/5.21 ! [A: real,B: real] :
% 5.01/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.21 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.01/5.21 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_le_eq_1_pos
% 5.01/5.21 thf(fact_2438_divide__le__eq__1__pos,axiom,
% 5.01/5.21 ! [A: rat,B: rat] :
% 5.01/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.21 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.01/5.21 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_le_eq_1_pos
% 5.01/5.21 thf(fact_2439_le__divide__eq__1__neg,axiom,
% 5.01/5.21 ! [A: real,B: real] :
% 5.01/5.21 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.21 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.01/5.21 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % le_divide_eq_1_neg
% 5.01/5.21 thf(fact_2440_le__divide__eq__1__neg,axiom,
% 5.01/5.21 ! [A: rat,B: rat] :
% 5.01/5.21 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.21 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.01/5.21 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % le_divide_eq_1_neg
% 5.01/5.21 thf(fact_2441_le__divide__eq__1__pos,axiom,
% 5.01/5.21 ! [A: real,B: real] :
% 5.01/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.21 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.01/5.21 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % le_divide_eq_1_pos
% 5.01/5.21 thf(fact_2442_le__divide__eq__1__pos,axiom,
% 5.01/5.21 ! [A: rat,B: rat] :
% 5.01/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.21 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.01/5.21 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % le_divide_eq_1_pos
% 5.01/5.21 thf(fact_2443_eq__divide__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [A: real,B: real,W: num] :
% 5.01/5.21 ( ( A
% 5.01/5.21 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.01/5.21 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.21 != zero_zero_real )
% 5.01/5.21 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.21 = B ) )
% 5.01/5.21 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.21 = zero_zero_real )
% 5.01/5.21 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % eq_divide_eq_numeral1(2)
% 5.01/5.21 thf(fact_2444_eq__divide__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [A: complex,B: complex,W: num] :
% 5.01/5.21 ( ( A
% 5.01/5.21 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.01/5.21 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.21 != zero_zero_complex )
% 5.01/5.21 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.21 = B ) )
% 5.01/5.21 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.21 = zero_zero_complex )
% 5.01/5.21 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % eq_divide_eq_numeral1(2)
% 5.01/5.21 thf(fact_2445_eq__divide__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [A: rat,B: rat,W: num] :
% 5.01/5.21 ( ( A
% 5.01/5.21 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.01/5.21 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.21 != zero_zero_rat )
% 5.01/5.21 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.21 = B ) )
% 5.01/5.21 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.21 = zero_zero_rat )
% 5.01/5.21 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % eq_divide_eq_numeral1(2)
% 5.01/5.21 thf(fact_2446_divide__eq__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [B: real,W: num,A: real] :
% 5.01/5.21 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.21 = A )
% 5.01/5.21 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.21 != zero_zero_real )
% 5.01/5.21 => ( B
% 5.01/5.21 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.01/5.21 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.21 = zero_zero_real )
% 5.01/5.21 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_eq_eq_numeral1(2)
% 5.01/5.21 thf(fact_2447_divide__eq__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [B: complex,W: num,A: complex] :
% 5.01/5.21 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.21 = A )
% 5.01/5.21 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.21 != zero_zero_complex )
% 5.01/5.21 => ( B
% 5.01/5.21 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.01/5.21 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.21 = zero_zero_complex )
% 5.01/5.21 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_eq_eq_numeral1(2)
% 5.01/5.21 thf(fact_2448_divide__eq__eq__numeral1_I2_J,axiom,
% 5.01/5.21 ! [B: rat,W: num,A: rat] :
% 5.01/5.21 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.21 = A )
% 5.01/5.21 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.21 != zero_zero_rat )
% 5.01/5.21 => ( B
% 5.01/5.21 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.01/5.21 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.21 = zero_zero_rat )
% 5.01/5.21 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % divide_eq_eq_numeral1(2)
% 5.01/5.21 thf(fact_2449_power__strict__decreasing__iff,axiom,
% 5.01/5.21 ! [B: real,M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.21 => ( ( ord_less_real @ B @ one_one_real )
% 5.01/5.21 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.01/5.21 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_strict_decreasing_iff
% 5.01/5.21 thf(fact_2450_power__strict__decreasing__iff,axiom,
% 5.01/5.21 ! [B: rat,M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.21 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.01/5.21 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.01/5.21 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_strict_decreasing_iff
% 5.01/5.21 thf(fact_2451_power__strict__decreasing__iff,axiom,
% 5.01/5.21 ! [B: nat,M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.21 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.01/5.21 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.01/5.21 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_strict_decreasing_iff
% 5.01/5.21 thf(fact_2452_power__strict__decreasing__iff,axiom,
% 5.01/5.21 ! [B: int,M: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.21 => ( ( ord_less_int @ B @ one_one_int )
% 5.01/5.21 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.01/5.21 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_strict_decreasing_iff
% 5.01/5.21 thf(fact_2453_power__mono__iff,axiom,
% 5.01/5.21 ! [A: real,B: real,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.01/5.21 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_mono_iff
% 5.01/5.21 thf(fact_2454_power__mono__iff,axiom,
% 5.01/5.21 ! [A: rat,B: rat,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.01/5.21 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_mono_iff
% 5.01/5.21 thf(fact_2455_power__mono__iff,axiom,
% 5.01/5.21 ! [A: nat,B: nat,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.01/5.21 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_mono_iff
% 5.01/5.21 thf(fact_2456_power__mono__iff,axiom,
% 5.01/5.21 ! [A: int,B: int,N: nat] :
% 5.01/5.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.21 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.01/5.21 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % power_mono_iff
% 5.01/5.21 thf(fact_2457_zero__eq__power2,axiom,
% 5.01/5.21 ! [A: rat] :
% 5.01/5.21 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = zero_zero_rat )
% 5.01/5.21 = ( A = zero_zero_rat ) ) ).
% 5.01/5.21
% 5.01/5.21 % zero_eq_power2
% 5.01/5.21 thf(fact_2458_zero__eq__power2,axiom,
% 5.01/5.21 ! [A: real] :
% 5.01/5.21 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = zero_zero_real )
% 5.01/5.21 = ( A = zero_zero_real ) ) ).
% 5.01/5.21
% 5.01/5.21 % zero_eq_power2
% 5.01/5.21 thf(fact_2459_zero__eq__power2,axiom,
% 5.01/5.21 ! [A: nat] :
% 5.01/5.21 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = zero_zero_nat )
% 5.01/5.21 = ( A = zero_zero_nat ) ) ).
% 5.01/5.21
% 5.01/5.21 % zero_eq_power2
% 5.01/5.21 thf(fact_2460_zero__eq__power2,axiom,
% 5.01/5.21 ! [A: int] :
% 5.01/5.21 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = zero_zero_int )
% 5.01/5.21 = ( A = zero_zero_int ) ) ).
% 5.01/5.21
% 5.01/5.21 % zero_eq_power2
% 5.01/5.21 thf(fact_2461_zero__eq__power2,axiom,
% 5.01/5.21 ! [A: complex] :
% 5.01/5.21 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = zero_zero_complex )
% 5.01/5.21 = ( A = zero_zero_complex ) ) ).
% 5.01/5.21
% 5.01/5.21 % zero_eq_power2
% 5.01/5.21 thf(fact_2462_dbl__dec__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(1)
% 5.01/5.21 thf(fact_2463_dbl__dec__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(1)
% 5.01/5.21 thf(fact_2464_dbl__dec__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.01/5.21 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(1)
% 5.01/5.21 thf(fact_2465_dbl__dec__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.01/5.21 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(1)
% 5.01/5.21 thf(fact_2466_dbl__dec__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_dec_simps(1)
% 5.01/5.21 thf(fact_2467_dbl__inc__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_inc_simps(1)
% 5.01/5.21 thf(fact_2468_dbl__inc__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_inc_simps(1)
% 5.01/5.21 thf(fact_2469_dbl__inc__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.01/5.21 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_inc_simps(1)
% 5.01/5.21 thf(fact_2470_dbl__inc__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.01/5.21 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_inc_simps(1)
% 5.01/5.21 thf(fact_2471_dbl__inc__simps_I1_J,axiom,
% 5.01/5.21 ! [K: num] :
% 5.01/5.21 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.01/5.21 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.01/5.21
% 5.01/5.21 % dbl_inc_simps(1)
% 5.01/5.21 thf(fact_2472_one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_nat ) ).
% 5.01/5.21
% 5.01/5.21 % one_mod_two_eq_one
% 5.01/5.21 thf(fact_2473_one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_int ) ).
% 5.01/5.21
% 5.01/5.21 % one_mod_two_eq_one
% 5.01/5.21 thf(fact_2474_one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_Code_integer ) ).
% 5.01/5.21
% 5.01/5.21 % one_mod_two_eq_one
% 5.01/5.21 thf(fact_2475_bits__one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_nat ) ).
% 5.01/5.21
% 5.01/5.21 % bits_one_mod_two_eq_one
% 5.01/5.21 thf(fact_2476_bits__one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_int ) ).
% 5.01/5.21
% 5.01/5.21 % bits_one_mod_two_eq_one
% 5.01/5.21 thf(fact_2477_bits__one__mod__two__eq__one,axiom,
% 5.01/5.21 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.21 = one_one_Code_integer ) ).
% 5.01/5.21
% 5.01/5.21 % bits_one_mod_two_eq_one
% 5.01/5.21 thf(fact_2478_of__nat__0__less__iff,axiom,
% 5.01/5.21 ! [N: nat] :
% 5.01/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.01/5.21 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_0_less_iff
% 5.01/5.21 thf(fact_2479_of__nat__0__less__iff,axiom,
% 5.01/5.21 ! [N: nat] :
% 5.01/5.21 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.21 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_0_less_iff
% 5.01/5.21 thf(fact_2480_of__nat__0__less__iff,axiom,
% 5.01/5.21 ! [N: nat] :
% 5.01/5.21 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.21 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.21
% 5.01/5.21 % of_nat_0_less_iff
% 5.01/5.21 thf(fact_2481_of__nat__0__less__iff,axiom,
% 5.01/5.21 ! [N: nat] :
% 5.01/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.01/5.22 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_0_less_iff
% 5.01/5.22 thf(fact_2482_of__nat__0__less__iff,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.22 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_0_less_iff
% 5.01/5.22 thf(fact_2483_mod2__Suc__Suc,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod2_Suc_Suc
% 5.01/5.22 thf(fact_2484_Suc__diff__1,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.01/5.22 = N ) ) ).
% 5.01/5.22
% 5.01/5.22 % Suc_diff_1
% 5.01/5.22 thf(fact_2485_Suc__times__numeral__mod__eq,axiom,
% 5.01/5.22 ! [K: num,N: nat] :
% 5.01/5.22 ( ( ( numeral_numeral_nat @ K )
% 5.01/5.22 != one_one_nat )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.22 = one_one_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % Suc_times_numeral_mod_eq
% 5.01/5.22 thf(fact_2486_one__div__two__eq__zero,axiom,
% 5.01/5.22 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % one_div_two_eq_zero
% 5.01/5.22 thf(fact_2487_one__div__two__eq__zero,axiom,
% 5.01/5.22 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % one_div_two_eq_zero
% 5.01/5.22 thf(fact_2488_bits__1__div__2,axiom,
% 5.01/5.22 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % bits_1_div_2
% 5.01/5.22 thf(fact_2489_bits__1__div__2,axiom,
% 5.01/5.22 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % bits_1_div_2
% 5.01/5.22 thf(fact_2490_power__decreasing__iff,axiom,
% 5.01/5.22 ! [B: real,M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ( ord_less_real @ B @ one_one_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.01/5.22 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_decreasing_iff
% 5.01/5.22 thf(fact_2491_power__decreasing__iff,axiom,
% 5.01/5.22 ! [B: rat,M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.01/5.22 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_decreasing_iff
% 5.01/5.22 thf(fact_2492_power__decreasing__iff,axiom,
% 5.01/5.22 ! [B: nat,M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.01/5.22 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_decreasing_iff
% 5.01/5.22 thf(fact_2493_power__decreasing__iff,axiom,
% 5.01/5.22 ! [B: int,M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ( ord_less_int @ B @ one_one_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.01/5.22 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_decreasing_iff
% 5.01/5.22 thf(fact_2494_power2__eq__iff__nonneg,axiom,
% 5.01/5.22 ! [X2: real,Y: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.22 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( X2 = Y ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_eq_iff_nonneg
% 5.01/5.22 thf(fact_2495_power2__eq__iff__nonneg,axiom,
% 5.01/5.22 ! [X2: rat,Y: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.22 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( X2 = Y ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_eq_iff_nonneg
% 5.01/5.22 thf(fact_2496_power2__eq__iff__nonneg,axiom,
% 5.01/5.22 ! [X2: nat,Y: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.01/5.22 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( X2 = Y ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_eq_iff_nonneg
% 5.01/5.22 thf(fact_2497_power2__eq__iff__nonneg,axiom,
% 5.01/5.22 ! [X2: int,Y: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.22 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( X2 = Y ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_eq_iff_nonneg
% 5.01/5.22 thf(fact_2498_power2__less__eq__zero__iff,axiom,
% 5.01/5.22 ! [A: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.01/5.22 = ( A = zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_less_eq_zero_iff
% 5.01/5.22 thf(fact_2499_power2__less__eq__zero__iff,axiom,
% 5.01/5.22 ! [A: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.01/5.22 = ( A = zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_less_eq_zero_iff
% 5.01/5.22 thf(fact_2500_power2__less__eq__zero__iff,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.01/5.22 = ( A = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % power2_less_eq_zero_iff
% 5.01/5.22 thf(fact_2501_zero__less__power2,axiom,
% 5.01/5.22 ! [A: real] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( A != zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_power2
% 5.01/5.22 thf(fact_2502_zero__less__power2,axiom,
% 5.01/5.22 ! [A: rat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( A != zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_power2
% 5.01/5.22 thf(fact_2503_zero__less__power2,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( A != zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_power2
% 5.01/5.22 thf(fact_2504_sum__power2__eq__zero__iff,axiom,
% 5.01/5.22 ! [X2: rat,Y: rat] :
% 5.01/5.22 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = zero_zero_rat )
% 5.01/5.22 = ( ( X2 = zero_zero_rat )
% 5.01/5.22 & ( Y = zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % sum_power2_eq_zero_iff
% 5.01/5.22 thf(fact_2505_sum__power2__eq__zero__iff,axiom,
% 5.01/5.22 ! [X2: real,Y: real] :
% 5.01/5.22 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = zero_zero_real )
% 5.01/5.22 = ( ( X2 = zero_zero_real )
% 5.01/5.22 & ( Y = zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % sum_power2_eq_zero_iff
% 5.01/5.22 thf(fact_2506_sum__power2__eq__zero__iff,axiom,
% 5.01/5.22 ! [X2: int,Y: int] :
% 5.01/5.22 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = zero_zero_int )
% 5.01/5.22 = ( ( X2 = zero_zero_int )
% 5.01/5.22 & ( Y = zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % sum_power2_eq_zero_iff
% 5.01/5.22 thf(fact_2507_not__mod__2__eq__1__eq__0,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 != one_one_nat )
% 5.01/5.22 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_1_eq_0
% 5.01/5.22 thf(fact_2508_not__mod__2__eq__1__eq__0,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 != one_one_int )
% 5.01/5.22 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_1_eq_0
% 5.01/5.22 thf(fact_2509_not__mod__2__eq__1__eq__0,axiom,
% 5.01/5.22 ! [A: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 != one_one_Code_integer )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_1_eq_0
% 5.01/5.22 thf(fact_2510_not__mod__2__eq__0__eq__1,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 != zero_zero_nat )
% 5.01/5.22 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_0_eq_1
% 5.01/5.22 thf(fact_2511_not__mod__2__eq__0__eq__1,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 != zero_zero_int )
% 5.01/5.22 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_0_eq_1
% 5.01/5.22 thf(fact_2512_not__mod__2__eq__0__eq__1,axiom,
% 5.01/5.22 ! [A: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 != zero_z3403309356797280102nteger )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_Code_integer ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod_2_eq_0_eq_1
% 5.01/5.22 thf(fact_2513_minus__1__mod__2__eq,axiom,
% 5.01/5.22 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_int ) ).
% 5.01/5.22
% 5.01/5.22 % minus_1_mod_2_eq
% 5.01/5.22 thf(fact_2514_minus__1__mod__2__eq,axiom,
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_Code_integer ) ).
% 5.01/5.22
% 5.01/5.22 % minus_1_mod_2_eq
% 5.01/5.22 thf(fact_2515_bits__minus__1__mod__2__eq,axiom,
% 5.01/5.22 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_int ) ).
% 5.01/5.22
% 5.01/5.22 % bits_minus_1_mod_2_eq
% 5.01/5.22 thf(fact_2516_bits__minus__1__mod__2__eq,axiom,
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_Code_integer ) ).
% 5.01/5.22
% 5.01/5.22 % bits_minus_1_mod_2_eq
% 5.01/5.22 thf(fact_2517_of__nat__zero__less__power__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.01/5.22 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_zero_less_power_iff
% 5.01/5.22 thf(fact_2518_of__nat__zero__less__power__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.01/5.22 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_zero_less_power_iff
% 5.01/5.22 thf(fact_2519_of__nat__zero__less__power__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.01/5.22 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_zero_less_power_iff
% 5.01/5.22 thf(fact_2520_of__nat__zero__less__power__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.01/5.22 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_zero_less_power_iff
% 5.01/5.22 thf(fact_2521_of__nat__zero__less__power__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat] :
% 5.01/5.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N ) )
% 5.01/5.22 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_zero_less_power_iff
% 5.01/5.22 thf(fact_2522_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 != ( suc @ zero_zero_nat ) )
% 5.01/5.22 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_mod2_eq_Suc_0_eq_0
% 5.01/5.22 thf(fact_2523_add__self__mod__2,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % add_self_mod_2
% 5.01/5.22 thf(fact_2524_mod__Suc__eq__mod__add3,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.01/5.22 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_Suc_eq_mod_add3
% 5.01/5.22 thf(fact_2525_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.01/5.22 ! [M: nat,V: num] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % Suc_mod_eq_add3_mod_numeral
% 5.01/5.22 thf(fact_2526_mod2__gr__0,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.22 = one_one_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod2_gr_0
% 5.01/5.22 thf(fact_2527_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.01/5.22 ! [B: nat,A: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.01/5.22 thf(fact_2528_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.01/5.22 ! [B: int,A: int] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.01/5.22 thf(fact_2529_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.01/5.22 ! [B: code_integer,A: code_integer] :
% 5.01/5.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.22 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.01/5.22 thf(fact_2530_VEBT_Osize_I4_J,axiom,
% 5.01/5.22 ! [X21: $o,X222: $o] :
% 5.01/5.22 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT.size(4)
% 5.01/5.22 thf(fact_2531_of__nat__mod,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_mod
% 5.01/5.22 thf(fact_2532_of__nat__mod,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_mod
% 5.01/5.22 thf(fact_2533_of__nat__mod,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % of_nat_mod
% 5.01/5.22 thf(fact_2534_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.22 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.01/5.22 thf(fact_2535_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.01/5.22 thf(fact_2536_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.01/5.22 thf(fact_2537_zero__reorient,axiom,
% 5.01/5.22 ! [X2: complex] :
% 5.01/5.22 ( ( zero_zero_complex = X2 )
% 5.01/5.22 = ( X2 = zero_zero_complex ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_reorient
% 5.01/5.22 thf(fact_2538_zero__reorient,axiom,
% 5.01/5.22 ! [X2: real] :
% 5.01/5.22 ( ( zero_zero_real = X2 )
% 5.01/5.22 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_reorient
% 5.01/5.22 thf(fact_2539_zero__reorient,axiom,
% 5.01/5.22 ! [X2: rat] :
% 5.01/5.22 ( ( zero_zero_rat = X2 )
% 5.01/5.22 = ( X2 = zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_reorient
% 5.01/5.22 thf(fact_2540_zero__reorient,axiom,
% 5.01/5.22 ! [X2: nat] :
% 5.01/5.22 ( ( zero_zero_nat = X2 )
% 5.01/5.22 = ( X2 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_reorient
% 5.01/5.22 thf(fact_2541_zero__reorient,axiom,
% 5.01/5.22 ! [X2: int] :
% 5.01/5.22 ( ( zero_zero_int = X2 )
% 5.01/5.22 = ( X2 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_reorient
% 5.01/5.22 thf(fact_2542_mod__eq__self__iff__div__eq__0,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ A @ B )
% 5.01/5.22 = A )
% 5.01/5.22 = ( ( divide_divide_nat @ A @ B )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eq_self_iff_div_eq_0
% 5.01/5.22 thf(fact_2543_mod__eq__self__iff__div__eq__0,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.22 = A )
% 5.01/5.22 = ( ( divide_divide_int @ A @ B )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eq_self_iff_div_eq_0
% 5.01/5.22 thf(fact_2544_mod__eq__self__iff__div__eq__0,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.22 = A )
% 5.01/5.22 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eq_self_iff_div_eq_0
% 5.01/5.22 thf(fact_2545_mod__Suc,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 = N )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.01/5.22 = zero_zero_nat ) )
% 5.01/5.22 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 != N )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.01/5.22 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_Suc
% 5.01/5.22 thf(fact_2546_mod__less__divisor,axiom,
% 5.01/5.22 ! [N: nat,M: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_less_divisor
% 5.01/5.22 thf(fact_2547_mod__eq__0D,axiom,
% 5.01/5.22 ! [M: nat,D: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ M @ D )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 => ? [Q3: nat] :
% 5.01/5.22 ( M
% 5.01/5.22 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eq_0D
% 5.01/5.22 thf(fact_2548_list__decode_Ocases,axiom,
% 5.01/5.22 ! [X2: nat] :
% 5.01/5.22 ( ( X2 != zero_zero_nat )
% 5.01/5.22 => ~ ! [N3: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( suc @ N3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % list_decode.cases
% 5.01/5.22 thf(fact_2549_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.01/5.22 ! [B: code_integer,A: code_integer] :
% 5.01/5.22 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.22 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.01/5.22 thf(fact_2550_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.01/5.22 ! [B: nat,A: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.01/5.22 thf(fact_2551_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.01/5.22 ! [B: int,A: int] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.01/5.22 thf(fact_2552_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.22 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.22 = A ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less
% 5.01/5.22 thf(fact_2553_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_nat @ A @ B )
% 5.01/5.22 => ( ( modulo_modulo_nat @ A @ B )
% 5.01/5.22 = A ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less
% 5.01/5.22 thf(fact_2554_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_int @ A @ B )
% 5.01/5.22 => ( ( modulo_modulo_int @ A @ B )
% 5.01/5.22 = A ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_less
% 5.01/5.22 thf(fact_2555_cong__exp__iff__simps_I2_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(2)
% 5.01/5.22 thf(fact_2556_cong__exp__iff__simps_I2_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = zero_zero_int )
% 5.01/5.22 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(2)
% 5.01/5.22 thf(fact_2557_cong__exp__iff__simps_I2_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = zero_z3403309356797280102nteger )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(2)
% 5.01/5.22 thf(fact_2558_cong__exp__iff__simps_I1_J,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(1)
% 5.01/5.22 thf(fact_2559_cong__exp__iff__simps_I1_J,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.01/5.22 = zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(1)
% 5.01/5.22 thf(fact_2560_cong__exp__iff__simps_I1_J,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(1)
% 5.01/5.22 thf(fact_2561_mod__le__divisor,axiom,
% 5.01/5.22 ! [N: nat,M: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_le_divisor
% 5.01/5.22 thf(fact_2562_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.01/5.22 ! [X2: produc9072475918466114483BT_nat] :
% 5.01/5.22 ( ! [A3: $o,B2: $o,X4: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ X4 ) )
% 5.01/5.22 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 5.01/5.22 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X4 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT_internal.naive_member.cases
% 5.01/5.22 thf(fact_2563_power__0__left,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.01/5.22 = one_one_rat ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.01/5.22 = zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_0_left
% 5.01/5.22 thf(fact_2564_power__0__left,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( ( power_power_real @ zero_zero_real @ N )
% 5.01/5.22 = one_one_real ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_real @ zero_zero_real @ N )
% 5.01/5.22 = zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_0_left
% 5.01/5.22 thf(fact_2565_power__0__left,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.01/5.22 = one_one_nat ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.01/5.22 = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_0_left
% 5.01/5.22 thf(fact_2566_power__0__left,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( ( power_power_int @ zero_zero_int @ N )
% 5.01/5.22 = one_one_int ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_int @ zero_zero_int @ N )
% 5.01/5.22 = zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_0_left
% 5.01/5.22 thf(fact_2567_power__0__left,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.01/5.22 = one_one_complex ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.01/5.22 = zero_zero_complex ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_0_left
% 5.01/5.22 thf(fact_2568_invar__vebt_Ointros_I1_J,axiom,
% 5.01/5.22 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % invar_vebt.intros(1)
% 5.01/5.22 thf(fact_2569_zero__power,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.01/5.22 = zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_power
% 5.01/5.22 thf(fact_2570_zero__power,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( power_power_real @ zero_zero_real @ N )
% 5.01/5.22 = zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_power
% 5.01/5.22 thf(fact_2571_zero__power,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_power
% 5.01/5.22 thf(fact_2572_zero__power,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( power_power_int @ zero_zero_int @ N )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_power
% 5.01/5.22 thf(fact_2573_zero__power,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.01/5.22 = zero_zero_complex ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_power
% 5.01/5.22 thf(fact_2574_mod__mult__right__eq,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_right_eq
% 5.01/5.22 thf(fact_2575_mod__mult__right__eq,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_right_eq
% 5.01/5.22 thf(fact_2576_mod__mult__right__eq,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_right_eq
% 5.01/5.22 thf(fact_2577_mod__mult__left__eq,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_left_eq
% 5.01/5.22 thf(fact_2578_mod__mult__left__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_left_eq
% 5.01/5.22 thf(fact_2579_mod__mult__left__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_left_eq
% 5.01/5.22 thf(fact_2580_mult__mod__right,axiom,
% 5.01/5.22 ! [C: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mod_right
% 5.01/5.22 thf(fact_2581_mult__mod__right,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mod_right
% 5.01/5.22 thf(fact_2582_mult__mod__right,axiom,
% 5.01/5.22 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mod_right
% 5.01/5.22 thf(fact_2583_mod__mult__mult2,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.01/5.22 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_mult2
% 5.01/5.22 thf(fact_2584_mod__mult__mult2,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.22 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_mult2
% 5.01/5.22 thf(fact_2585_mod__mult__mult2,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.22 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_mult2
% 5.01/5.22 thf(fact_2586_mod__mult__cong,axiom,
% 5.01/5.22 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ A @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_cong
% 5.01/5.22 thf(fact_2587_mod__mult__cong,axiom,
% 5.01/5.22 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ C )
% 5.01/5.22 = ( modulo_modulo_int @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo_modulo_int @ B @ C )
% 5.01/5.22 = ( modulo_modulo_int @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_cong
% 5.01/5.22 thf(fact_2588_mod__mult__cong,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_cong
% 5.01/5.22 thf(fact_2589_mod__mult__eq,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_eq
% 5.01/5.22 thf(fact_2590_mod__mult__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_eq
% 5.01/5.22 thf(fact_2591_mod__mult__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_mult_eq
% 5.01/5.22 thf(fact_2592_mod__add__eq,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_eq
% 5.01/5.22 thf(fact_2593_mod__add__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_eq
% 5.01/5.22 thf(fact_2594_mod__add__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_eq
% 5.01/5.22 thf(fact_2595_mod__add__cong,axiom,
% 5.01/5.22 ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ A @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( plus_plus_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_cong
% 5.01/5.22 thf(fact_2596_mod__add__cong,axiom,
% 5.01/5.22 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ C )
% 5.01/5.22 = ( modulo_modulo_int @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo_modulo_int @ B @ C )
% 5.01/5.22 = ( modulo_modulo_int @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( plus_plus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_cong
% 5.01/5.22 thf(fact_2597_mod__add__cong,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_cong
% 5.01/5.22 thf(fact_2598_mod__add__left__eq,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_left_eq
% 5.01/5.22 thf(fact_2599_mod__add__left__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_left_eq
% 5.01/5.22 thf(fact_2600_mod__add__left__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_left_eq
% 5.01/5.22 thf(fact_2601_mod__add__right__eq,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_right_eq
% 5.01/5.22 thf(fact_2602_mod__add__right__eq,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_right_eq
% 5.01/5.22 thf(fact_2603_mod__add__right__eq,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_add_right_eq
% 5.01/5.22 thf(fact_2604_mod__diff__right__eq,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_right_eq
% 5.01/5.22 thf(fact_2605_mod__diff__right__eq,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_right_eq
% 5.01/5.22 thf(fact_2606_mod__diff__left__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_left_eq
% 5.01/5.22 thf(fact_2607_mod__diff__left__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_left_eq
% 5.01/5.22 thf(fact_2608_mod__diff__cong,axiom,
% 5.01/5.22 ! [A: int,C: int,A5: int,B: int,B5: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ C )
% 5.01/5.22 = ( modulo_modulo_int @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo_modulo_int @ B @ C )
% 5.01/5.22 = ( modulo_modulo_int @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( minus_minus_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_cong
% 5.01/5.22 thf(fact_2609_mod__diff__cong,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 5.01/5.22 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ B5 @ C ) )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_cong
% 5.01/5.22 thf(fact_2610_mod__diff__eq,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_eq
% 5.01/5.22 thf(fact_2611_mod__diff__eq,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_diff_eq
% 5.01/5.22 thf(fact_2612_mod__minus__eq,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.01/5.22 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_eq
% 5.01/5.22 thf(fact_2613_mod__minus__eq,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_eq
% 5.01/5.22 thf(fact_2614_mod__minus__cong,axiom,
% 5.01/5.22 ! [A: int,B: int,A5: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.22 = ( modulo_modulo_int @ A5 @ B ) )
% 5.01/5.22 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.22 = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_cong
% 5.01/5.22 thf(fact_2615_mod__minus__cong,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,A5: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.22 = ( modulo364778990260209775nteger @ A5 @ B ) )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_cong
% 5.01/5.22 thf(fact_2616_mod__minus__right,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.22 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_right
% 5.01/5.22 thf(fact_2617_mod__minus__right,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.01/5.22 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_minus_right
% 5.01/5.22 thf(fact_2618_power__mod,axiom,
% 5.01/5.22 ! [A: nat,B: nat,N: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.01/5.22 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_mod
% 5.01/5.22 thf(fact_2619_power__mod,axiom,
% 5.01/5.22 ! [A: int,B: int,N: nat] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.01/5.22 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_mod
% 5.01/5.22 thf(fact_2620_power__mod,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,N: nat] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_mod
% 5.01/5.22 thf(fact_2621_mod__Suc__Suc__eq,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.01/5.22 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_Suc_Suc_eq
% 5.01/5.22 thf(fact_2622_mod__Suc__eq,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.01/5.22 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_Suc_eq
% 5.01/5.22 thf(fact_2623_mod__less__eq__dividend,axiom,
% 5.01/5.22 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.01/5.22
% 5.01/5.22 % mod_less_eq_dividend
% 5.01/5.22 thf(fact_2624_VEBT_Oexhaust,axiom,
% 5.01/5.22 ! [Y: vEBT_VEBT] :
% 5.01/5.22 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.01/5.22 ( Y
% 5.01/5.22 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.01/5.22 => ~ ! [X212: $o,X223: $o] :
% 5.01/5.22 ( Y
% 5.01/5.22 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT.exhaust
% 5.01/5.22 thf(fact_2625_VEBT_Odistinct_I1_J,axiom,
% 5.01/5.22 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.01/5.22 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.01/5.22 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT.distinct(1)
% 5.01/5.22 thf(fact_2626_VEBT__internal_Ospace_H_Ocases,axiom,
% 5.01/5.22 ! [X2: vEBT_VEBT] :
% 5.01/5.22 ( ! [A3: $o,B2: $o] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.22 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT_internal.space'.cases
% 5.01/5.22 thf(fact_2627_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.01/5.22 ! [X2: produc9072475918466114483BT_nat] :
% 5.01/5.22 ( ! [Uu: $o,Uv: $o,D2: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 ) )
% 5.01/5.22 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Deg3: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Deg3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % VEBT_internal.valid'.cases
% 5.01/5.22 thf(fact_2628_zero__le,axiom,
% 5.01/5.22 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le
% 5.01/5.22 thf(fact_2629_le__numeral__extra_I3_J,axiom,
% 5.01/5.22 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.01/5.22
% 5.01/5.22 % le_numeral_extra(3)
% 5.01/5.22 thf(fact_2630_le__numeral__extra_I3_J,axiom,
% 5.01/5.22 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.01/5.22
% 5.01/5.22 % le_numeral_extra(3)
% 5.01/5.22 thf(fact_2631_le__numeral__extra_I3_J,axiom,
% 5.01/5.22 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.01/5.22
% 5.01/5.22 % le_numeral_extra(3)
% 5.01/5.22 thf(fact_2632_le__numeral__extra_I3_J,axiom,
% 5.01/5.22 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.01/5.22
% 5.01/5.22 % le_numeral_extra(3)
% 5.01/5.22 thf(fact_2633_gr__zeroI,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % gr_zeroI
% 5.01/5.22 thf(fact_2634_not__less__zero,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % not_less_zero
% 5.01/5.22 thf(fact_2635_gr__implies__not__zero,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ M @ N )
% 5.01/5.22 => ( N != zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % gr_implies_not_zero
% 5.01/5.22 thf(fact_2636_zero__less__iff__neq__zero,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 = ( N != zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_iff_neq_zero
% 5.01/5.22 thf(fact_2637_field__lbound__gt__zero,axiom,
% 5.01/5.22 ! [D1: real,D22: real] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.01/5.22 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.01/5.22 => ? [E2: real] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.22 & ( ord_less_real @ E2 @ D1 )
% 5.01/5.22 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % field_lbound_gt_zero
% 5.01/5.22 thf(fact_2638_field__lbound__gt__zero,axiom,
% 5.01/5.22 ! [D1: rat,D22: rat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.01/5.22 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.01/5.22 => ? [E2: rat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.01/5.22 & ( ord_less_rat @ E2 @ D1 )
% 5.01/5.22 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % field_lbound_gt_zero
% 5.01/5.22 thf(fact_2639_less__numeral__extra_I3_J,axiom,
% 5.01/5.22 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.01/5.22
% 5.01/5.22 % less_numeral_extra(3)
% 5.01/5.22 thf(fact_2640_less__numeral__extra_I3_J,axiom,
% 5.01/5.22 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.01/5.22
% 5.01/5.22 % less_numeral_extra(3)
% 5.01/5.22 thf(fact_2641_less__numeral__extra_I3_J,axiom,
% 5.01/5.22 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % less_numeral_extra(3)
% 5.01/5.22 thf(fact_2642_less__numeral__extra_I3_J,axiom,
% 5.01/5.22 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % less_numeral_extra(3)
% 5.01/5.22 thf(fact_2643_zero__neq__numeral,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( zero_zero_complex
% 5.01/5.22 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_numeral
% 5.01/5.22 thf(fact_2644_zero__neq__numeral,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( zero_zero_real
% 5.01/5.22 != ( numeral_numeral_real @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_numeral
% 5.01/5.22 thf(fact_2645_zero__neq__numeral,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( zero_zero_rat
% 5.01/5.22 != ( numeral_numeral_rat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_numeral
% 5.01/5.22 thf(fact_2646_zero__neq__numeral,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( zero_zero_nat
% 5.01/5.22 != ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_numeral
% 5.01/5.22 thf(fact_2647_zero__neq__numeral,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ( zero_zero_int
% 5.01/5.22 != ( numeral_numeral_int @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_numeral
% 5.01/5.22 thf(fact_2648_mult__right__cancel,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( C != zero_zero_real )
% 5.01/5.22 => ( ( ( times_times_real @ A @ C )
% 5.01/5.22 = ( times_times_real @ B @ C ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_cancel
% 5.01/5.22 thf(fact_2649_mult__right__cancel,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( C != zero_zero_rat )
% 5.01/5.22 => ( ( ( times_times_rat @ A @ C )
% 5.01/5.22 = ( times_times_rat @ B @ C ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_cancel
% 5.01/5.22 thf(fact_2650_mult__right__cancel,axiom,
% 5.01/5.22 ! [C: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( C != zero_zero_nat )
% 5.01/5.22 => ( ( ( times_times_nat @ A @ C )
% 5.01/5.22 = ( times_times_nat @ B @ C ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_cancel
% 5.01/5.22 thf(fact_2651_mult__right__cancel,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( C != zero_zero_int )
% 5.01/5.22 => ( ( ( times_times_int @ A @ C )
% 5.01/5.22 = ( times_times_int @ B @ C ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_cancel
% 5.01/5.22 thf(fact_2652_mult__right__cancel,axiom,
% 5.01/5.22 ! [C: complex,A: complex,B: complex] :
% 5.01/5.22 ( ( C != zero_zero_complex )
% 5.01/5.22 => ( ( ( times_times_complex @ A @ C )
% 5.01/5.22 = ( times_times_complex @ B @ C ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_cancel
% 5.01/5.22 thf(fact_2653_mult__left__cancel,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( C != zero_zero_real )
% 5.01/5.22 => ( ( ( times_times_real @ C @ A )
% 5.01/5.22 = ( times_times_real @ C @ B ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_cancel
% 5.01/5.22 thf(fact_2654_mult__left__cancel,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( C != zero_zero_rat )
% 5.01/5.22 => ( ( ( times_times_rat @ C @ A )
% 5.01/5.22 = ( times_times_rat @ C @ B ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_cancel
% 5.01/5.22 thf(fact_2655_mult__left__cancel,axiom,
% 5.01/5.22 ! [C: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( C != zero_zero_nat )
% 5.01/5.22 => ( ( ( times_times_nat @ C @ A )
% 5.01/5.22 = ( times_times_nat @ C @ B ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_cancel
% 5.01/5.22 thf(fact_2656_mult__left__cancel,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( C != zero_zero_int )
% 5.01/5.22 => ( ( ( times_times_int @ C @ A )
% 5.01/5.22 = ( times_times_int @ C @ B ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_cancel
% 5.01/5.22 thf(fact_2657_mult__left__cancel,axiom,
% 5.01/5.22 ! [C: complex,A: complex,B: complex] :
% 5.01/5.22 ( ( C != zero_zero_complex )
% 5.01/5.22 => ( ( ( times_times_complex @ C @ A )
% 5.01/5.22 = ( times_times_complex @ C @ B ) )
% 5.01/5.22 = ( A = B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_cancel
% 5.01/5.22 thf(fact_2658_no__zero__divisors,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( A != zero_zero_real )
% 5.01/5.22 => ( ( B != zero_zero_real )
% 5.01/5.22 => ( ( times_times_real @ A @ B )
% 5.01/5.22 != zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % no_zero_divisors
% 5.01/5.22 thf(fact_2659_no__zero__divisors,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( A != zero_zero_rat )
% 5.01/5.22 => ( ( B != zero_zero_rat )
% 5.01/5.22 => ( ( times_times_rat @ A @ B )
% 5.01/5.22 != zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % no_zero_divisors
% 5.01/5.22 thf(fact_2660_no__zero__divisors,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( A != zero_zero_nat )
% 5.01/5.22 => ( ( B != zero_zero_nat )
% 5.01/5.22 => ( ( times_times_nat @ A @ B )
% 5.01/5.22 != zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % no_zero_divisors
% 5.01/5.22 thf(fact_2661_no__zero__divisors,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( A != zero_zero_int )
% 5.01/5.22 => ( ( B != zero_zero_int )
% 5.01/5.22 => ( ( times_times_int @ A @ B )
% 5.01/5.22 != zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % no_zero_divisors
% 5.01/5.22 thf(fact_2662_no__zero__divisors,axiom,
% 5.01/5.22 ! [A: complex,B: complex] :
% 5.01/5.22 ( ( A != zero_zero_complex )
% 5.01/5.22 => ( ( B != zero_zero_complex )
% 5.01/5.22 => ( ( times_times_complex @ A @ B )
% 5.01/5.22 != zero_zero_complex ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % no_zero_divisors
% 5.01/5.22 thf(fact_2663_divisors__zero,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ( times_times_real @ A @ B )
% 5.01/5.22 = zero_zero_real )
% 5.01/5.22 => ( ( A = zero_zero_real )
% 5.01/5.22 | ( B = zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % divisors_zero
% 5.01/5.22 thf(fact_2664_divisors__zero,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ( times_times_rat @ A @ B )
% 5.01/5.22 = zero_zero_rat )
% 5.01/5.22 => ( ( A = zero_zero_rat )
% 5.01/5.22 | ( B = zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % divisors_zero
% 5.01/5.22 thf(fact_2665_divisors__zero,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ( times_times_nat @ A @ B )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 => ( ( A = zero_zero_nat )
% 5.01/5.22 | ( B = zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % divisors_zero
% 5.01/5.22 thf(fact_2666_divisors__zero,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ( times_times_int @ A @ B )
% 5.01/5.22 = zero_zero_int )
% 5.01/5.22 => ( ( A = zero_zero_int )
% 5.01/5.22 | ( B = zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % divisors_zero
% 5.01/5.22 thf(fact_2667_divisors__zero,axiom,
% 5.01/5.22 ! [A: complex,B: complex] :
% 5.01/5.22 ( ( ( times_times_complex @ A @ B )
% 5.01/5.22 = zero_zero_complex )
% 5.01/5.22 => ( ( A = zero_zero_complex )
% 5.01/5.22 | ( B = zero_zero_complex ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % divisors_zero
% 5.01/5.22 thf(fact_2668_mult__not__zero,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ( times_times_real @ A @ B )
% 5.01/5.22 != zero_zero_real )
% 5.01/5.22 => ( ( A != zero_zero_real )
% 5.01/5.22 & ( B != zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_not_zero
% 5.01/5.22 thf(fact_2669_mult__not__zero,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ( times_times_rat @ A @ B )
% 5.01/5.22 != zero_zero_rat )
% 5.01/5.22 => ( ( A != zero_zero_rat )
% 5.01/5.22 & ( B != zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_not_zero
% 5.01/5.22 thf(fact_2670_mult__not__zero,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ( times_times_nat @ A @ B )
% 5.01/5.22 != zero_zero_nat )
% 5.01/5.22 => ( ( A != zero_zero_nat )
% 5.01/5.22 & ( B != zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_not_zero
% 5.01/5.22 thf(fact_2671_mult__not__zero,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ( times_times_int @ A @ B )
% 5.01/5.22 != zero_zero_int )
% 5.01/5.22 => ( ( A != zero_zero_int )
% 5.01/5.22 & ( B != zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_not_zero
% 5.01/5.22 thf(fact_2672_mult__not__zero,axiom,
% 5.01/5.22 ! [A: complex,B: complex] :
% 5.01/5.22 ( ( ( times_times_complex @ A @ B )
% 5.01/5.22 != zero_zero_complex )
% 5.01/5.22 => ( ( A != zero_zero_complex )
% 5.01/5.22 & ( B != zero_zero_complex ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_not_zero
% 5.01/5.22 thf(fact_2673_comm__monoid__add__class_Oadd__0,axiom,
% 5.01/5.22 ! [A: complex] :
% 5.01/5.22 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % comm_monoid_add_class.add_0
% 5.01/5.22 thf(fact_2674_comm__monoid__add__class_Oadd__0,axiom,
% 5.01/5.22 ! [A: real] :
% 5.01/5.22 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % comm_monoid_add_class.add_0
% 5.01/5.22 thf(fact_2675_comm__monoid__add__class_Oadd__0,axiom,
% 5.01/5.22 ! [A: rat] :
% 5.01/5.22 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % comm_monoid_add_class.add_0
% 5.01/5.22 thf(fact_2676_comm__monoid__add__class_Oadd__0,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % comm_monoid_add_class.add_0
% 5.01/5.22 thf(fact_2677_comm__monoid__add__class_Oadd__0,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % comm_monoid_add_class.add_0
% 5.01/5.22 thf(fact_2678_add_Ocomm__neutral,axiom,
% 5.01/5.22 ! [A: complex] :
% 5.01/5.22 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.comm_neutral
% 5.01/5.22 thf(fact_2679_add_Ocomm__neutral,axiom,
% 5.01/5.22 ! [A: real] :
% 5.01/5.22 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.comm_neutral
% 5.01/5.22 thf(fact_2680_add_Ocomm__neutral,axiom,
% 5.01/5.22 ! [A: rat] :
% 5.01/5.22 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.comm_neutral
% 5.01/5.22 thf(fact_2681_add_Ocomm__neutral,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.comm_neutral
% 5.01/5.22 thf(fact_2682_add_Ocomm__neutral,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.comm_neutral
% 5.01/5.22 thf(fact_2683_add_Ogroup__left__neutral,axiom,
% 5.01/5.22 ! [A: complex] :
% 5.01/5.22 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.group_left_neutral
% 5.01/5.22 thf(fact_2684_add_Ogroup__left__neutral,axiom,
% 5.01/5.22 ! [A: real] :
% 5.01/5.22 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.group_left_neutral
% 5.01/5.22 thf(fact_2685_add_Ogroup__left__neutral,axiom,
% 5.01/5.22 ! [A: rat] :
% 5.01/5.22 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.group_left_neutral
% 5.01/5.22 thf(fact_2686_add_Ogroup__left__neutral,axiom,
% 5.01/5.22 ! [A: int] :
% 5.01/5.22 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.01/5.22 = A ) ).
% 5.01/5.22
% 5.01/5.22 % add.group_left_neutral
% 5.01/5.22 thf(fact_2687_zero__neq__one,axiom,
% 5.01/5.22 zero_zero_complex != one_one_complex ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_one
% 5.01/5.22 thf(fact_2688_zero__neq__one,axiom,
% 5.01/5.22 zero_zero_real != one_one_real ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_one
% 5.01/5.22 thf(fact_2689_zero__neq__one,axiom,
% 5.01/5.22 zero_zero_rat != one_one_rat ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_one
% 5.01/5.22 thf(fact_2690_zero__neq__one,axiom,
% 5.01/5.22 zero_zero_nat != one_one_nat ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_one
% 5.01/5.22 thf(fact_2691_zero__neq__one,axiom,
% 5.01/5.22 zero_zero_int != one_one_int ).
% 5.01/5.22
% 5.01/5.22 % zero_neq_one
% 5.01/5.22 thf(fact_2692_eq__iff__diff__eq__0,axiom,
% 5.01/5.22 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.01/5.22 = ( ^ [A4: real,B3: real] :
% 5.01/5.22 ( ( minus_minus_real @ A4 @ B3 )
% 5.01/5.22 = zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % eq_iff_diff_eq_0
% 5.01/5.22 thf(fact_2693_eq__iff__diff__eq__0,axiom,
% 5.01/5.22 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.01/5.22 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.22 ( ( minus_minus_rat @ A4 @ B3 )
% 5.01/5.22 = zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % eq_iff_diff_eq_0
% 5.01/5.22 thf(fact_2694_eq__iff__diff__eq__0,axiom,
% 5.01/5.22 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.01/5.22 = ( ^ [A4: int,B3: int] :
% 5.01/5.22 ( ( minus_minus_int @ A4 @ B3 )
% 5.01/5.22 = zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % eq_iff_diff_eq_0
% 5.01/5.22 thf(fact_2695_eq__iff__diff__eq__0,axiom,
% 5.01/5.22 ( ( ^ [Y5: complex,Z4: complex] : ( Y5 = Z4 ) )
% 5.01/5.22 = ( ^ [A4: complex,B3: complex] :
% 5.01/5.22 ( ( minus_minus_complex @ A4 @ B3 )
% 5.01/5.22 = zero_zero_complex ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % eq_iff_diff_eq_0
% 5.01/5.22 thf(fact_2696_power__not__zero,axiom,
% 5.01/5.22 ! [A: rat,N: nat] :
% 5.01/5.22 ( ( A != zero_zero_rat )
% 5.01/5.22 => ( ( power_power_rat @ A @ N )
% 5.01/5.22 != zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_not_zero
% 5.01/5.22 thf(fact_2697_power__not__zero,axiom,
% 5.01/5.22 ! [A: real,N: nat] :
% 5.01/5.22 ( ( A != zero_zero_real )
% 5.01/5.22 => ( ( power_power_real @ A @ N )
% 5.01/5.22 != zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_not_zero
% 5.01/5.22 thf(fact_2698_power__not__zero,axiom,
% 5.01/5.22 ! [A: nat,N: nat] :
% 5.01/5.22 ( ( A != zero_zero_nat )
% 5.01/5.22 => ( ( power_power_nat @ A @ N )
% 5.01/5.22 != zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_not_zero
% 5.01/5.22 thf(fact_2699_power__not__zero,axiom,
% 5.01/5.22 ! [A: int,N: nat] :
% 5.01/5.22 ( ( A != zero_zero_int )
% 5.01/5.22 => ( ( power_power_int @ A @ N )
% 5.01/5.22 != zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_not_zero
% 5.01/5.22 thf(fact_2700_power__not__zero,axiom,
% 5.01/5.22 ! [A: complex,N: nat] :
% 5.01/5.22 ( ( A != zero_zero_complex )
% 5.01/5.22 => ( ( power_power_complex @ A @ N )
% 5.01/5.22 != zero_zero_complex ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_not_zero
% 5.01/5.22 thf(fact_2701_num_Osize_I4_J,axiom,
% 5.01/5.22 ( ( size_size_num @ one )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % num.size(4)
% 5.01/5.22 thf(fact_2702_not0__implies__Suc,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( N != zero_zero_nat )
% 5.01/5.22 => ? [M4: nat] :
% 5.01/5.22 ( N
% 5.01/5.22 = ( suc @ M4 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % not0_implies_Suc
% 5.01/5.22 thf(fact_2703_Zero__not__Suc,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( zero_zero_nat
% 5.01/5.22 != ( suc @ M ) ) ).
% 5.01/5.22
% 5.01/5.22 % Zero_not_Suc
% 5.01/5.22 thf(fact_2704_Zero__neq__Suc,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( zero_zero_nat
% 5.01/5.22 != ( suc @ M ) ) ).
% 5.01/5.22
% 5.01/5.22 % Zero_neq_Suc
% 5.01/5.22 thf(fact_2705_Suc__neq__Zero,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( ( suc @ M )
% 5.01/5.22 != zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % Suc_neq_Zero
% 5.01/5.22 thf(fact_2706_zero__induct,axiom,
% 5.01/5.22 ! [P: nat > $o,K: nat] :
% 5.01/5.22 ( ( P @ K )
% 5.01/5.22 => ( ! [N3: nat] :
% 5.01/5.22 ( ( P @ ( suc @ N3 ) )
% 5.01/5.22 => ( P @ N3 ) )
% 5.01/5.22 => ( P @ zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_induct
% 5.01/5.22 thf(fact_2707_diff__induct,axiom,
% 5.01/5.22 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.01/5.22 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 5.01/5.22 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.01/5.22 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.22 ( ( P @ X4 @ Y3 )
% 5.01/5.22 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 5.01/5.22 => ( P @ M @ N ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % diff_induct
% 5.01/5.22 thf(fact_2708_nat__induct,axiom,
% 5.01/5.22 ! [P: nat > $o,N: nat] :
% 5.01/5.22 ( ( P @ zero_zero_nat )
% 5.01/5.22 => ( ! [N3: nat] :
% 5.01/5.22 ( ( P @ N3 )
% 5.01/5.22 => ( P @ ( suc @ N3 ) ) )
% 5.01/5.22 => ( P @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % nat_induct
% 5.01/5.22 thf(fact_2709_vebt__buildup_Ocases,axiom,
% 5.01/5.22 ! [X2: nat] :
% 5.01/5.22 ( ( X2 != zero_zero_nat )
% 5.01/5.22 => ( ( X2
% 5.01/5.22 != ( suc @ zero_zero_nat ) )
% 5.01/5.22 => ~ ! [Va: nat] :
% 5.01/5.22 ( X2
% 5.01/5.22 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % vebt_buildup.cases
% 5.01/5.22 thf(fact_2710_old_Onat_Oexhaust,axiom,
% 5.01/5.22 ! [Y: nat] :
% 5.01/5.22 ( ( Y != zero_zero_nat )
% 5.01/5.22 => ~ ! [Nat3: nat] :
% 5.01/5.22 ( Y
% 5.01/5.22 != ( suc @ Nat3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % old.nat.exhaust
% 5.01/5.22 thf(fact_2711_nat_OdiscI,axiom,
% 5.01/5.22 ! [Nat: nat,X23: nat] :
% 5.01/5.22 ( ( Nat
% 5.01/5.22 = ( suc @ X23 ) )
% 5.01/5.22 => ( Nat != zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % nat.discI
% 5.01/5.22 thf(fact_2712_old_Onat_Odistinct_I1_J,axiom,
% 5.01/5.22 ! [Nat2: nat] :
% 5.01/5.22 ( zero_zero_nat
% 5.01/5.22 != ( suc @ Nat2 ) ) ).
% 5.01/5.22
% 5.01/5.22 % old.nat.distinct(1)
% 5.01/5.22 thf(fact_2713_old_Onat_Odistinct_I2_J,axiom,
% 5.01/5.22 ! [Nat2: nat] :
% 5.01/5.22 ( ( suc @ Nat2 )
% 5.01/5.22 != zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % old.nat.distinct(2)
% 5.01/5.22 thf(fact_2714_nat_Odistinct_I1_J,axiom,
% 5.01/5.22 ! [X23: nat] :
% 5.01/5.22 ( zero_zero_nat
% 5.01/5.22 != ( suc @ X23 ) ) ).
% 5.01/5.22
% 5.01/5.22 % nat.distinct(1)
% 5.01/5.22 thf(fact_2715_bot__nat__0_Oextremum__strict,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % bot_nat_0.extremum_strict
% 5.01/5.22 thf(fact_2716_gr0I,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( N != zero_zero_nat )
% 5.01/5.22 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % gr0I
% 5.01/5.22 thf(fact_2717_not__gr0,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.01/5.22 = ( N = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % not_gr0
% 5.01/5.22 thf(fact_2718_not__less0,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % not_less0
% 5.01/5.22 thf(fact_2719_less__zeroE,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % less_zeroE
% 5.01/5.22 thf(fact_2720_gr__implies__not0,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ M @ N )
% 5.01/5.22 => ( N != zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % gr_implies_not0
% 5.01/5.22 thf(fact_2721_infinite__descent0,axiom,
% 5.01/5.22 ! [P: nat > $o,N: nat] :
% 5.01/5.22 ( ( P @ zero_zero_nat )
% 5.01/5.22 => ( ! [N3: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.22 => ( ~ ( P @ N3 )
% 5.01/5.22 => ? [M2: nat] :
% 5.01/5.22 ( ( ord_less_nat @ M2 @ N3 )
% 5.01/5.22 & ~ ( P @ M2 ) ) ) )
% 5.01/5.22 => ( P @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % infinite_descent0
% 5.01/5.22 thf(fact_2722_less__eq__nat_Osimps_I1_J,axiom,
% 5.01/5.22 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.01/5.22
% 5.01/5.22 % less_eq_nat.simps(1)
% 5.01/5.22 thf(fact_2723_bot__nat__0_Oextremum__unique,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 = ( A = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % bot_nat_0.extremum_unique
% 5.01/5.22 thf(fact_2724_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.01/5.22 ! [A: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 => ( A = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % bot_nat_0.extremum_uniqueI
% 5.01/5.22 thf(fact_2725_le__0__eq,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.01/5.22 = ( N = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % le_0_eq
% 5.01/5.22 thf(fact_2726_plus__nat_Oadd__0,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.01/5.22 = N ) ).
% 5.01/5.22
% 5.01/5.22 % plus_nat.add_0
% 5.01/5.22 thf(fact_2727_add__eq__self__zero,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ( plus_plus_nat @ M @ N )
% 5.01/5.22 = M )
% 5.01/5.22 => ( N = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_eq_self_zero
% 5.01/5.22 thf(fact_2728_diffs0__imp__equal,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ( minus_minus_nat @ M @ N )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 => ( ( ( minus_minus_nat @ N @ M )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 => ( M = N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % diffs0_imp_equal
% 5.01/5.22 thf(fact_2729_minus__nat_Odiff__0,axiom,
% 5.01/5.22 ! [M: nat] :
% 5.01/5.22 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.01/5.22 = M ) ).
% 5.01/5.22
% 5.01/5.22 % minus_nat.diff_0
% 5.01/5.22 thf(fact_2730_mult__0,axiom,
% 5.01/5.22 ! [N: nat] :
% 5.01/5.22 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.01/5.22 = zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % mult_0
% 5.01/5.22 thf(fact_2731_nat__mult__eq__cancel__disj,axiom,
% 5.01/5.22 ! [K: nat,M: nat,N: nat] :
% 5.01/5.22 ( ( ( times_times_nat @ K @ M )
% 5.01/5.22 = ( times_times_nat @ K @ N ) )
% 5.01/5.22 = ( ( K = zero_zero_nat )
% 5.01/5.22 | ( M = N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % nat_mult_eq_cancel_disj
% 5.01/5.22 thf(fact_2732_cong__exp__iff__simps_I3_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 != zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(3)
% 5.01/5.22 thf(fact_2733_cong__exp__iff__simps_I3_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 != zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(3)
% 5.01/5.22 thf(fact_2734_cong__exp__iff__simps_I3_J,axiom,
% 5.01/5.22 ! [N: num,Q2: num] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 != zero_z3403309356797280102nteger ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(3)
% 5.01/5.22 thf(fact_2735_split__mod,axiom,
% 5.01/5.22 ! [P: nat > $o,M: nat,N: nat] :
% 5.01/5.22 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.22 = ( ( ( N = zero_zero_nat )
% 5.01/5.22 => ( P @ M ) )
% 5.01/5.22 & ( ( N != zero_zero_nat )
% 5.01/5.22 => ! [I4: nat,J3: nat] :
% 5.01/5.22 ( ( ord_less_nat @ J3 @ N )
% 5.01/5.22 => ( ( M
% 5.01/5.22 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.01/5.22 => ( P @ J3 ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mod
% 5.01/5.22 thf(fact_2736_power__eq__imp__eq__base,axiom,
% 5.01/5.22 ! [A: real,N: nat,B: real] :
% 5.01/5.22 ( ( ( power_power_real @ A @ N )
% 5.01/5.22 = ( power_power_real @ B @ N ) )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_imp_eq_base
% 5.01/5.22 thf(fact_2737_power__eq__imp__eq__base,axiom,
% 5.01/5.22 ! [A: rat,N: nat,B: rat] :
% 5.01/5.22 ( ( ( power_power_rat @ A @ N )
% 5.01/5.22 = ( power_power_rat @ B @ N ) )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_imp_eq_base
% 5.01/5.22 thf(fact_2738_power__eq__imp__eq__base,axiom,
% 5.01/5.22 ! [A: nat,N: nat,B: nat] :
% 5.01/5.22 ( ( ( power_power_nat @ A @ N )
% 5.01/5.22 = ( power_power_nat @ B @ N ) )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_imp_eq_base
% 5.01/5.22 thf(fact_2739_power__eq__imp__eq__base,axiom,
% 5.01/5.22 ! [A: int,N: nat,B: int] :
% 5.01/5.22 ( ( ( power_power_int @ A @ N )
% 5.01/5.22 = ( power_power_int @ B @ N ) )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_imp_eq_base
% 5.01/5.22 thf(fact_2740_power__eq__iff__eq__base,axiom,
% 5.01/5.22 ! [N: nat,A: real,B: real] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ( ( power_power_real @ A @ N )
% 5.01/5.22 = ( power_power_real @ B @ N ) )
% 5.01/5.22 = ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_iff_eq_base
% 5.01/5.22 thf(fact_2741_power__eq__iff__eq__base,axiom,
% 5.01/5.22 ! [N: nat,A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ( ( power_power_rat @ A @ N )
% 5.01/5.22 = ( power_power_rat @ B @ N ) )
% 5.01/5.22 = ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_iff_eq_base
% 5.01/5.22 thf(fact_2742_power__eq__iff__eq__base,axiom,
% 5.01/5.22 ! [N: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ( ( power_power_nat @ A @ N )
% 5.01/5.22 = ( power_power_nat @ B @ N ) )
% 5.01/5.22 = ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_iff_eq_base
% 5.01/5.22 thf(fact_2743_power__eq__iff__eq__base,axiom,
% 5.01/5.22 ! [N: nat,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ( ( power_power_int @ A @ N )
% 5.01/5.22 = ( power_power_int @ B @ N ) )
% 5.01/5.22 = ( A = B ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_eq_iff_eq_base
% 5.01/5.22 thf(fact_2744_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.01/5.22 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.22 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.01/5.22 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.22 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.01/5.22 thf(fact_2745_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.01/5.22 ! [C: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.22 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.01/5.22 thf(fact_2746_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.22 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.01/5.22 thf(fact_2747_cong__exp__iff__simps_I7_J,axiom,
% 5.01/5.22 ! [Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(7)
% 5.01/5.22 thf(fact_2748_cong__exp__iff__simps_I7_J,axiom,
% 5.01/5.22 ! [Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(7)
% 5.01/5.22 thf(fact_2749_cong__exp__iff__simps_I7_J,axiom,
% 5.01/5.22 ! [Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(7)
% 5.01/5.22 thf(fact_2750_cong__exp__iff__simps_I11_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.22 = zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(11)
% 5.01/5.22 thf(fact_2751_cong__exp__iff__simps_I11_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.01/5.22 = zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(11)
% 5.01/5.22 thf(fact_2752_cong__exp__iff__simps_I11_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.01/5.22 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(11)
% 5.01/5.22 thf(fact_2753_cong__exp__iff__simps_I9_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(9)
% 5.01/5.22 thf(fact_2754_cong__exp__iff__simps_I9_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(9)
% 5.01/5.22 thf(fact_2755_cong__exp__iff__simps_I9_J,axiom,
% 5.01/5.22 ! [M: num,Q2: num,N: num] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.22 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(9)
% 5.01/5.22 thf(fact_2756_cong__exp__iff__simps_I4_J,axiom,
% 5.01/5.22 ! [M: num,N: num] :
% 5.01/5.22 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.01/5.22 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(4)
% 5.01/5.22 thf(fact_2757_cong__exp__iff__simps_I4_J,axiom,
% 5.01/5.22 ! [M: num,N: num] :
% 5.01/5.22 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.01/5.22 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(4)
% 5.01/5.22 thf(fact_2758_cong__exp__iff__simps_I4_J,axiom,
% 5.01/5.22 ! [M: num,N: num] :
% 5.01/5.22 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.01/5.22 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % cong_exp_iff_simps(4)
% 5.01/5.22 thf(fact_2759_mod__eqE,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( ( modulo_modulo_int @ A @ C )
% 5.01/5.22 = ( modulo_modulo_int @ B @ C ) )
% 5.01/5.22 => ~ ! [D2: int] :
% 5.01/5.22 ( B
% 5.01/5.22 != ( plus_plus_int @ A @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eqE
% 5.01/5.22 thf(fact_2760_mod__eqE,axiom,
% 5.01/5.22 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.22 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.01/5.22 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.01/5.22 => ~ ! [D2: code_integer] :
% 5.01/5.22 ( B
% 5.01/5.22 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_eqE
% 5.01/5.22 thf(fact_2761_div__add1__eq,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.01/5.22 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % div_add1_eq
% 5.01/5.22 thf(fact_2762_div__add1__eq,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.01/5.22 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % div_add1_eq
% 5.01/5.22 thf(fact_2763_div__add1__eq,axiom,
% 5.01/5.22 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.22 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.01/5.22 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % div_add1_eq
% 5.01/5.22 thf(fact_2764_Suc__times__mod__eq,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.01/5.22 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.01/5.22 = one_one_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % Suc_times_mod_eq
% 5.01/5.22 thf(fact_2765_mod__induct,axiom,
% 5.01/5.22 ! [P: nat > $o,N: nat,P4: nat,M: nat] :
% 5.01/5.22 ( ( P @ N )
% 5.01/5.22 => ( ( ord_less_nat @ N @ P4 )
% 5.01/5.22 => ( ( ord_less_nat @ M @ P4 )
% 5.01/5.22 => ( ! [N3: nat] :
% 5.01/5.22 ( ( ord_less_nat @ N3 @ P4 )
% 5.01/5.22 => ( ( P @ N3 )
% 5.01/5.22 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P4 ) ) ) )
% 5.01/5.22 => ( P @ M ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_induct
% 5.01/5.22 thf(fact_2766_mod__Suc__le__divisor,axiom,
% 5.01/5.22 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.01/5.22
% 5.01/5.22 % mod_Suc_le_divisor
% 5.01/5.22 thf(fact_2767_power__strict__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,N: nat] :
% 5.01/5.22 ( ( ord_less_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_strict_mono
% 5.01/5.22 thf(fact_2768_power__strict__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,N: nat] :
% 5.01/5.22 ( ( ord_less_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_strict_mono
% 5.01/5.22 thf(fact_2769_power__strict__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,N: nat] :
% 5.01/5.22 ( ( ord_less_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_strict_mono
% 5.01/5.22 thf(fact_2770_power__strict__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,N: nat] :
% 5.01/5.22 ( ( ord_less_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.22 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % power_strict_mono
% 5.01/5.22 thf(fact_2771_mod__if,axiom,
% 5.01/5.22 ( modulo_modulo_nat
% 5.01/5.22 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N4 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_if
% 5.01/5.22 thf(fact_2772_mod__geq,axiom,
% 5.01/5.22 ! [M: nat,N: nat] :
% 5.01/5.22 ( ~ ( ord_less_nat @ M @ N )
% 5.01/5.22 => ( ( modulo_modulo_nat @ M @ N )
% 5.01/5.22 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mod_geq
% 5.01/5.22 thf(fact_2773_le__mod__geq,axiom,
% 5.01/5.22 ! [N: nat,M: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.22 => ( ( modulo_modulo_nat @ M @ N )
% 5.01/5.22 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % le_mod_geq
% 5.01/5.22 thf(fact_2774_nat__mod__eq__iff,axiom,
% 5.01/5.22 ! [X2: nat,N: nat,Y: nat] :
% 5.01/5.22 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.01/5.22 = ( modulo_modulo_nat @ Y @ N ) )
% 5.01/5.22 = ( ? [Q1: nat,Q22: nat] :
% 5.01/5.22 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 5.01/5.22 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % nat_mod_eq_iff
% 5.01/5.22 thf(fact_2775_dbl__def,axiom,
% 5.01/5.22 ( neg_numeral_dbl_real
% 5.01/5.22 = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % dbl_def
% 5.01/5.22 thf(fact_2776_dbl__def,axiom,
% 5.01/5.22 ( neg_numeral_dbl_rat
% 5.01/5.22 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % dbl_def
% 5.01/5.22 thf(fact_2777_dbl__def,axiom,
% 5.01/5.22 ( neg_numeral_dbl_int
% 5.01/5.22 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % dbl_def
% 5.01/5.22 thf(fact_2778_not__numeral__le__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_le_zero
% 5.01/5.22 thf(fact_2779_not__numeral__le__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_le_zero
% 5.01/5.22 thf(fact_2780_not__numeral__le__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_le_zero
% 5.01/5.22 thf(fact_2781_not__numeral__le__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_le_zero
% 5.01/5.22 thf(fact_2782_zero__le__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_numeral
% 5.01/5.22 thf(fact_2783_zero__le__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_numeral
% 5.01/5.22 thf(fact_2784_zero__le__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_numeral
% 5.01/5.22 thf(fact_2785_zero__le__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_numeral
% 5.01/5.22 thf(fact_2786_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.01/5.22 thf(fact_2787_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.01/5.22 thf(fact_2788_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.01/5.22 thf(fact_2789_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.01/5.22 thf(fact_2790_zero__le__mult__iff,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.22 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_mult_iff
% 5.01/5.22 thf(fact_2791_zero__le__mult__iff,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.22 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_mult_iff
% 5.01/5.22 thf(fact_2792_zero__le__mult__iff,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.01/5.22 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_mult_iff
% 5.01/5.22 thf(fact_2793_mult__nonneg__nonpos2,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos2
% 5.01/5.22 thf(fact_2794_mult__nonneg__nonpos2,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos2
% 5.01/5.22 thf(fact_2795_mult__nonneg__nonpos2,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos2
% 5.01/5.22 thf(fact_2796_mult__nonneg__nonpos2,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos2
% 5.01/5.22 thf(fact_2797_mult__nonpos__nonneg,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonneg
% 5.01/5.22 thf(fact_2798_mult__nonpos__nonneg,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonneg
% 5.01/5.22 thf(fact_2799_mult__nonpos__nonneg,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonneg
% 5.01/5.22 thf(fact_2800_mult__nonpos__nonneg,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonneg
% 5.01/5.22 thf(fact_2801_mult__nonneg__nonpos,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos
% 5.01/5.22 thf(fact_2802_mult__nonneg__nonpos,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos
% 5.01/5.22 thf(fact_2803_mult__nonneg__nonpos,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos
% 5.01/5.22 thf(fact_2804_mult__nonneg__nonpos,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonpos
% 5.01/5.22 thf(fact_2805_mult__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonneg
% 5.01/5.22 thf(fact_2806_mult__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonneg
% 5.01/5.22 thf(fact_2807_mult__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonneg
% 5.01/5.22 thf(fact_2808_mult__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonneg_nonneg
% 5.01/5.22 thf(fact_2809_split__mult__neg__le,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.01/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_neg_le
% 5.01/5.22 thf(fact_2810_split__mult__neg__le,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.01/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_neg_le
% 5.01/5.22 thf(fact_2811_split__mult__neg__le,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.01/5.22 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_neg_le
% 5.01/5.22 thf(fact_2812_split__mult__neg__le,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.01/5.22 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_neg_le
% 5.01/5.22 thf(fact_2813_mult__le__0__iff,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.01/5.22 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.01/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_le_0_iff
% 5.01/5.22 thf(fact_2814_mult__le__0__iff,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.22 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.01/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_le_0_iff
% 5.01/5.22 thf(fact_2815_mult__le__0__iff,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.01/5.22 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.01/5.22 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_le_0_iff
% 5.01/5.22 thf(fact_2816_mult__right__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono
% 5.01/5.22 thf(fact_2817_mult__right__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono
% 5.01/5.22 thf(fact_2818_mult__right__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono
% 5.01/5.22 thf(fact_2819_mult__right__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono
% 5.01/5.22 thf(fact_2820_mult__right__mono__neg,axiom,
% 5.01/5.22 ! [B: real,A: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono_neg
% 5.01/5.22 thf(fact_2821_mult__right__mono__neg,axiom,
% 5.01/5.22 ! [B: rat,A: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono_neg
% 5.01/5.22 thf(fact_2822_mult__right__mono__neg,axiom,
% 5.01/5.22 ! [B: int,A: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_right_mono_neg
% 5.01/5.22 thf(fact_2823_mult__left__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono
% 5.01/5.22 thf(fact_2824_mult__left__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono
% 5.01/5.22 thf(fact_2825_mult__left__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono
% 5.01/5.22 thf(fact_2826_mult__left__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono
% 5.01/5.22 thf(fact_2827_mult__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonpos
% 5.01/5.22 thf(fact_2828_mult__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonpos
% 5.01/5.22 thf(fact_2829_mult__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_nonpos_nonpos
% 5.01/5.22 thf(fact_2830_mult__left__mono__neg,axiom,
% 5.01/5.22 ! [B: real,A: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono_neg
% 5.01/5.22 thf(fact_2831_mult__left__mono__neg,axiom,
% 5.01/5.22 ! [B: rat,A: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono_neg
% 5.01/5.22 thf(fact_2832_mult__left__mono__neg,axiom,
% 5.01/5.22 ! [B: int,A: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ B @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_left_mono_neg
% 5.01/5.22 thf(fact_2833_split__mult__pos__le,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.01/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_pos_le
% 5.01/5.22 thf(fact_2834_split__mult__pos__le,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.01/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_pos_le
% 5.01/5.22 thf(fact_2835_split__mult__pos__le,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.01/5.22 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.01/5.22 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % split_mult_pos_le
% 5.01/5.22 thf(fact_2836_zero__le__square,axiom,
% 5.01/5.22 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_square
% 5.01/5.22 thf(fact_2837_zero__le__square,axiom,
% 5.01/5.22 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_square
% 5.01/5.22 thf(fact_2838_zero__le__square,axiom,
% 5.01/5.22 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_le_square
% 5.01/5.22 thf(fact_2839_mult__mono_H,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono'
% 5.01/5.22 thf(fact_2840_mult__mono_H,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono'
% 5.01/5.22 thf(fact_2841_mult__mono_H,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono'
% 5.01/5.22 thf(fact_2842_mult__mono_H,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono'
% 5.01/5.22 thf(fact_2843_mult__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono
% 5.01/5.22 thf(fact_2844_mult__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono
% 5.01/5.22 thf(fact_2845_mult__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono
% 5.01/5.22 thf(fact_2846_mult__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ C @ D )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_mono
% 5.01/5.22 thf(fact_2847_zdiv__int,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.01/5.22 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % zdiv_int
% 5.01/5.22 thf(fact_2848_zero__less__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_numeral
% 5.01/5.22 thf(fact_2849_zero__less__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_numeral
% 5.01/5.22 thf(fact_2850_zero__less__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_numeral
% 5.01/5.22 thf(fact_2851_zero__less__numeral,axiom,
% 5.01/5.22 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.01/5.22
% 5.01/5.22 % zero_less_numeral
% 5.01/5.22 thf(fact_2852_not__numeral__less__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_less_zero
% 5.01/5.22 thf(fact_2853_not__numeral__less__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_less_zero
% 5.01/5.22 thf(fact_2854_not__numeral__less__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_less_zero
% 5.01/5.22 thf(fact_2855_not__numeral__less__zero,axiom,
% 5.01/5.22 ! [N: num] :
% 5.01/5.22 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % not_numeral_less_zero
% 5.01/5.22 thf(fact_2856_add__nonpos__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: real,Y: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.01/5.22 => ( ( ( plus_plus_real @ X2 @ Y )
% 5.01/5.22 = zero_zero_real )
% 5.01/5.22 = ( ( X2 = zero_zero_real )
% 5.01/5.22 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_eq_0_iff
% 5.01/5.22 thf(fact_2857_add__nonpos__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: rat,Y: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.01/5.22 => ( ( ( plus_plus_rat @ X2 @ Y )
% 5.01/5.22 = zero_zero_rat )
% 5.01/5.22 = ( ( X2 = zero_zero_rat )
% 5.01/5.22 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_eq_0_iff
% 5.01/5.22 thf(fact_2858_add__nonpos__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: nat,Y: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.01/5.22 => ( ( ( plus_plus_nat @ X2 @ Y )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 = ( ( X2 = zero_zero_nat )
% 5.01/5.22 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_eq_0_iff
% 5.01/5.22 thf(fact_2859_add__nonpos__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: int,Y: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.01/5.22 => ( ( ( plus_plus_int @ X2 @ Y )
% 5.01/5.22 = zero_zero_int )
% 5.01/5.22 = ( ( X2 = zero_zero_int )
% 5.01/5.22 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_eq_0_iff
% 5.01/5.22 thf(fact_2860_add__nonneg__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: real,Y: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.22 => ( ( ( plus_plus_real @ X2 @ Y )
% 5.01/5.22 = zero_zero_real )
% 5.01/5.22 = ( ( X2 = zero_zero_real )
% 5.01/5.22 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_eq_0_iff
% 5.01/5.22 thf(fact_2861_add__nonneg__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: rat,Y: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.22 => ( ( ( plus_plus_rat @ X2 @ Y )
% 5.01/5.22 = zero_zero_rat )
% 5.01/5.22 = ( ( X2 = zero_zero_rat )
% 5.01/5.22 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_eq_0_iff
% 5.01/5.22 thf(fact_2862_add__nonneg__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: nat,Y: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.01/5.22 => ( ( ( plus_plus_nat @ X2 @ Y )
% 5.01/5.22 = zero_zero_nat )
% 5.01/5.22 = ( ( X2 = zero_zero_nat )
% 5.01/5.22 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_eq_0_iff
% 5.01/5.22 thf(fact_2863_add__nonneg__eq__0__iff,axiom,
% 5.01/5.22 ! [X2: int,Y: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.22 => ( ( ( plus_plus_int @ X2 @ Y )
% 5.01/5.22 = zero_zero_int )
% 5.01/5.22 = ( ( X2 = zero_zero_int )
% 5.01/5.22 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_eq_0_iff
% 5.01/5.22 thf(fact_2864_add__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.01/5.22 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_nonpos
% 5.01/5.22 thf(fact_2865_add__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_nonpos
% 5.01/5.22 thf(fact_2866_add__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.01/5.22 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_nonpos
% 5.01/5.22 thf(fact_2867_add__nonpos__nonpos,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.22 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonpos_nonpos
% 5.01/5.22 thf(fact_2868_add__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_nonneg
% 5.01/5.22 thf(fact_2869_add__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_nonneg
% 5.01/5.22 thf(fact_2870_add__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_nonneg
% 5.01/5.22 thf(fact_2871_add__nonneg__nonneg,axiom,
% 5.01/5.22 ! [A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.22 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_nonneg_nonneg
% 5.01/5.22 thf(fact_2872_add__increasing2,axiom,
% 5.01/5.22 ! [C: real,B: real,A: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ A )
% 5.01/5.22 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing2
% 5.01/5.22 thf(fact_2873_add__increasing2,axiom,
% 5.01/5.22 ! [C: rat,B: rat,A: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.22 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing2
% 5.01/5.22 thf(fact_2874_add__increasing2,axiom,
% 5.01/5.22 ! [C: nat,B: nat,A: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.22 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing2
% 5.01/5.22 thf(fact_2875_add__increasing2,axiom,
% 5.01/5.22 ! [C: int,B: int,A: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ A )
% 5.01/5.22 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing2
% 5.01/5.22 thf(fact_2876_add__decreasing2,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ A @ B )
% 5.01/5.22 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing2
% 5.01/5.22 thf(fact_2877_add__decreasing2,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.22 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing2
% 5.01/5.22 thf(fact_2878_add__decreasing2,axiom,
% 5.01/5.22 ! [C: nat,A: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing2
% 5.01/5.22 thf(fact_2879_add__decreasing2,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ A @ B )
% 5.01/5.22 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing2
% 5.01/5.22 thf(fact_2880_add__increasing,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.22 => ( ( ord_less_eq_real @ B @ C )
% 5.01/5.22 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing
% 5.01/5.22 thf(fact_2881_add__increasing,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.22 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.22 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing
% 5.01/5.22 thf(fact_2882_add__increasing,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.22 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.22 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing
% 5.01/5.22 thf(fact_2883_add__increasing,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.22 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.22 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_increasing
% 5.01/5.22 thf(fact_2884_add__decreasing,axiom,
% 5.01/5.22 ! [A: real,C: real,B: real] :
% 5.01/5.22 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_eq_real @ C @ B )
% 5.01/5.22 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing
% 5.01/5.22 thf(fact_2885_add__decreasing,axiom,
% 5.01/5.22 ! [A: rat,C: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_eq_rat @ C @ B )
% 5.01/5.22 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing
% 5.01/5.22 thf(fact_2886_add__decreasing,axiom,
% 5.01/5.22 ! [A: nat,C: nat,B: nat] :
% 5.01/5.22 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.22 => ( ( ord_less_eq_nat @ C @ B )
% 5.01/5.22 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing
% 5.01/5.22 thf(fact_2887_add__decreasing,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_eq_int @ C @ B )
% 5.01/5.22 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % add_decreasing
% 5.01/5.22 thf(fact_2888_zero__less__one__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.01/5.22
% 5.01/5.22 % zero_less_one_class.zero_le_one
% 5.01/5.22 thf(fact_2889_zero__less__one__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.01/5.22
% 5.01/5.22 % zero_less_one_class.zero_le_one
% 5.01/5.22 thf(fact_2890_zero__less__one__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.01/5.22
% 5.01/5.22 % zero_less_one_class.zero_le_one
% 5.01/5.22 thf(fact_2891_zero__less__one__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.01/5.22
% 5.01/5.22 % zero_less_one_class.zero_le_one
% 5.01/5.22 thf(fact_2892_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.01/5.22
% 5.01/5.22 % linordered_nonzero_semiring_class.zero_le_one
% 5.01/5.22 thf(fact_2893_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.01/5.22
% 5.01/5.22 % linordered_nonzero_semiring_class.zero_le_one
% 5.01/5.22 thf(fact_2894_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.01/5.22
% 5.01/5.22 % linordered_nonzero_semiring_class.zero_le_one
% 5.01/5.22 thf(fact_2895_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.01/5.22 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.01/5.22
% 5.01/5.22 % linordered_nonzero_semiring_class.zero_le_one
% 5.01/5.22 thf(fact_2896_not__one__le__zero,axiom,
% 5.01/5.22 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.01/5.22
% 5.01/5.22 % not_one_le_zero
% 5.01/5.22 thf(fact_2897_not__one__le__zero,axiom,
% 5.01/5.22 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.01/5.22
% 5.01/5.22 % not_one_le_zero
% 5.01/5.22 thf(fact_2898_not__one__le__zero,axiom,
% 5.01/5.22 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.01/5.22
% 5.01/5.22 % not_one_le_zero
% 5.01/5.22 thf(fact_2899_not__one__le__zero,axiom,
% 5.01/5.22 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.01/5.22
% 5.01/5.22 % not_one_le_zero
% 5.01/5.22 thf(fact_2900_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.01/5.22 thf(fact_2901_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.01/5.22 thf(fact_2902_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.01/5.22 thf(fact_2903_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.01/5.22 thf(fact_2904_mult__less__cancel__right__disj,axiom,
% 5.01/5.22 ! [A: real,C: real,B: real] :
% 5.01/5.22 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.22 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 & ( ord_less_real @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.22 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_right_disj
% 5.01/5.22 thf(fact_2905_mult__less__cancel__right__disj,axiom,
% 5.01/5.22 ! [A: rat,C: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 & ( ord_less_rat @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_right_disj
% 5.01/5.22 thf(fact_2906_mult__less__cancel__right__disj,axiom,
% 5.01/5.22 ! [A: int,C: int,B: int] :
% 5.01/5.22 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.22 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 & ( ord_less_int @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.22 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_right_disj
% 5.01/5.22 thf(fact_2907_mult__strict__right__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono
% 5.01/5.22 thf(fact_2908_mult__strict__right__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono
% 5.01/5.22 thf(fact_2909_mult__strict__right__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono
% 5.01/5.22 thf(fact_2910_mult__strict__right__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono
% 5.01/5.22 thf(fact_2911_mult__strict__right__mono__neg,axiom,
% 5.01/5.22 ! [B: real,A: real,C: real] :
% 5.01/5.22 ( ( ord_less_real @ B @ A )
% 5.01/5.22 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono_neg
% 5.01/5.22 thf(fact_2912_mult__strict__right__mono__neg,axiom,
% 5.01/5.22 ! [B: rat,A: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_rat @ B @ A )
% 5.01/5.22 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono_neg
% 5.01/5.22 thf(fact_2913_mult__strict__right__mono__neg,axiom,
% 5.01/5.22 ! [B: int,A: int,C: int] :
% 5.01/5.22 ( ( ord_less_int @ B @ A )
% 5.01/5.22 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_right_mono_neg
% 5.01/5.22 thf(fact_2914_mult__less__cancel__left__disj,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.22 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 & ( ord_less_real @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.22 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_disj
% 5.01/5.22 thf(fact_2915_mult__less__cancel__left__disj,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 & ( ord_less_rat @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.22 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_disj
% 5.01/5.22 thf(fact_2916_mult__less__cancel__left__disj,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.22 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 & ( ord_less_int @ A @ B ) )
% 5.01/5.22 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.22 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_disj
% 5.01/5.22 thf(fact_2917_mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: real,B: real,C: real] :
% 5.01/5.22 ( ( ord_less_real @ A @ B )
% 5.01/5.22 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono
% 5.01/5.22 thf(fact_2918_mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: rat,B: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_rat @ A @ B )
% 5.01/5.22 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono
% 5.01/5.22 thf(fact_2919_mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: nat,B: nat,C: nat] :
% 5.01/5.22 ( ( ord_less_nat @ A @ B )
% 5.01/5.22 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.22 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono
% 5.01/5.22 thf(fact_2920_mult__strict__left__mono,axiom,
% 5.01/5.22 ! [A: int,B: int,C: int] :
% 5.01/5.22 ( ( ord_less_int @ A @ B )
% 5.01/5.22 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono
% 5.01/5.22 thf(fact_2921_mult__strict__left__mono__neg,axiom,
% 5.01/5.22 ! [B: real,A: real,C: real] :
% 5.01/5.22 ( ( ord_less_real @ B @ A )
% 5.01/5.22 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono_neg
% 5.01/5.22 thf(fact_2922_mult__strict__left__mono__neg,axiom,
% 5.01/5.22 ! [B: rat,A: rat,C: rat] :
% 5.01/5.22 ( ( ord_less_rat @ B @ A )
% 5.01/5.22 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono_neg
% 5.01/5.22 thf(fact_2923_mult__strict__left__mono__neg,axiom,
% 5.01/5.22 ! [B: int,A: int,C: int] :
% 5.01/5.22 ( ( ord_less_int @ B @ A )
% 5.01/5.22 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_strict_left_mono_neg
% 5.01/5.22 thf(fact_2924_mult__less__cancel__left__pos,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.22 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.22 = ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_pos
% 5.01/5.22 thf(fact_2925_mult__less__cancel__left__pos,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.22 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.22 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_pos
% 5.01/5.22 thf(fact_2926_mult__less__cancel__left__pos,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.22 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.22 = ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_pos
% 5.01/5.22 thf(fact_2927_mult__less__cancel__left__neg,axiom,
% 5.01/5.22 ! [C: real,A: real,B: real] :
% 5.01/5.22 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.22 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.22 = ( ord_less_real @ B @ A ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_neg
% 5.01/5.22 thf(fact_2928_mult__less__cancel__left__neg,axiom,
% 5.01/5.22 ! [C: rat,A: rat,B: rat] :
% 5.01/5.22 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.22 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.22 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.01/5.22
% 5.01/5.22 % mult_less_cancel_left_neg
% 5.01/5.22 thf(fact_2929_mult__less__cancel__left__neg,axiom,
% 5.01/5.22 ! [C: int,A: int,B: int] :
% 5.01/5.22 ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.22 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 = ( ord_less_int @ B @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_left_neg
% 5.01/5.23 thf(fact_2930_zero__less__mult__pos2,axiom,
% 5.01/5.23 ! [B: real,A: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos2
% 5.01/5.23 thf(fact_2931_zero__less__mult__pos2,axiom,
% 5.01/5.23 ! [B: rat,A: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos2
% 5.01/5.23 thf(fact_2932_zero__less__mult__pos2,axiom,
% 5.01/5.23 ! [B: nat,A: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos2
% 5.01/5.23 thf(fact_2933_zero__less__mult__pos2,axiom,
% 5.01/5.23 ! [B: int,A: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos2
% 5.01/5.23 thf(fact_2934_zero__less__mult__pos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos
% 5.01/5.23 thf(fact_2935_zero__less__mult__pos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos
% 5.01/5.23 thf(fact_2936_zero__less__mult__pos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos
% 5.01/5.23 thf(fact_2937_zero__less__mult__pos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_pos
% 5.01/5.23 thf(fact_2938_zero__less__mult__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.01/5.23 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_iff
% 5.01/5.23 thf(fact_2939_zero__less__mult__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.01/5.23 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_iff
% 5.01/5.23 thf(fact_2940_zero__less__mult__iff,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.01/5.23 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_mult_iff
% 5.01/5.23 thf(fact_2941_mult__pos__neg2,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg2
% 5.01/5.23 thf(fact_2942_mult__pos__neg2,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg2
% 5.01/5.23 thf(fact_2943_mult__pos__neg2,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg2
% 5.01/5.23 thf(fact_2944_mult__pos__neg2,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg2
% 5.01/5.23 thf(fact_2945_mult__pos__pos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_pos
% 5.01/5.23 thf(fact_2946_mult__pos__pos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_pos
% 5.01/5.23 thf(fact_2947_mult__pos__pos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_pos
% 5.01/5.23 thf(fact_2948_mult__pos__pos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_pos
% 5.01/5.23 thf(fact_2949_mult__pos__neg,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg
% 5.01/5.23 thf(fact_2950_mult__pos__neg,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg
% 5.01/5.23 thf(fact_2951_mult__pos__neg,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg
% 5.01/5.23 thf(fact_2952_mult__pos__neg,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_pos_neg
% 5.01/5.23 thf(fact_2953_mult__neg__pos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_pos
% 5.01/5.23 thf(fact_2954_mult__neg__pos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_pos
% 5.01/5.23 thf(fact_2955_mult__neg__pos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_pos
% 5.01/5.23 thf(fact_2956_mult__neg__pos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_pos
% 5.01/5.23 thf(fact_2957_mult__less__0__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.01/5.23 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_0_iff
% 5.01/5.23 thf(fact_2958_mult__less__0__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.01/5.23 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_0_iff
% 5.01/5.23 thf(fact_2959_mult__less__0__iff,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.01/5.23 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.01/5.23 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_0_iff
% 5.01/5.23 thf(fact_2960_not__square__less__zero,axiom,
% 5.01/5.23 ! [A: real] :
% 5.01/5.23 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % not_square_less_zero
% 5.01/5.23 thf(fact_2961_not__square__less__zero,axiom,
% 5.01/5.23 ! [A: rat] :
% 5.01/5.23 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % not_square_less_zero
% 5.01/5.23 thf(fact_2962_not__square__less__zero,axiom,
% 5.01/5.23 ! [A: int] :
% 5.01/5.23 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % not_square_less_zero
% 5.01/5.23 thf(fact_2963_mult__neg__neg,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_neg
% 5.01/5.23 thf(fact_2964_mult__neg__neg,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_neg
% 5.01/5.23 thf(fact_2965_mult__neg__neg,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_neg_neg
% 5.01/5.23 thf(fact_2966_le__iff__diff__le__0,axiom,
% 5.01/5.23 ( ord_less_eq_real
% 5.01/5.23 = ( ^ [A4: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_iff_diff_le_0
% 5.01/5.23 thf(fact_2967_le__iff__diff__le__0,axiom,
% 5.01/5.23 ( ord_less_eq_rat
% 5.01/5.23 = ( ^ [A4: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_iff_diff_le_0
% 5.01/5.23 thf(fact_2968_le__iff__diff__le__0,axiom,
% 5.01/5.23 ( ord_less_eq_int
% 5.01/5.23 = ( ^ [A4: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_iff_diff_le_0
% 5.01/5.23 thf(fact_2969_pos__add__strict,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ B @ C )
% 5.01/5.23 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % pos_add_strict
% 5.01/5.23 thf(fact_2970_pos__add__strict,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ B @ C )
% 5.01/5.23 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % pos_add_strict
% 5.01/5.23 thf(fact_2971_pos__add__strict,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ B @ C )
% 5.01/5.23 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % pos_add_strict
% 5.01/5.23 thf(fact_2972_pos__add__strict,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ B @ C )
% 5.01/5.23 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % pos_add_strict
% 5.01/5.23 thf(fact_2973_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ B )
% 5.01/5.23 => ~ ! [C3: nat] :
% 5.01/5.23 ( ( B
% 5.01/5.23 = ( plus_plus_nat @ A @ C3 ) )
% 5.01/5.23 => ( C3 = zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % canonically_ordered_monoid_add_class.lessE
% 5.01/5.23 thf(fact_2974_add__pos__pos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_pos
% 5.01/5.23 thf(fact_2975_add__pos__pos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_pos
% 5.01/5.23 thf(fact_2976_add__pos__pos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_pos
% 5.01/5.23 thf(fact_2977_add__pos__pos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_pos
% 5.01/5.23 thf(fact_2978_add__neg__neg,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_neg
% 5.01/5.23 thf(fact_2979_add__neg__neg,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_neg
% 5.01/5.23 thf(fact_2980_add__neg__neg,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.01/5.23 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.01/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_neg
% 5.01/5.23 thf(fact_2981_add__neg__neg,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_neg
% 5.01/5.23 thf(fact_2982_add__less__zeroD,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.23 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_less_zeroD
% 5.01/5.23 thf(fact_2983_add__less__zeroD,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y ) @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_less_zeroD
% 5.01/5.23 thf(fact_2984_add__less__zeroD,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y ) @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.01/5.23 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_less_zeroD
% 5.01/5.23 thf(fact_2985_less__numeral__extra_I1_J,axiom,
% 5.01/5.23 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.01/5.23
% 5.01/5.23 % less_numeral_extra(1)
% 5.01/5.23 thf(fact_2986_less__numeral__extra_I1_J,axiom,
% 5.01/5.23 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.01/5.23
% 5.01/5.23 % less_numeral_extra(1)
% 5.01/5.23 thf(fact_2987_less__numeral__extra_I1_J,axiom,
% 5.01/5.23 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.01/5.23
% 5.01/5.23 % less_numeral_extra(1)
% 5.01/5.23 thf(fact_2988_less__numeral__extra_I1_J,axiom,
% 5.01/5.23 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.01/5.23
% 5.01/5.23 % less_numeral_extra(1)
% 5.01/5.23 thf(fact_2989_not__one__less__zero,axiom,
% 5.01/5.23 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % not_one_less_zero
% 5.01/5.23 thf(fact_2990_not__one__less__zero,axiom,
% 5.01/5.23 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % not_one_less_zero
% 5.01/5.23 thf(fact_2991_not__one__less__zero,axiom,
% 5.01/5.23 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.01/5.23
% 5.01/5.23 % not_one_less_zero
% 5.01/5.23 thf(fact_2992_not__one__less__zero,axiom,
% 5.01/5.23 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % not_one_less_zero
% 5.01/5.23 thf(fact_2993_zero__less__one,axiom,
% 5.01/5.23 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.01/5.23
% 5.01/5.23 % zero_less_one
% 5.01/5.23 thf(fact_2994_zero__less__one,axiom,
% 5.01/5.23 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.01/5.23
% 5.01/5.23 % zero_less_one
% 5.01/5.23 thf(fact_2995_zero__less__one,axiom,
% 5.01/5.23 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.01/5.23
% 5.01/5.23 % zero_less_one
% 5.01/5.23 thf(fact_2996_zero__less__one,axiom,
% 5.01/5.23 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.01/5.23
% 5.01/5.23 % zero_less_one
% 5.01/5.23 thf(fact_2997_divide__right__mono__neg,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_right_mono_neg
% 5.01/5.23 thf(fact_2998_divide__right__mono__neg,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_right_mono_neg
% 5.01/5.23 thf(fact_2999_divide__nonpos__nonpos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_nonpos
% 5.01/5.23 thf(fact_3000_divide__nonpos__nonpos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_nonpos
% 5.01/5.23 thf(fact_3001_divide__nonpos__nonneg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_nonneg
% 5.01/5.23 thf(fact_3002_divide__nonpos__nonneg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_nonneg
% 5.01/5.23 thf(fact_3003_divide__nonneg__nonpos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_nonpos
% 5.01/5.23 thf(fact_3004_divide__nonneg__nonpos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_nonpos
% 5.01/5.23 thf(fact_3005_divide__nonneg__nonneg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_nonneg
% 5.01/5.23 thf(fact_3006_divide__nonneg__nonneg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_nonneg
% 5.01/5.23 thf(fact_3007_zero__le__divide__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.01/5.23 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_divide_iff
% 5.01/5.23 thf(fact_3008_zero__le__divide__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.01/5.23 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_divide_iff
% 5.01/5.23 thf(fact_3009_divide__right__mono,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_right_mono
% 5.01/5.23 thf(fact_3010_divide__right__mono,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_right_mono
% 5.01/5.23 thf(fact_3011_divide__le__0__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.01/5.23 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.01/5.23 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_le_0_iff
% 5.01/5.23 thf(fact_3012_divide__le__0__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.23 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.01/5.23 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_le_0_iff
% 5.01/5.23 thf(fact_3013_less__iff__diff__less__0,axiom,
% 5.01/5.23 ( ord_less_real
% 5.01/5.23 = ( ^ [A4: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A4 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % less_iff_diff_less_0
% 5.01/5.23 thf(fact_3014_less__iff__diff__less__0,axiom,
% 5.01/5.23 ( ord_less_rat
% 5.01/5.23 = ( ^ [A4: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A4 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % less_iff_diff_less_0
% 5.01/5.23 thf(fact_3015_less__iff__diff__less__0,axiom,
% 5.01/5.23 ( ord_less_int
% 5.01/5.23 = ( ^ [A4: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A4 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % less_iff_diff_less_0
% 5.01/5.23 thf(fact_3016_zero__le__power,axiom,
% 5.01/5.23 ! [A: real,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_power
% 5.01/5.23 thf(fact_3017_zero__le__power,axiom,
% 5.01/5.23 ! [A: rat,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_power
% 5.01/5.23 thf(fact_3018_zero__le__power,axiom,
% 5.01/5.23 ! [A: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_power
% 5.01/5.23 thf(fact_3019_zero__le__power,axiom,
% 5.01/5.23 ! [A: int,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_le_power
% 5.01/5.23 thf(fact_3020_power__mono,axiom,
% 5.01/5.23 ! [A: real,B: real,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_mono
% 5.01/5.23 thf(fact_3021_power__mono,axiom,
% 5.01/5.23 ! [A: rat,B: rat,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_mono
% 5.01/5.23 thf(fact_3022_power__mono,axiom,
% 5.01/5.23 ! [A: nat,B: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_mono
% 5.01/5.23 thf(fact_3023_power__mono,axiom,
% 5.01/5.23 ! [A: int,B: int,N: nat] :
% 5.01/5.23 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_mono
% 5.01/5.23 thf(fact_3024_divide__strict__right__mono__neg,axiom,
% 5.01/5.23 ! [B: real,A: real,C: real] :
% 5.01/5.23 ( ( ord_less_real @ B @ A )
% 5.01/5.23 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_strict_right_mono_neg
% 5.01/5.23 thf(fact_3025_divide__strict__right__mono__neg,axiom,
% 5.01/5.23 ! [B: rat,A: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_rat @ B @ A )
% 5.01/5.23 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_strict_right_mono_neg
% 5.01/5.23 thf(fact_3026_divide__strict__right__mono,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_strict_right_mono
% 5.01/5.23 thf(fact_3027_divide__strict__right__mono,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_strict_right_mono
% 5.01/5.23 thf(fact_3028_zero__less__divide__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.01/5.23 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_divide_iff
% 5.01/5.23 thf(fact_3029_zero__less__divide__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.01/5.23 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_divide_iff
% 5.01/5.23 thf(fact_3030_divide__less__cancel,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ B @ A ) )
% 5.01/5.23 & ( C != zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_less_cancel
% 5.01/5.23 thf(fact_3031_divide__less__cancel,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ B @ A ) )
% 5.01/5.23 & ( C != zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_less_cancel
% 5.01/5.23 thf(fact_3032_divide__less__0__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.01/5.23 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_less_0_iff
% 5.01/5.23 thf(fact_3033_divide__less__0__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.01/5.23 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_less_0_iff
% 5.01/5.23 thf(fact_3034_divide__pos__pos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_pos_pos
% 5.01/5.23 thf(fact_3035_divide__pos__pos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_pos_pos
% 5.01/5.23 thf(fact_3036_divide__pos__neg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_pos_neg
% 5.01/5.23 thf(fact_3037_divide__pos__neg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_pos_neg
% 5.01/5.23 thf(fact_3038_divide__neg__pos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_neg_pos
% 5.01/5.23 thf(fact_3039_divide__neg__pos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_neg_pos
% 5.01/5.23 thf(fact_3040_divide__neg__neg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_neg_neg
% 5.01/5.23 thf(fact_3041_divide__neg__neg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_neg_neg
% 5.01/5.23 thf(fact_3042_zero__less__power,axiom,
% 5.01/5.23 ! [A: real,N: nat] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_power
% 5.01/5.23 thf(fact_3043_zero__less__power,axiom,
% 5.01/5.23 ! [A: rat,N: nat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_power
% 5.01/5.23 thf(fact_3044_zero__less__power,axiom,
% 5.01/5.23 ! [A: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_power
% 5.01/5.23 thf(fact_3045_zero__less__power,axiom,
% 5.01/5.23 ! [A: int,N: nat] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_power
% 5.01/5.23 thf(fact_3046_zero__neq__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ( zero_zero_real
% 5.01/5.23 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_numeral
% 5.01/5.23 thf(fact_3047_zero__neq__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ( zero_zero_int
% 5.01/5.23 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_numeral
% 5.01/5.23 thf(fact_3048_zero__neq__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ( zero_zero_complex
% 5.01/5.23 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_numeral
% 5.01/5.23 thf(fact_3049_zero__neq__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ( zero_z3403309356797280102nteger
% 5.01/5.23 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_numeral
% 5.01/5.23 thf(fact_3050_zero__neq__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ( zero_zero_rat
% 5.01/5.23 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_numeral
% 5.01/5.23 thf(fact_3051_nonzero__eq__divide__eq,axiom,
% 5.01/5.23 ! [C: complex,A: complex,B: complex] :
% 5.01/5.23 ( ( C != zero_zero_complex )
% 5.01/5.23 => ( ( A
% 5.01/5.23 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.23 = ( ( times_times_complex @ A @ C )
% 5.01/5.23 = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_eq_divide_eq
% 5.01/5.23 thf(fact_3052_nonzero__eq__divide__eq,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( C != zero_zero_real )
% 5.01/5.23 => ( ( A
% 5.01/5.23 = ( divide_divide_real @ B @ C ) )
% 5.01/5.23 = ( ( times_times_real @ A @ C )
% 5.01/5.23 = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_eq_divide_eq
% 5.01/5.23 thf(fact_3053_nonzero__eq__divide__eq,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( C != zero_zero_rat )
% 5.01/5.23 => ( ( A
% 5.01/5.23 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.23 = ( ( times_times_rat @ A @ C )
% 5.01/5.23 = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_eq_divide_eq
% 5.01/5.23 thf(fact_3054_nonzero__divide__eq__eq,axiom,
% 5.01/5.23 ! [C: complex,B: complex,A: complex] :
% 5.01/5.23 ( ( C != zero_zero_complex )
% 5.01/5.23 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_divide_eq_eq
% 5.01/5.23 thf(fact_3055_nonzero__divide__eq__eq,axiom,
% 5.01/5.23 ! [C: real,B: real,A: real] :
% 5.01/5.23 ( ( C != zero_zero_real )
% 5.01/5.23 => ( ( ( divide_divide_real @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_divide_eq_eq
% 5.01/5.23 thf(fact_3056_nonzero__divide__eq__eq,axiom,
% 5.01/5.23 ! [C: rat,B: rat,A: rat] :
% 5.01/5.23 ( ( C != zero_zero_rat )
% 5.01/5.23 => ( ( ( divide_divide_rat @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_divide_eq_eq
% 5.01/5.23 thf(fact_3057_eq__divide__imp,axiom,
% 5.01/5.23 ! [C: complex,A: complex,B: complex] :
% 5.01/5.23 ( ( C != zero_zero_complex )
% 5.01/5.23 => ( ( ( times_times_complex @ A @ C )
% 5.01/5.23 = B )
% 5.01/5.23 => ( A
% 5.01/5.23 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_imp
% 5.01/5.23 thf(fact_3058_eq__divide__imp,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( C != zero_zero_real )
% 5.01/5.23 => ( ( ( times_times_real @ A @ C )
% 5.01/5.23 = B )
% 5.01/5.23 => ( A
% 5.01/5.23 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_imp
% 5.01/5.23 thf(fact_3059_eq__divide__imp,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( C != zero_zero_rat )
% 5.01/5.23 => ( ( ( times_times_rat @ A @ C )
% 5.01/5.23 = B )
% 5.01/5.23 => ( A
% 5.01/5.23 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_imp
% 5.01/5.23 thf(fact_3060_divide__eq__imp,axiom,
% 5.01/5.23 ! [C: complex,B: complex,A: complex] :
% 5.01/5.23 ( ( C != zero_zero_complex )
% 5.01/5.23 => ( ( B
% 5.01/5.23 = ( times_times_complex @ A @ C ) )
% 5.01/5.23 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.01/5.23 = A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_imp
% 5.01/5.23 thf(fact_3061_divide__eq__imp,axiom,
% 5.01/5.23 ! [C: real,B: real,A: real] :
% 5.01/5.23 ( ( C != zero_zero_real )
% 5.01/5.23 => ( ( B
% 5.01/5.23 = ( times_times_real @ A @ C ) )
% 5.01/5.23 => ( ( divide_divide_real @ B @ C )
% 5.01/5.23 = A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_imp
% 5.01/5.23 thf(fact_3062_divide__eq__imp,axiom,
% 5.01/5.23 ! [C: rat,B: rat,A: rat] :
% 5.01/5.23 ( ( C != zero_zero_rat )
% 5.01/5.23 => ( ( B
% 5.01/5.23 = ( times_times_rat @ A @ C ) )
% 5.01/5.23 => ( ( divide_divide_rat @ B @ C )
% 5.01/5.23 = A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_imp
% 5.01/5.23 thf(fact_3063_eq__divide__eq,axiom,
% 5.01/5.23 ! [A: complex,B: complex,C: complex] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.23 = ( ( ( C != zero_zero_complex )
% 5.01/5.23 => ( ( times_times_complex @ A @ C )
% 5.01/5.23 = B ) )
% 5.01/5.23 & ( ( C = zero_zero_complex )
% 5.01/5.23 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_eq
% 5.01/5.23 thf(fact_3064_eq__divide__eq,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( divide_divide_real @ B @ C ) )
% 5.01/5.23 = ( ( ( C != zero_zero_real )
% 5.01/5.23 => ( ( times_times_real @ A @ C )
% 5.01/5.23 = B ) )
% 5.01/5.23 & ( ( C = zero_zero_real )
% 5.01/5.23 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_eq
% 5.01/5.23 thf(fact_3065_eq__divide__eq,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.23 = ( ( ( C != zero_zero_rat )
% 5.01/5.23 => ( ( times_times_rat @ A @ C )
% 5.01/5.23 = B ) )
% 5.01/5.23 & ( ( C = zero_zero_rat )
% 5.01/5.23 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_divide_eq
% 5.01/5.23 thf(fact_3066_divide__eq__eq,axiom,
% 5.01/5.23 ! [B: complex,C: complex,A: complex] :
% 5.01/5.23 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( ( ( C != zero_zero_complex )
% 5.01/5.23 => ( B
% 5.01/5.23 = ( times_times_complex @ A @ C ) ) )
% 5.01/5.23 & ( ( C = zero_zero_complex )
% 5.01/5.23 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_eq
% 5.01/5.23 thf(fact_3067_divide__eq__eq,axiom,
% 5.01/5.23 ! [B: real,C: real,A: real] :
% 5.01/5.23 ( ( ( divide_divide_real @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( ( ( C != zero_zero_real )
% 5.01/5.23 => ( B
% 5.01/5.23 = ( times_times_real @ A @ C ) ) )
% 5.01/5.23 & ( ( C = zero_zero_real )
% 5.01/5.23 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_eq
% 5.01/5.23 thf(fact_3068_divide__eq__eq,axiom,
% 5.01/5.23 ! [B: rat,C: rat,A: rat] :
% 5.01/5.23 ( ( ( divide_divide_rat @ B @ C )
% 5.01/5.23 = A )
% 5.01/5.23 = ( ( ( C != zero_zero_rat )
% 5.01/5.23 => ( B
% 5.01/5.23 = ( times_times_rat @ A @ C ) ) )
% 5.01/5.23 & ( ( C = zero_zero_rat )
% 5.01/5.23 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_eq_eq
% 5.01/5.23 thf(fact_3069_frac__eq__eq,axiom,
% 5.01/5.23 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 5.01/5.23 ( ( Y != zero_zero_complex )
% 5.01/5.23 => ( ( Z != zero_zero_complex )
% 5.01/5.23 => ( ( ( divide1717551699836669952omplex @ X2 @ Y )
% 5.01/5.23 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.01/5.23 = ( ( times_times_complex @ X2 @ Z )
% 5.01/5.23 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_eq_eq
% 5.01/5.23 thf(fact_3070_frac__eq__eq,axiom,
% 5.01/5.23 ! [Y: real,Z: real,X2: real,W: real] :
% 5.01/5.23 ( ( Y != zero_zero_real )
% 5.01/5.23 => ( ( Z != zero_zero_real )
% 5.01/5.23 => ( ( ( divide_divide_real @ X2 @ Y )
% 5.01/5.23 = ( divide_divide_real @ W @ Z ) )
% 5.01/5.23 = ( ( times_times_real @ X2 @ Z )
% 5.01/5.23 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_eq_eq
% 5.01/5.23 thf(fact_3071_frac__eq__eq,axiom,
% 5.01/5.23 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.01/5.23 ( ( Y != zero_zero_rat )
% 5.01/5.23 => ( ( Z != zero_zero_rat )
% 5.01/5.23 => ( ( ( divide_divide_rat @ X2 @ Y )
% 5.01/5.23 = ( divide_divide_rat @ W @ Z ) )
% 5.01/5.23 = ( ( times_times_rat @ X2 @ Z )
% 5.01/5.23 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_eq_eq
% 5.01/5.23 thf(fact_3072_right__inverse__eq,axiom,
% 5.01/5.23 ! [B: complex,A: complex] :
% 5.01/5.23 ( ( B != zero_zero_complex )
% 5.01/5.23 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.01/5.23 = one_one_complex )
% 5.01/5.23 = ( A = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % right_inverse_eq
% 5.01/5.23 thf(fact_3073_right__inverse__eq,axiom,
% 5.01/5.23 ! [B: real,A: real] :
% 5.01/5.23 ( ( B != zero_zero_real )
% 5.01/5.23 => ( ( ( divide_divide_real @ A @ B )
% 5.01/5.23 = one_one_real )
% 5.01/5.23 = ( A = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % right_inverse_eq
% 5.01/5.23 thf(fact_3074_right__inverse__eq,axiom,
% 5.01/5.23 ! [B: rat,A: rat] :
% 5.01/5.23 ( ( B != zero_zero_rat )
% 5.01/5.23 => ( ( ( divide_divide_rat @ A @ B )
% 5.01/5.23 = one_one_rat )
% 5.01/5.23 = ( A = B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % right_inverse_eq
% 5.01/5.23 thf(fact_3075_neg__eq__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ( uminus_uminus_real @ A )
% 5.01/5.23 = B )
% 5.01/5.23 = ( ( plus_plus_real @ A @ B )
% 5.01/5.23 = zero_zero_real ) ) ).
% 5.01/5.23
% 5.01/5.23 % neg_eq_iff_add_eq_0
% 5.01/5.23 thf(fact_3076_neg__eq__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ( uminus_uminus_int @ A )
% 5.01/5.23 = B )
% 5.01/5.23 = ( ( plus_plus_int @ A @ B )
% 5.01/5.23 = zero_zero_int ) ) ).
% 5.01/5.23
% 5.01/5.23 % neg_eq_iff_add_eq_0
% 5.01/5.23 thf(fact_3077_neg__eq__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: complex,B: complex] :
% 5.01/5.23 ( ( ( uminus1482373934393186551omplex @ A )
% 5.01/5.23 = B )
% 5.01/5.23 = ( ( plus_plus_complex @ A @ B )
% 5.01/5.23 = zero_zero_complex ) ) ).
% 5.01/5.23
% 5.01/5.23 % neg_eq_iff_add_eq_0
% 5.01/5.23 thf(fact_3078_neg__eq__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( ( uminus1351360451143612070nteger @ A )
% 5.01/5.23 = B )
% 5.01/5.23 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.01/5.23 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.23
% 5.01/5.23 % neg_eq_iff_add_eq_0
% 5.01/5.23 thf(fact_3079_neg__eq__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ( uminus_uminus_rat @ A )
% 5.01/5.23 = B )
% 5.01/5.23 = ( ( plus_plus_rat @ A @ B )
% 5.01/5.23 = zero_zero_rat ) ) ).
% 5.01/5.23
% 5.01/5.23 % neg_eq_iff_add_eq_0
% 5.01/5.23 thf(fact_3080_eq__neg__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( uminus_uminus_real @ B ) )
% 5.01/5.23 = ( ( plus_plus_real @ A @ B )
% 5.01/5.23 = zero_zero_real ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_neg_iff_add_eq_0
% 5.01/5.23 thf(fact_3081_eq__neg__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( uminus_uminus_int @ B ) )
% 5.01/5.23 = ( ( plus_plus_int @ A @ B )
% 5.01/5.23 = zero_zero_int ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_neg_iff_add_eq_0
% 5.01/5.23 thf(fact_3082_eq__neg__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: complex,B: complex] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( uminus1482373934393186551omplex @ B ) )
% 5.01/5.23 = ( ( plus_plus_complex @ A @ B )
% 5.01/5.23 = zero_zero_complex ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_neg_iff_add_eq_0
% 5.01/5.23 thf(fact_3083_eq__neg__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( uminus1351360451143612070nteger @ B ) )
% 5.01/5.23 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.01/5.23 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_neg_iff_add_eq_0
% 5.01/5.23 thf(fact_3084_eq__neg__iff__add__eq__0,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( A
% 5.01/5.23 = ( uminus_uminus_rat @ B ) )
% 5.01/5.23 = ( ( plus_plus_rat @ A @ B )
% 5.01/5.23 = zero_zero_rat ) ) ).
% 5.01/5.23
% 5.01/5.23 % eq_neg_iff_add_eq_0
% 5.01/5.23 thf(fact_3085_add_Oinverse__unique,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ( plus_plus_real @ A @ B )
% 5.01/5.23 = zero_zero_real )
% 5.01/5.23 => ( ( uminus_uminus_real @ A )
% 5.01/5.23 = B ) ) ).
% 5.01/5.23
% 5.01/5.23 % add.inverse_unique
% 5.01/5.23 thf(fact_3086_add_Oinverse__unique,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ( plus_plus_int @ A @ B )
% 5.01/5.23 = zero_zero_int )
% 5.01/5.23 => ( ( uminus_uminus_int @ A )
% 5.01/5.23 = B ) ) ).
% 5.01/5.23
% 5.01/5.23 % add.inverse_unique
% 5.01/5.23 thf(fact_3087_add_Oinverse__unique,axiom,
% 5.01/5.23 ! [A: complex,B: complex] :
% 5.01/5.23 ( ( ( plus_plus_complex @ A @ B )
% 5.01/5.23 = zero_zero_complex )
% 5.01/5.23 => ( ( uminus1482373934393186551omplex @ A )
% 5.01/5.23 = B ) ) ).
% 5.01/5.23
% 5.01/5.23 % add.inverse_unique
% 5.01/5.23 thf(fact_3088_add_Oinverse__unique,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.01/5.23 = zero_z3403309356797280102nteger )
% 5.01/5.23 => ( ( uminus1351360451143612070nteger @ A )
% 5.01/5.23 = B ) ) ).
% 5.01/5.23
% 5.01/5.23 % add.inverse_unique
% 5.01/5.23 thf(fact_3089_add_Oinverse__unique,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ( plus_plus_rat @ A @ B )
% 5.01/5.23 = zero_zero_rat )
% 5.01/5.23 => ( ( uminus_uminus_rat @ A )
% 5.01/5.23 = B ) ) ).
% 5.01/5.23
% 5.01/5.23 % add.inverse_unique
% 5.01/5.23 thf(fact_3090_ab__group__add__class_Oab__left__minus,axiom,
% 5.01/5.23 ! [A: real] :
% 5.01/5.23 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.01/5.23 = zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % ab_group_add_class.ab_left_minus
% 5.01/5.23 thf(fact_3091_ab__group__add__class_Oab__left__minus,axiom,
% 5.01/5.23 ! [A: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.01/5.23 = zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % ab_group_add_class.ab_left_minus
% 5.01/5.23 thf(fact_3092_ab__group__add__class_Oab__left__minus,axiom,
% 5.01/5.23 ! [A: complex] :
% 5.01/5.23 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.01/5.23 = zero_zero_complex ) ).
% 5.01/5.23
% 5.01/5.23 % ab_group_add_class.ab_left_minus
% 5.01/5.23 thf(fact_3093_ab__group__add__class_Oab__left__minus,axiom,
% 5.01/5.23 ! [A: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.01/5.23 = zero_z3403309356797280102nteger ) ).
% 5.01/5.23
% 5.01/5.23 % ab_group_add_class.ab_left_minus
% 5.01/5.23 thf(fact_3094_ab__group__add__class_Oab__left__minus,axiom,
% 5.01/5.23 ! [A: rat] :
% 5.01/5.23 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.01/5.23 = zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % ab_group_add_class.ab_left_minus
% 5.01/5.23 thf(fact_3095_add__eq__0__iff,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ( plus_plus_real @ A @ B )
% 5.01/5.23 = zero_zero_real )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( uminus_uminus_real @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_eq_0_iff
% 5.01/5.23 thf(fact_3096_add__eq__0__iff,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ( plus_plus_int @ A @ B )
% 5.01/5.23 = zero_zero_int )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( uminus_uminus_int @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_eq_0_iff
% 5.01/5.23 thf(fact_3097_add__eq__0__iff,axiom,
% 5.01/5.23 ! [A: complex,B: complex] :
% 5.01/5.23 ( ( ( plus_plus_complex @ A @ B )
% 5.01/5.23 = zero_zero_complex )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_eq_0_iff
% 5.01/5.23 thf(fact_3098_add__eq__0__iff,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.01/5.23 = zero_z3403309356797280102nteger )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_eq_0_iff
% 5.01/5.23 thf(fact_3099_add__eq__0__iff,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ( plus_plus_rat @ A @ B )
% 5.01/5.23 = zero_zero_rat )
% 5.01/5.23 = ( B
% 5.01/5.23 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_eq_0_iff
% 5.01/5.23 thf(fact_3100_zero__neq__neg__one,axiom,
% 5.01/5.23 ( zero_zero_real
% 5.01/5.23 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_one
% 5.01/5.23 thf(fact_3101_zero__neq__neg__one,axiom,
% 5.01/5.23 ( zero_zero_int
% 5.01/5.23 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_one
% 5.01/5.23 thf(fact_3102_zero__neq__neg__one,axiom,
% 5.01/5.23 ( zero_zero_complex
% 5.01/5.23 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_one
% 5.01/5.23 thf(fact_3103_zero__neq__neg__one,axiom,
% 5.01/5.23 ( zero_z3403309356797280102nteger
% 5.01/5.23 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_one
% 5.01/5.23 thf(fact_3104_zero__neq__neg__one,axiom,
% 5.01/5.23 ( zero_zero_rat
% 5.01/5.23 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.01/5.23
% 5.01/5.23 % zero_neq_neg_one
% 5.01/5.23 thf(fact_3105_of__nat__0__le__iff,axiom,
% 5.01/5.23 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_0_le_iff
% 5.01/5.23 thf(fact_3106_of__nat__0__le__iff,axiom,
% 5.01/5.23 ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_0_le_iff
% 5.01/5.23 thf(fact_3107_of__nat__0__le__iff,axiom,
% 5.01/5.23 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_0_le_iff
% 5.01/5.23 thf(fact_3108_of__nat__0__le__iff,axiom,
% 5.01/5.23 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_0_le_iff
% 5.01/5.23 thf(fact_3109_of__nat__0__le__iff,axiom,
% 5.01/5.23 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_0_le_iff
% 5.01/5.23 thf(fact_3110_of__nat__less__0__iff,axiom,
% 5.01/5.23 ! [M: nat] :
% 5.01/5.23 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_less_0_iff
% 5.01/5.23 thf(fact_3111_of__nat__less__0__iff,axiom,
% 5.01/5.23 ! [M: nat] :
% 5.01/5.23 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_less_0_iff
% 5.01/5.23 thf(fact_3112_of__nat__less__0__iff,axiom,
% 5.01/5.23 ! [M: nat] :
% 5.01/5.23 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_less_0_iff
% 5.01/5.23 thf(fact_3113_of__nat__less__0__iff,axiom,
% 5.01/5.23 ! [M: nat] :
% 5.01/5.23 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_less_0_iff
% 5.01/5.23 thf(fact_3114_of__nat__less__0__iff,axiom,
% 5.01/5.23 ! [M: nat] :
% 5.01/5.23 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_less_0_iff
% 5.01/5.23 thf(fact_3115_nonzero__minus__divide__divide,axiom,
% 5.01/5.23 ! [B: real,A: real] :
% 5.01/5.23 ( ( B != zero_zero_real )
% 5.01/5.23 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.01/5.23 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_divide
% 5.01/5.23 thf(fact_3116_nonzero__minus__divide__divide,axiom,
% 5.01/5.23 ! [B: complex,A: complex] :
% 5.01/5.23 ( ( B != zero_zero_complex )
% 5.01/5.23 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.01/5.23 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_divide
% 5.01/5.23 thf(fact_3117_nonzero__minus__divide__divide,axiom,
% 5.01/5.23 ! [B: rat,A: rat] :
% 5.01/5.23 ( ( B != zero_zero_rat )
% 5.01/5.23 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.01/5.23 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_divide
% 5.01/5.23 thf(fact_3118_nonzero__minus__divide__right,axiom,
% 5.01/5.23 ! [B: real,A: real] :
% 5.01/5.23 ( ( B != zero_zero_real )
% 5.01/5.23 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.23 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_right
% 5.01/5.23 thf(fact_3119_nonzero__minus__divide__right,axiom,
% 5.01/5.23 ! [B: complex,A: complex] :
% 5.01/5.23 ( ( B != zero_zero_complex )
% 5.01/5.23 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.23 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_right
% 5.01/5.23 thf(fact_3120_nonzero__minus__divide__right,axiom,
% 5.01/5.23 ! [B: rat,A: rat] :
% 5.01/5.23 ( ( B != zero_zero_rat )
% 5.01/5.23 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.23 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nonzero_minus_divide_right
% 5.01/5.23 thf(fact_3121_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 5.01/5.23 ! [A: $o,B: $o] :
% 5.01/5.23 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A @ B ) )
% 5.01/5.23 = one_one_real ) ).
% 5.01/5.23
% 5.01/5.23 % VEBT_internal.cnt.simps(1)
% 5.01/5.23 thf(fact_3122_power__0,axiom,
% 5.01/5.23 ! [A: rat] :
% 5.01/5.23 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.01/5.23 = one_one_rat ) ).
% 5.01/5.23
% 5.01/5.23 % power_0
% 5.01/5.23 thf(fact_3123_power__0,axiom,
% 5.01/5.23 ! [A: real] :
% 5.01/5.23 ( ( power_power_real @ A @ zero_zero_nat )
% 5.01/5.23 = one_one_real ) ).
% 5.01/5.23
% 5.01/5.23 % power_0
% 5.01/5.23 thf(fact_3124_power__0,axiom,
% 5.01/5.23 ! [A: nat] :
% 5.01/5.23 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.01/5.23 = one_one_nat ) ).
% 5.01/5.23
% 5.01/5.23 % power_0
% 5.01/5.23 thf(fact_3125_power__0,axiom,
% 5.01/5.23 ! [A: int] :
% 5.01/5.23 ( ( power_power_int @ A @ zero_zero_nat )
% 5.01/5.23 = one_one_int ) ).
% 5.01/5.23
% 5.01/5.23 % power_0
% 5.01/5.23 thf(fact_3126_power__0,axiom,
% 5.01/5.23 ! [A: complex] :
% 5.01/5.23 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.01/5.23 = one_one_complex ) ).
% 5.01/5.23
% 5.01/5.23 % power_0
% 5.01/5.23 thf(fact_3127_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.01/5.23 != zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3128_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.01/5.23 != zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3129_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.01/5.23 != zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3130_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.01/5.23 != zero_zero_complex ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3131_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.01/5.23 != zero_zero_nat ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3132_of__nat__neq__0,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( semiri4939895301339042750nteger @ ( suc @ N ) )
% 5.01/5.23 != zero_z3403309356797280102nteger ) ).
% 5.01/5.23
% 5.01/5.23 % of_nat_neq_0
% 5.01/5.23 thf(fact_3133_less__Suc__eq__0__disj,axiom,
% 5.01/5.23 ! [M: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.01/5.23 = ( ( M = zero_zero_nat )
% 5.01/5.23 | ? [J3: nat] :
% 5.01/5.23 ( ( M
% 5.01/5.23 = ( suc @ J3 ) )
% 5.01/5.23 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % less_Suc_eq_0_disj
% 5.01/5.23 thf(fact_3134_gr0__implies__Suc,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.23 => ? [M4: nat] :
% 5.01/5.23 ( N
% 5.01/5.23 = ( suc @ M4 ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % gr0_implies_Suc
% 5.01/5.23 thf(fact_3135_All__less__Suc2,axiom,
% 5.01/5.23 ! [N: nat,P: nat > $o] :
% 5.01/5.23 ( ( ! [I4: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.01/5.23 => ( P @ I4 ) ) )
% 5.01/5.23 = ( ( P @ zero_zero_nat )
% 5.01/5.23 & ! [I4: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I4 @ N )
% 5.01/5.23 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % All_less_Suc2
% 5.01/5.23 thf(fact_3136_gr0__conv__Suc,axiom,
% 5.01/5.23 ! [N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.23 = ( ? [M3: nat] :
% 5.01/5.23 ( N
% 5.01/5.23 = ( suc @ M3 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % gr0_conv_Suc
% 5.01/5.23 thf(fact_3137_Ex__less__Suc2,axiom,
% 5.01/5.23 ! [N: nat,P: nat > $o] :
% 5.01/5.23 ( ( ? [I4: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.01/5.23 & ( P @ I4 ) ) )
% 5.01/5.23 = ( ( P @ zero_zero_nat )
% 5.01/5.23 | ? [I4: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I4 @ N )
% 5.01/5.23 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % Ex_less_Suc2
% 5.01/5.23 thf(fact_3138_add__is__1,axiom,
% 5.01/5.23 ! [M: nat,N: nat] :
% 5.01/5.23 ( ( ( plus_plus_nat @ M @ N )
% 5.01/5.23 = ( suc @ zero_zero_nat ) )
% 5.01/5.23 = ( ( ( M
% 5.01/5.23 = ( suc @ zero_zero_nat ) )
% 5.01/5.23 & ( N = zero_zero_nat ) )
% 5.01/5.23 | ( ( M = zero_zero_nat )
% 5.01/5.23 & ( N
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_is_1
% 5.01/5.23 thf(fact_3139_one__is__add,axiom,
% 5.01/5.23 ! [M: nat,N: nat] :
% 5.01/5.23 ( ( ( suc @ zero_zero_nat )
% 5.01/5.23 = ( plus_plus_nat @ M @ N ) )
% 5.01/5.23 = ( ( ( M
% 5.01/5.23 = ( suc @ zero_zero_nat ) )
% 5.01/5.23 & ( N = zero_zero_nat ) )
% 5.01/5.23 | ( ( M = zero_zero_nat )
% 5.01/5.23 & ( N
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % one_is_add
% 5.01/5.23 thf(fact_3140_ex__least__nat__le,axiom,
% 5.01/5.23 ! [P: nat > $o,N: nat] :
% 5.01/5.23 ( ( P @ N )
% 5.01/5.23 => ( ~ ( P @ zero_zero_nat )
% 5.01/5.23 => ? [K3: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ K3 @ N )
% 5.01/5.23 & ! [I2: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I2 @ K3 )
% 5.01/5.23 => ~ ( P @ I2 ) )
% 5.01/5.23 & ( P @ K3 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % ex_least_nat_le
% 5.01/5.23 thf(fact_3141_less__imp__add__positive,axiom,
% 5.01/5.23 ! [I: nat,J: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I @ J )
% 5.01/5.23 => ? [K3: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.01/5.23 & ( ( plus_plus_nat @ I @ K3 )
% 5.01/5.23 = J ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % less_imp_add_positive
% 5.01/5.23 thf(fact_3142_diff__less,axiom,
% 5.01/5.23 ! [N: nat,M: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.23 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % diff_less
% 5.01/5.23 thf(fact_3143_mult__less__mono2,axiom,
% 5.01/5.23 ! [I: nat,J: nat,K: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I @ J )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_mono2
% 5.01/5.23 thf(fact_3144_mult__less__mono1,axiom,
% 5.01/5.23 ! [I: nat,J: nat,K: nat] :
% 5.01/5.23 ( ( ord_less_nat @ I @ J )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_mono1
% 5.01/5.23 thf(fact_3145_nat__mult__less__cancel1,axiom,
% 5.01/5.23 ! [K: nat,M: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.23 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.23 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nat_mult_less_cancel1
% 5.01/5.23 thf(fact_3146_nat__mult__eq__cancel1,axiom,
% 5.01/5.23 ! [K: nat,M: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.23 => ( ( ( times_times_nat @ K @ M )
% 5.01/5.23 = ( times_times_nat @ K @ N ) )
% 5.01/5.23 = ( M = N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nat_mult_eq_cancel1
% 5.01/5.23 thf(fact_3147_One__nat__def,axiom,
% 5.01/5.23 ( one_one_nat
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % One_nat_def
% 5.01/5.23 thf(fact_3148_divmod__digit__0_I2_J,axiom,
% 5.01/5.23 ! [B: nat,A: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.01/5.23 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(2)
% 5.01/5.23 thf(fact_3149_divmod__digit__0_I2_J,axiom,
% 5.01/5.23 ! [B: int,A: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.01/5.23 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(2)
% 5.01/5.23 thf(fact_3150_divmod__digit__0_I2_J,axiom,
% 5.01/5.23 ! [B: code_integer,A: code_integer] :
% 5.01/5.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.23 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.01/5.23 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(2)
% 5.01/5.23 thf(fact_3151_option_Osize_I3_J,axiom,
% 5.01/5.23 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % option.size(3)
% 5.01/5.23 thf(fact_3152_option_Osize_I3_J,axiom,
% 5.01/5.23 ( ( size_size_option_num @ none_num )
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % option.size(3)
% 5.01/5.23 thf(fact_3153_option_Osize_I4_J,axiom,
% 5.01/5.23 ! [X23: product_prod_nat_nat] :
% 5.01/5.23 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % option.size(4)
% 5.01/5.23 thf(fact_3154_option_Osize_I4_J,axiom,
% 5.01/5.23 ! [X23: num] :
% 5.01/5.23 ( ( size_size_option_num @ ( some_num @ X23 ) )
% 5.01/5.23 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % option.size(4)
% 5.01/5.23 thf(fact_3155_diff__add__0,axiom,
% 5.01/5.23 ! [N: nat,M: nat] :
% 5.01/5.23 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.23 = zero_zero_nat ) ).
% 5.01/5.23
% 5.01/5.23 % diff_add_0
% 5.01/5.23 thf(fact_3156_bits__stable__imp__add__self,axiom,
% 5.01/5.23 ! [A: nat] :
% 5.01/5.23 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.23 = A )
% 5.01/5.23 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.23 = zero_zero_nat ) ) ).
% 5.01/5.23
% 5.01/5.23 % bits_stable_imp_add_self
% 5.01/5.23 thf(fact_3157_bits__stable__imp__add__self,axiom,
% 5.01/5.23 ! [A: int] :
% 5.01/5.23 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.23 = A )
% 5.01/5.23 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.01/5.23 = zero_zero_int ) ) ).
% 5.01/5.23
% 5.01/5.23 % bits_stable_imp_add_self
% 5.01/5.23 thf(fact_3158_bits__stable__imp__add__self,axiom,
% 5.01/5.23 ! [A: code_integer] :
% 5.01/5.23 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.23 = A )
% 5.01/5.23 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.01/5.23 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.23
% 5.01/5.23 % bits_stable_imp_add_self
% 5.01/5.23 thf(fact_3159_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.01/5.23 ! [M: nat,N: nat] :
% 5.01/5.23 ( ( ( divide_divide_nat @ M @ N )
% 5.01/5.23 = zero_zero_nat )
% 5.01/5.23 = ( ( ord_less_nat @ M @ N )
% 5.01/5.23 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % Euclidean_Division.div_eq_0_iff
% 5.01/5.23 thf(fact_3160_nat__power__less__imp__less,axiom,
% 5.01/5.23 ! [I: nat,M: nat,N: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.01/5.23 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.01/5.23 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nat_power_less_imp_less
% 5.01/5.23 thf(fact_3161_mult__eq__self__implies__10,axiom,
% 5.01/5.23 ! [M: nat,N: nat] :
% 5.01/5.23 ( ( M
% 5.01/5.23 = ( times_times_nat @ M @ N ) )
% 5.01/5.23 => ( ( N = one_one_nat )
% 5.01/5.23 | ( M = zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_eq_self_implies_10
% 5.01/5.23 thf(fact_3162_VEBT__internal_Omembermima_Ocases,axiom,
% 5.01/5.23 ! [X2: produc9072475918466114483BT_nat] :
% 5.01/5.23 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 5.01/5.23 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) )
% 5.01/5.23 => ( ! [Mi3: nat,Ma3: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X4 ) )
% 5.01/5.23 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT,X4: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ X4 ) )
% 5.01/5.23 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X4: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X4 ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % VEBT_internal.membermima.cases
% 5.01/5.23 thf(fact_3163_divmod__digit__0_I1_J,axiom,
% 5.01/5.23 ! [B: nat,A: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.23 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(1)
% 5.01/5.23 thf(fact_3164_divmod__digit__0_I1_J,axiom,
% 5.01/5.23 ! [B: int,A: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.23 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(1)
% 5.01/5.23 thf(fact_3165_divmod__digit__0_I1_J,axiom,
% 5.01/5.23 ! [B: code_integer,A: code_integer] :
% 5.01/5.23 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.23 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.23 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.23 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divmod_digit_0(1)
% 5.01/5.23 thf(fact_3166_cong__exp__iff__simps_I6_J,axiom,
% 5.01/5.23 ! [Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(6)
% 5.01/5.23 thf(fact_3167_cong__exp__iff__simps_I6_J,axiom,
% 5.01/5.23 ! [Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(6)
% 5.01/5.23 thf(fact_3168_cong__exp__iff__simps_I6_J,axiom,
% 5.01/5.23 ! [Q2: num,N: num] :
% 5.01/5.23 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(6)
% 5.01/5.23 thf(fact_3169_cong__exp__iff__simps_I8_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num] :
% 5.01/5.23 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(8)
% 5.01/5.23 thf(fact_3170_cong__exp__iff__simps_I8_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num] :
% 5.01/5.23 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(8)
% 5.01/5.23 thf(fact_3171_cong__exp__iff__simps_I8_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num] :
% 5.01/5.23 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(8)
% 5.01/5.23 thf(fact_3172_div__mult1__eq,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat] :
% 5.01/5.23 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.23 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult1_eq
% 5.01/5.23 thf(fact_3173_div__mult1__eq,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int] :
% 5.01/5.23 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.23 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult1_eq
% 5.01/5.23 thf(fact_3174_div__mult1__eq,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.23 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.23 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult1_eq
% 5.01/5.23 thf(fact_3175_cancel__div__mod__rules_I2_J,axiom,
% 5.01/5.23 ! [B: nat,A: nat,C: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_plus_nat @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(2)
% 5.01/5.23 thf(fact_3176_cancel__div__mod__rules_I2_J,axiom,
% 5.01/5.23 ! [B: int,A: int,C: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_plus_int @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(2)
% 5.01/5.23 thf(fact_3177_cancel__div__mod__rules_I2_J,axiom,
% 5.01/5.23 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(2)
% 5.01/5.23 thf(fact_3178_cancel__div__mod__rules_I1_J,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_plus_nat @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(1)
% 5.01/5.23 thf(fact_3179_cancel__div__mod__rules_I1_J,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_plus_int @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(1)
% 5.01/5.23 thf(fact_3180_cancel__div__mod__rules_I1_J,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.01/5.23 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.01/5.23
% 5.01/5.23 % cancel_div_mod_rules(1)
% 5.01/5.23 thf(fact_3181_mod__div__decomp,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( A
% 5.01/5.23 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_decomp
% 5.01/5.23 thf(fact_3182_mod__div__decomp,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( A
% 5.01/5.23 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_decomp
% 5.01/5.23 thf(fact_3183_mod__div__decomp,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( A
% 5.01/5.23 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_decomp
% 5.01/5.23 thf(fact_3184_div__mult__mod__eq,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult_mod_eq
% 5.01/5.23 thf(fact_3185_div__mult__mod__eq,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult_mod_eq
% 5.01/5.23 thf(fact_3186_div__mult__mod__eq,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % div_mult_mod_eq
% 5.01/5.23 thf(fact_3187_mod__div__mult__eq,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_mult_eq
% 5.01/5.23 thf(fact_3188_mod__div__mult__eq,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_mult_eq
% 5.01/5.23 thf(fact_3189_mod__div__mult__eq,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_div_mult_eq
% 5.01/5.23 thf(fact_3190_mod__mult__div__eq,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_mult_div_eq
% 5.01/5.23 thf(fact_3191_mod__mult__div__eq,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_mult_div_eq
% 5.01/5.23 thf(fact_3192_mod__mult__div__eq,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mod_mult_div_eq
% 5.01/5.23 thf(fact_3193_mult__div__mod__eq,axiom,
% 5.01/5.23 ! [B: nat,A: nat] :
% 5.01/5.23 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mult_div_mod_eq
% 5.01/5.23 thf(fact_3194_mult__div__mod__eq,axiom,
% 5.01/5.23 ! [B: int,A: int] :
% 5.01/5.23 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mult_div_mod_eq
% 5.01/5.23 thf(fact_3195_mult__div__mod__eq,axiom,
% 5.01/5.23 ! [B: code_integer,A: code_integer] :
% 5.01/5.23 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.23 = A ) ).
% 5.01/5.23
% 5.01/5.23 % mult_div_mod_eq
% 5.01/5.23 thf(fact_3196_minus__mult__div__eq__mod,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.01/5.23 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mult_div_eq_mod
% 5.01/5.23 thf(fact_3197_minus__mult__div__eq__mod,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.01/5.23 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mult_div_eq_mod
% 5.01/5.23 thf(fact_3198_minus__mult__div__eq__mod,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.01/5.23 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mult_div_eq_mod
% 5.01/5.23 thf(fact_3199_minus__mod__eq__mult__div,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.23 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_mult_div
% 5.01/5.23 thf(fact_3200_minus__mod__eq__mult__div,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.23 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_mult_div
% 5.01/5.23 thf(fact_3201_minus__mod__eq__mult__div,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.23 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_mult_div
% 5.01/5.23 thf(fact_3202_minus__mod__eq__div__mult,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.23 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_div_mult
% 5.01/5.23 thf(fact_3203_minus__mod__eq__div__mult,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.23 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_div_mult
% 5.01/5.23 thf(fact_3204_minus__mod__eq__div__mult,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.23 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_mod_eq_div_mult
% 5.01/5.23 thf(fact_3205_minus__div__mult__eq__mod,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.01/5.23 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_div_mult_eq_mod
% 5.01/5.23 thf(fact_3206_minus__div__mult__eq__mod,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.01/5.23 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_div_mult_eq_mod
% 5.01/5.23 thf(fact_3207_minus__div__mult__eq__mod,axiom,
% 5.01/5.23 ! [A: code_integer,B: code_integer] :
% 5.01/5.23 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.01/5.23 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.01/5.23
% 5.01/5.23 % minus_div_mult_eq_mod
% 5.01/5.23 thf(fact_3208_cong__exp__iff__simps_I10_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(10)
% 5.01/5.23 thf(fact_3209_cong__exp__iff__simps_I10_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(10)
% 5.01/5.23 thf(fact_3210_cong__exp__iff__simps_I10_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(10)
% 5.01/5.23 thf(fact_3211_cong__exp__iff__simps_I12_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(12)
% 5.01/5.23 thf(fact_3212_cong__exp__iff__simps_I12_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(12)
% 5.01/5.23 thf(fact_3213_cong__exp__iff__simps_I12_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(12)
% 5.01/5.23 thf(fact_3214_cong__exp__iff__simps_I13_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.23 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.23 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(13)
% 5.01/5.23 thf(fact_3215_cong__exp__iff__simps_I13_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.23 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.01/5.23 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(13)
% 5.01/5.23 thf(fact_3216_cong__exp__iff__simps_I13_J,axiom,
% 5.01/5.23 ! [M: num,Q2: num,N: num] :
% 5.01/5.23 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.01/5.23 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.01/5.23 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.01/5.23 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % cong_exp_iff_simps(13)
% 5.01/5.23 thf(fact_3217_mod__eq__nat1E,axiom,
% 5.01/5.23 ! [M: nat,Q2: nat,N: nat] :
% 5.01/5.23 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.01/5.23 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.23 => ~ ! [S3: nat] :
% 5.01/5.23 ( M
% 5.01/5.23 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_eq_nat1E
% 5.01/5.23 thf(fact_3218_mod__eq__nat2E,axiom,
% 5.01/5.23 ! [M: nat,Q2: nat,N: nat] :
% 5.01/5.23 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.01/5.23 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.23 => ~ ! [S3: nat] :
% 5.01/5.23 ( N
% 5.01/5.23 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_eq_nat2E
% 5.01/5.23 thf(fact_3219_nat__mod__eq__lemma,axiom,
% 5.01/5.23 ! [X2: nat,N: nat,Y: nat] :
% 5.01/5.23 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.01/5.23 = ( modulo_modulo_nat @ Y @ N ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.23 => ? [Q3: nat] :
% 5.01/5.23 ( X2
% 5.01/5.23 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % nat_mod_eq_lemma
% 5.01/5.23 thf(fact_3220_mod__mult2__eq,axiom,
% 5.01/5.23 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.23 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.01/5.23 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mod_mult2_eq
% 5.01/5.23 thf(fact_3221_modulo__nat__def,axiom,
% 5.01/5.23 ( modulo_modulo_nat
% 5.01/5.23 = ( ^ [M3: nat,N4: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N4 ) @ N4 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % modulo_nat_def
% 5.01/5.23 thf(fact_3222_mult__less__le__imp__less,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_le_imp_less
% 5.01/5.23 thf(fact_3223_mult__less__le__imp__less,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_le_imp_less
% 5.01/5.23 thf(fact_3224_mult__less__le__imp__less,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_nat @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_le_imp_less
% 5.01/5.23 thf(fact_3225_mult__less__le__imp__less,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ B )
% 5.01/5.23 => ( ( ord_less_eq_int @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_le_imp_less
% 5.01/5.23 thf(fact_3226_mult__le__less__imp__less,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_real @ C @ D )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_less_imp_less
% 5.01/5.23 thf(fact_3227_mult__le__less__imp__less,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_rat @ C @ D )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_less_imp_less
% 5.01/5.23 thf(fact_3228_mult__le__less__imp__less,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.23 => ( ( ord_less_nat @ C @ D )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_less_imp_less
% 5.01/5.23 thf(fact_3229_mult__le__less__imp__less,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.23 => ( ( ord_less_int @ C @ D )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_less_imp_less
% 5.01/5.23 thf(fact_3230_mult__right__le__imp__le,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_imp_le
% 5.01/5.23 thf(fact_3231_mult__right__le__imp__le,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_imp_le
% 5.01/5.23 thf(fact_3232_mult__right__le__imp__le,axiom,
% 5.01/5.23 ! [A: nat,C: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_imp_le
% 5.01/5.23 thf(fact_3233_mult__right__le__imp__le,axiom,
% 5.01/5.23 ! [A: int,C: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_imp_le
% 5.01/5.23 thf(fact_3234_mult__left__le__imp__le,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_imp_le
% 5.01/5.23 thf(fact_3235_mult__left__le__imp__le,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_imp_le
% 5.01/5.23 thf(fact_3236_mult__left__le__imp__le,axiom,
% 5.01/5.23 ! [C: nat,A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_imp_le
% 5.01/5.23 thf(fact_3237_mult__left__le__imp__le,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_imp_le
% 5.01/5.23 thf(fact_3238_mult__le__cancel__left__pos,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_pos
% 5.01/5.23 thf(fact_3239_mult__le__cancel__left__pos,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_pos
% 5.01/5.23 thf(fact_3240_mult__le__cancel__left__pos,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_pos
% 5.01/5.23 thf(fact_3241_mult__le__cancel__left__neg,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_neg
% 5.01/5.23 thf(fact_3242_mult__le__cancel__left__neg,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_neg
% 5.01/5.23 thf(fact_3243_mult__le__cancel__left__neg,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left_neg
% 5.01/5.23 thf(fact_3244_mult__less__cancel__right,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_right
% 5.01/5.23 thf(fact_3245_mult__less__cancel__right,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_right
% 5.01/5.23 thf(fact_3246_mult__less__cancel__right,axiom,
% 5.01/5.23 ! [A: int,C: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_right
% 5.01/5.23 thf(fact_3247_mult__strict__mono_H,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_real @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono'
% 5.01/5.23 thf(fact_3248_mult__strict__mono_H,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_rat @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono'
% 5.01/5.23 thf(fact_3249_mult__strict__mono_H,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ B )
% 5.01/5.23 => ( ( ord_less_nat @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono'
% 5.01/5.23 thf(fact_3250_mult__strict__mono_H,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ B )
% 5.01/5.23 => ( ( ord_less_int @ C @ D )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono'
% 5.01/5.23 thf(fact_3251_mult__right__less__imp__less,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_less_imp_less
% 5.01/5.23 thf(fact_3252_mult__right__less__imp__less,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_less_imp_less
% 5.01/5.23 thf(fact_3253_mult__right__less__imp__less,axiom,
% 5.01/5.23 ! [A: nat,C: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_less_imp_less
% 5.01/5.23 thf(fact_3254_mult__right__less__imp__less,axiom,
% 5.01/5.23 ! [A: int,C: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_less_imp_less
% 5.01/5.23 thf(fact_3255_mult__less__cancel__left,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_left
% 5.01/5.23 thf(fact_3256_mult__less__cancel__left,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_left
% 5.01/5.23 thf(fact_3257_mult__less__cancel__left,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_less_cancel_left
% 5.01/5.23 thf(fact_3258_mult__strict__mono,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ B )
% 5.01/5.23 => ( ( ord_less_real @ C @ D )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono
% 5.01/5.23 thf(fact_3259_mult__strict__mono,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ B )
% 5.01/5.23 => ( ( ord_less_rat @ C @ D )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono
% 5.01/5.23 thf(fact_3260_mult__strict__mono,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ B )
% 5.01/5.23 => ( ( ord_less_nat @ C @ D )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono
% 5.01/5.23 thf(fact_3261_mult__strict__mono,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ B )
% 5.01/5.23 => ( ( ord_less_int @ C @ D )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_strict_mono
% 5.01/5.23 thf(fact_3262_mult__left__less__imp__less,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_less_imp_less
% 5.01/5.23 thf(fact_3263_mult__left__less__imp__less,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_less_imp_less
% 5.01/5.23 thf(fact_3264_mult__left__less__imp__less,axiom,
% 5.01/5.23 ! [C: nat,A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_less_imp_less
% 5.01/5.23 thf(fact_3265_mult__left__less__imp__less,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_less_imp_less
% 5.01/5.23 thf(fact_3266_mult__le__cancel__right,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_right
% 5.01/5.23 thf(fact_3267_mult__le__cancel__right,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_right
% 5.01/5.23 thf(fact_3268_mult__le__cancel__right,axiom,
% 5.01/5.23 ! [A: int,C: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_eq_int @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.23 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_right
% 5.01/5.23 thf(fact_3269_mult__le__cancel__left,axiom,
% 5.01/5.23 ! [C: real,A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left
% 5.01/5.23 thf(fact_3270_mult__le__cancel__left,axiom,
% 5.01/5.23 ! [C: rat,A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left
% 5.01/5.23 thf(fact_3271_mult__le__cancel__left,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.23 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ord_less_eq_int @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.23 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_cancel_left
% 5.01/5.23 thf(fact_3272_field__le__epsilon,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ! [E2: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.23 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.01/5.23 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.23
% 5.01/5.23 % field_le_epsilon
% 5.01/5.23 thf(fact_3273_field__le__epsilon,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ! [E2: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.01/5.23 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.01/5.23 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.01/5.23
% 5.01/5.23 % field_le_epsilon
% 5.01/5.23 thf(fact_3274_add__neg__nonpos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_nonpos
% 5.01/5.23 thf(fact_3275_add__neg__nonpos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_nonpos
% 5.01/5.23 thf(fact_3276_add__neg__nonpos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.01/5.23 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.01/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_nonpos
% 5.01/5.23 thf(fact_3277_add__neg__nonpos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_neg_nonpos
% 5.01/5.23 thf(fact_3278_add__nonneg__pos,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonneg_pos
% 5.01/5.23 thf(fact_3279_add__nonneg__pos,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonneg_pos
% 5.01/5.23 thf(fact_3280_add__nonneg__pos,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonneg_pos
% 5.01/5.23 thf(fact_3281_add__nonneg__pos,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonneg_pos
% 5.01/5.23 thf(fact_3282_add__nonpos__neg,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonpos_neg
% 5.01/5.23 thf(fact_3283_add__nonpos__neg,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonpos_neg
% 5.01/5.23 thf(fact_3284_add__nonpos__neg,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.01/5.23 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.01/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonpos_neg
% 5.01/5.23 thf(fact_3285_add__nonpos__neg,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_nonpos_neg
% 5.01/5.23 thf(fact_3286_add__pos__nonneg,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_nonneg
% 5.01/5.23 thf(fact_3287_add__pos__nonneg,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_nonneg
% 5.01/5.23 thf(fact_3288_add__pos__nonneg,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_nonneg
% 5.01/5.23 thf(fact_3289_add__pos__nonneg,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_pos_nonneg
% 5.01/5.23 thf(fact_3290_add__strict__increasing,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_eq_real @ B @ C )
% 5.01/5.23 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing
% 5.01/5.23 thf(fact_3291_add__strict__increasing,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.23 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing
% 5.01/5.23 thf(fact_3292_add__strict__increasing,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.23 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing
% 5.01/5.23 thf(fact_3293_add__strict__increasing,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.23 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing
% 5.01/5.23 thf(fact_3294_add__strict__increasing2,axiom,
% 5.01/5.23 ! [A: real,B: real,C: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ( ord_less_real @ B @ C )
% 5.01/5.23 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing2
% 5.01/5.23 thf(fact_3295_add__strict__increasing2,axiom,
% 5.01/5.23 ! [A: rat,B: rat,C: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ( ord_less_rat @ B @ C )
% 5.01/5.23 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing2
% 5.01/5.23 thf(fact_3296_add__strict__increasing2,axiom,
% 5.01/5.23 ! [A: nat,B: nat,C: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ B @ C )
% 5.01/5.23 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing2
% 5.01/5.23 thf(fact_3297_add__strict__increasing2,axiom,
% 5.01/5.23 ! [A: int,B: int,C: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ B @ C )
% 5.01/5.23 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % add_strict_increasing2
% 5.01/5.23 thf(fact_3298_sum__squares__le__zero__iff,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.01/5.23 = ( ( X2 = zero_zero_real )
% 5.01/5.23 & ( Y = zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_le_zero_iff
% 5.01/5.23 thf(fact_3299_sum__squares__le__zero__iff,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.01/5.23 = ( ( X2 = zero_zero_rat )
% 5.01/5.23 & ( Y = zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_le_zero_iff
% 5.01/5.23 thf(fact_3300_sum__squares__le__zero__iff,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.01/5.23 = ( ( X2 = zero_zero_int )
% 5.01/5.23 & ( Y = zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_le_zero_iff
% 5.01/5.23 thf(fact_3301_sum__squares__ge__zero,axiom,
% 5.01/5.23 ! [X2: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_ge_zero
% 5.01/5.23 thf(fact_3302_sum__squares__ge__zero,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_ge_zero
% 5.01/5.23 thf(fact_3303_sum__squares__ge__zero,axiom,
% 5.01/5.23 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_ge_zero
% 5.01/5.23 thf(fact_3304_mult__left__le,axiom,
% 5.01/5.23 ! [C: real,A: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.23 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le
% 5.01/5.23 thf(fact_3305_mult__left__le,axiom,
% 5.01/5.23 ! [C: rat,A: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.23 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le
% 5.01/5.23 thf(fact_3306_mult__left__le,axiom,
% 5.01/5.23 ! [C: nat,A: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le
% 5.01/5.23 thf(fact_3307_mult__left__le,axiom,
% 5.01/5.23 ! [C: int,A: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le
% 5.01/5.23 thf(fact_3308_mult__le__one,axiom,
% 5.01/5.23 ! [A: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_one
% 5.01/5.23 thf(fact_3309_mult__le__one,axiom,
% 5.01/5.23 ! [A: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_one
% 5.01/5.23 thf(fact_3310_mult__le__one,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.01/5.23 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_one
% 5.01/5.23 thf(fact_3311_mult__le__one,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.01/5.23 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_le_one
% 5.01/5.23 thf(fact_3312_mult__right__le__one__le,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_one_le
% 5.01/5.23 thf(fact_3313_mult__right__le__one__le,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_one_le
% 5.01/5.23 thf(fact_3314_mult__right__le__one__le,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.23 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.01/5.23 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_right_le_one_le
% 5.01/5.23 thf(fact_3315_mult__left__le__one__le,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( times_times_real @ Y @ X2 ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_one_le
% 5.01/5.23 thf(fact_3316_mult__left__le__one__le,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X2 ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_one_le
% 5.01/5.23 thf(fact_3317_mult__left__le__one__le,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.23 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.01/5.23 => ( ord_less_eq_int @ ( times_times_int @ Y @ X2 ) @ X2 ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % mult_left_le_one_le
% 5.01/5.23 thf(fact_3318_frac__le,axiom,
% 5.01/5.23 ! [Y: real,X2: real,W: real,Z: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.01/5.23 => ( ( ord_less_eq_real @ W @ Z )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_le
% 5.01/5.23 thf(fact_3319_frac__le,axiom,
% 5.01/5.23 ! [Y: rat,X2: rat,W: rat,Z: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.01/5.23 => ( ( ord_less_eq_rat @ W @ Z )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_le
% 5.01/5.23 thf(fact_3320_frac__less,axiom,
% 5.01/5.23 ! [X2: real,Y: real,W: real,Z: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.01/5.23 => ( ( ord_less_eq_real @ W @ Z )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_less
% 5.01/5.23 thf(fact_3321_frac__less,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat,W: rat,Z: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.01/5.23 => ( ( ord_less_eq_rat @ W @ Z )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_less
% 5.01/5.23 thf(fact_3322_frac__less2,axiom,
% 5.01/5.23 ! [X2: real,Y: real,W: real,Z: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.01/5.23 => ( ( ord_less_real @ W @ Z )
% 5.01/5.23 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_less2
% 5.01/5.23 thf(fact_3323_frac__less2,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat,W: rat,Z: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.01/5.23 => ( ( ord_less_rat @ W @ Z )
% 5.01/5.23 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % frac_less2
% 5.01/5.23 thf(fact_3324_divide__le__cancel,axiom,
% 5.01/5.23 ! [A: real,C: real,B: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.23 => ( ord_less_eq_real @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_le_cancel
% 5.01/5.23 thf(fact_3325_divide__le__cancel,axiom,
% 5.01/5.23 ! [A: rat,C: rat,B: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.23 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.23 => ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.23 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_le_cancel
% 5.01/5.23 thf(fact_3326_divide__nonneg__neg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_neg
% 5.01/5.23 thf(fact_3327_divide__nonneg__neg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_neg
% 5.01/5.23 thf(fact_3328_divide__nonneg__pos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_pos
% 5.01/5.23 thf(fact_3329_divide__nonneg__pos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonneg_pos
% 5.01/5.23 thf(fact_3330_divide__nonpos__neg,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.01/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_neg
% 5.01/5.23 thf(fact_3331_divide__nonpos__neg,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.01/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_neg
% 5.01/5.23 thf(fact_3332_divide__nonpos__pos,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.23 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.23 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_pos
% 5.01/5.23 thf(fact_3333_divide__nonpos__pos,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.23 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.23 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % divide_nonpos_pos
% 5.01/5.23 thf(fact_3334_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.01/5.23 ! [A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.23 => ( ( ord_less_nat @ A @ B )
% 5.01/5.23 => ( ( divide_divide_nat @ A @ B )
% 5.01/5.23 = zero_zero_nat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % unique_euclidean_semiring_numeral_class.div_less
% 5.01/5.23 thf(fact_3335_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.01/5.23 ! [A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.23 => ( ( ord_less_int @ A @ B )
% 5.01/5.23 => ( ( divide_divide_int @ A @ B )
% 5.01/5.23 = zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % unique_euclidean_semiring_numeral_class.div_less
% 5.01/5.23 thf(fact_3336_div__positive,axiom,
% 5.01/5.23 ! [B: nat,A: nat] :
% 5.01/5.23 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.23 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % div_positive
% 5.01/5.23 thf(fact_3337_div__positive,axiom,
% 5.01/5.23 ! [B: int,A: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ( ord_less_eq_int @ B @ A )
% 5.01/5.23 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % div_positive
% 5.01/5.23 thf(fact_3338_sum__squares__gt__zero__iff,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) )
% 5.01/5.23 = ( ( X2 != zero_zero_real )
% 5.01/5.23 | ( Y != zero_zero_real ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_gt_zero_iff
% 5.01/5.23 thf(fact_3339_sum__squares__gt__zero__iff,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.01/5.23 = ( ( X2 != zero_zero_rat )
% 5.01/5.23 | ( Y != zero_zero_rat ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_gt_zero_iff
% 5.01/5.23 thf(fact_3340_sum__squares__gt__zero__iff,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) )
% 5.01/5.23 = ( ( X2 != zero_zero_int )
% 5.01/5.23 | ( Y != zero_zero_int ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % sum_squares_gt_zero_iff
% 5.01/5.23 thf(fact_3341_not__sum__squares__lt__zero,axiom,
% 5.01/5.23 ! [X2: real,Y: real] :
% 5.01/5.23 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % not_sum_squares_lt_zero
% 5.01/5.23 thf(fact_3342_not__sum__squares__lt__zero,axiom,
% 5.01/5.23 ! [X2: rat,Y: rat] :
% 5.01/5.23 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % not_sum_squares_lt_zero
% 5.01/5.23 thf(fact_3343_not__sum__squares__lt__zero,axiom,
% 5.01/5.23 ! [X2: int,Y: int] :
% 5.01/5.23 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % not_sum_squares_lt_zero
% 5.01/5.23 thf(fact_3344_power__less__imp__less__base,axiom,
% 5.01/5.23 ! [A: real,N: nat,B: real] :
% 5.01/5.23 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.01/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.23 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_less_imp_less_base
% 5.01/5.23 thf(fact_3345_power__less__imp__less__base,axiom,
% 5.01/5.23 ! [A: rat,N: nat,B: rat] :
% 5.01/5.23 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.01/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.23 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_less_imp_less_base
% 5.01/5.23 thf(fact_3346_power__less__imp__less__base,axiom,
% 5.01/5.23 ! [A: nat,N: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.01/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.23 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_less_imp_less_base
% 5.01/5.23 thf(fact_3347_power__less__imp__less__base,axiom,
% 5.01/5.23 ! [A: int,N: nat,B: int] :
% 5.01/5.23 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.01/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.23 => ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % power_less_imp_less_base
% 5.01/5.23 thf(fact_3348_not__zero__le__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_le_neg_numeral
% 5.01/5.23 thf(fact_3349_not__zero__le__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_le_neg_numeral
% 5.01/5.23 thf(fact_3350_not__zero__le__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_le_neg_numeral
% 5.01/5.23 thf(fact_3351_not__zero__le__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_le_neg_numeral
% 5.01/5.23 thf(fact_3352_neg__numeral__le__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_le_zero
% 5.01/5.23 thf(fact_3353_neg__numeral__le__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_le_zero
% 5.01/5.23 thf(fact_3354_neg__numeral__le__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_le_zero
% 5.01/5.23 thf(fact_3355_neg__numeral__le__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_le_zero
% 5.01/5.23 thf(fact_3356_zero__less__two,axiom,
% 5.01/5.23 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_two
% 5.01/5.23 thf(fact_3357_zero__less__two,axiom,
% 5.01/5.23 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_two
% 5.01/5.23 thf(fact_3358_zero__less__two,axiom,
% 5.01/5.23 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_two
% 5.01/5.23 thf(fact_3359_zero__less__two,axiom,
% 5.01/5.23 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.01/5.23
% 5.01/5.23 % zero_less_two
% 5.01/5.23 thf(fact_3360_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.01/5.23 ! [C: nat,A: nat,B: nat] :
% 5.01/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.01/5.23 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.23 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.01/5.23 thf(fact_3361_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.01/5.23 ! [C: int,A: int,B: int] :
% 5.01/5.23 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.23 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.23 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.01/5.23 thf(fact_3362_not__zero__less__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_less_neg_numeral
% 5.01/5.23 thf(fact_3363_not__zero__less__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_less_neg_numeral
% 5.01/5.23 thf(fact_3364_not__zero__less__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_less_neg_numeral
% 5.01/5.23 thf(fact_3365_not__zero__less__neg__numeral,axiom,
% 5.01/5.23 ! [N: num] :
% 5.01/5.23 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.01/5.23
% 5.01/5.23 % not_zero_less_neg_numeral
% 5.01/5.23 thf(fact_3366_neg__numeral__less__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_less_zero
% 5.01/5.23 thf(fact_3367_neg__numeral__less__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_less_zero
% 5.01/5.23 thf(fact_3368_neg__numeral__less__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_less_zero
% 5.01/5.23 thf(fact_3369_neg__numeral__less__zero,axiom,
% 5.01/5.23 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.01/5.23
% 5.01/5.23 % neg_numeral_less_zero
% 5.01/5.23 thf(fact_3370_le__minus__one__simps_I3_J,axiom,
% 5.01/5.23 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_minus_one_simps(3)
% 5.01/5.23 thf(fact_3371_le__minus__one__simps_I3_J,axiom,
% 5.01/5.23 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_minus_one_simps(3)
% 5.01/5.23 thf(fact_3372_le__minus__one__simps_I3_J,axiom,
% 5.01/5.23 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_minus_one_simps(3)
% 5.01/5.23 thf(fact_3373_le__minus__one__simps_I3_J,axiom,
% 5.01/5.23 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.23
% 5.01/5.23 % le_minus_one_simps(3)
% 5.01/5.23 thf(fact_3374_le__minus__one__simps_I1_J,axiom,
% 5.01/5.23 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.01/5.23
% 5.01/5.23 % le_minus_one_simps(1)
% 5.01/5.23 thf(fact_3375_le__minus__one__simps_I1_J,axiom,
% 5.01/5.23 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.01/5.24
% 5.01/5.24 % le_minus_one_simps(1)
% 5.01/5.24 thf(fact_3376_le__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.01/5.24
% 5.01/5.24 % le_minus_one_simps(1)
% 5.01/5.24 thf(fact_3377_le__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.01/5.24
% 5.01/5.24 % le_minus_one_simps(1)
% 5.01/5.24 thf(fact_3378_divide__less__eq,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq
% 5.01/5.24 thf(fact_3379_divide__less__eq,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq
% 5.01/5.24 thf(fact_3380_less__divide__eq,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq
% 5.01/5.24 thf(fact_3381_less__divide__eq,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq
% 5.01/5.24 thf(fact_3382_neg__divide__less__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_divide_less_eq
% 5.01/5.24 thf(fact_3383_neg__divide__less__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_divide_less_eq
% 5.01/5.24 thf(fact_3384_neg__less__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_less_divide_eq
% 5.01/5.24 thf(fact_3385_neg__less__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_less_divide_eq
% 5.01/5.24 thf(fact_3386_pos__divide__less__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_divide_less_eq
% 5.01/5.24 thf(fact_3387_pos__divide__less__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_divide_less_eq
% 5.01/5.24 thf(fact_3388_pos__less__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_less_divide_eq
% 5.01/5.24 thf(fact_3389_pos__less__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_less_divide_eq
% 5.01/5.24 thf(fact_3390_mult__imp__div__pos__less,axiom,
% 5.01/5.24 ! [Y: real,X2: real,Z: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y ) )
% 5.01/5.24 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_div_pos_less
% 5.01/5.24 thf(fact_3391_mult__imp__div__pos__less,axiom,
% 5.01/5.24 ! [Y: rat,X2: rat,Z: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y ) )
% 5.01/5.24 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_div_pos_less
% 5.01/5.24 thf(fact_3392_mult__imp__less__div__pos,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X2 )
% 5.01/5.24 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_less_div_pos
% 5.01/5.24 thf(fact_3393_mult__imp__less__div__pos,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X2 )
% 5.01/5.24 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_less_div_pos
% 5.01/5.24 thf(fact_3394_divide__strict__left__mono,axiom,
% 5.01/5.24 ! [B: real,A: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ B @ A )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.24 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_strict_left_mono
% 5.01/5.24 thf(fact_3395_divide__strict__left__mono,axiom,
% 5.01/5.24 ! [B: rat,A: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ B @ A )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.24 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_strict_left_mono
% 5.01/5.24 thf(fact_3396_divide__strict__left__mono__neg,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ A @ B )
% 5.01/5.24 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.24 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_strict_left_mono_neg
% 5.01/5.24 thf(fact_3397_divide__strict__left__mono__neg,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ A @ B )
% 5.01/5.24 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.24 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_strict_left_mono_neg
% 5.01/5.24 thf(fact_3398_power__le__one,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_one
% 5.01/5.24 thf(fact_3399_power__le__one,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_one
% 5.01/5.24 thf(fact_3400_power__le__one,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_one
% 5.01/5.24 thf(fact_3401_power__le__one,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_one
% 5.01/5.24 thf(fact_3402_divide__less__eq__1,axiom,
% 5.01/5.24 ! [B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 & ( ord_less_real @ B @ A ) )
% 5.01/5.24 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.24 & ( ord_less_real @ A @ B ) )
% 5.01/5.24 | ( A = zero_zero_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_1
% 5.01/5.24 thf(fact_3403_divide__less__eq__1,axiom,
% 5.01/5.24 ! [B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 & ( ord_less_rat @ B @ A ) )
% 5.01/5.24 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.24 & ( ord_less_rat @ A @ B ) )
% 5.01/5.24 | ( A = zero_zero_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_1
% 5.01/5.24 thf(fact_3404_less__divide__eq__1,axiom,
% 5.01/5.24 ! [B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 & ( ord_less_real @ A @ B ) )
% 5.01/5.24 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.24 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_1
% 5.01/5.24 thf(fact_3405_less__divide__eq__1,axiom,
% 5.01/5.24 ! [B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 & ( ord_less_rat @ A @ B ) )
% 5.01/5.24 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.24 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_1
% 5.01/5.24 thf(fact_3406_less__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(1)
% 5.01/5.24 thf(fact_3407_less__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(1)
% 5.01/5.24 thf(fact_3408_less__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(1)
% 5.01/5.24 thf(fact_3409_less__minus__one__simps_I1_J,axiom,
% 5.01/5.24 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(1)
% 5.01/5.24 thf(fact_3410_less__minus__one__simps_I3_J,axiom,
% 5.01/5.24 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(3)
% 5.01/5.24 thf(fact_3411_less__minus__one__simps_I3_J,axiom,
% 5.01/5.24 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(3)
% 5.01/5.24 thf(fact_3412_less__minus__one__simps_I3_J,axiom,
% 5.01/5.24 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(3)
% 5.01/5.24 thf(fact_3413_less__minus__one__simps_I3_J,axiom,
% 5.01/5.24 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_one_simps(3)
% 5.01/5.24 thf(fact_3414_eq__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: complex,C: complex] :
% 5.01/5.24 ( ( ( numera6690914467698888265omplex @ W )
% 5.01/5.24 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( ( numera6690914467698888265omplex @ W )
% 5.01/5.24 = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3415_eq__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ( numeral_numeral_real @ W )
% 5.01/5.24 = ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( ( numeral_numeral_real @ W )
% 5.01/5.24 = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3416_eq__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ( numeral_numeral_rat @ W )
% 5.01/5.24 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( ( numeral_numeral_rat @ W )
% 5.01/5.24 = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3417_divide__eq__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: complex,C: complex,W: num] :
% 5.01/5.24 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.01/5.24 = ( numera6690914467698888265omplex @ W ) )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( ( numera6690914467698888265omplex @ W )
% 5.01/5.24 = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(1)
% 5.01/5.24 thf(fact_3418_divide__eq__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ( divide_divide_real @ B @ C )
% 5.01/5.24 = ( numeral_numeral_real @ W ) )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( ( numeral_numeral_real @ W )
% 5.01/5.24 = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(1)
% 5.01/5.24 thf(fact_3419_divide__eq__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ( divide_divide_rat @ B @ C )
% 5.01/5.24 = ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( ( numeral_numeral_rat @ W )
% 5.01/5.24 = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(1)
% 5.01/5.24 thf(fact_3420_add__divide__eq__if__simps_I2_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(2)
% 5.01/5.24 thf(fact_3421_add__divide__eq__if__simps_I2_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(2)
% 5.01/5.24 thf(fact_3422_add__divide__eq__if__simps_I2_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(2)
% 5.01/5.24 thf(fact_3423_add__divide__eq__if__simps_I1_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(1)
% 5.01/5.24 thf(fact_3424_add__divide__eq__if__simps_I1_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(1)
% 5.01/5.24 thf(fact_3425_add__divide__eq__if__simps_I1_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(1)
% 5.01/5.24 thf(fact_3426_add__frac__eq,axiom,
% 5.01/5.24 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 5.01/5.24 ( ( Y != zero_zero_complex )
% 5.01/5.24 => ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_eq
% 5.01/5.24 thf(fact_3427_add__frac__eq,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real,W: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_eq
% 5.01/5.24 thf(fact_3428_add__frac__eq,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_eq
% 5.01/5.24 thf(fact_3429_add__frac__num,axiom,
% 5.01/5.24 ! [Y: complex,X2: complex,Z: complex] :
% 5.01/5.24 ( ( Y != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ Z )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_num
% 5.01/5.24 thf(fact_3430_add__frac__num,axiom,
% 5.01/5.24 ! [Y: real,X2: real,Z: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y ) @ Z )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_num
% 5.01/5.24 thf(fact_3431_add__frac__num,axiom,
% 5.01/5.24 ! [Y: rat,X2: rat,Z: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_frac_num
% 5.01/5.24 thf(fact_3432_add__num__frac,axiom,
% 5.01/5.24 ! [Y: complex,Z: complex,X2: complex] :
% 5.01/5.24 ( ( Y != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_num_frac
% 5.01/5.24 thf(fact_3433_add__num__frac,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_num_frac
% 5.01/5.24 thf(fact_3434_add__num__frac,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_num_frac
% 5.01/5.24 thf(fact_3435_add__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_iff
% 5.01/5.24 thf(fact_3436_add__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_iff
% 5.01/5.24 thf(fact_3437_add__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_iff
% 5.01/5.24 thf(fact_3438_divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_add_eq_iff
% 5.01/5.24 thf(fact_3439_divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_add_eq_iff
% 5.01/5.24 thf(fact_3440_divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_add_eq_iff
% 5.01/5.24 thf(fact_3441_div__add__self1,axiom,
% 5.01/5.24 ! [B: nat,A: nat] :
% 5.01/5.24 ( ( B != zero_zero_nat )
% 5.01/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.01/5.24 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_add_self1
% 5.01/5.24 thf(fact_3442_div__add__self1,axiom,
% 5.01/5.24 ! [B: int,A: int] :
% 5.01/5.24 ( ( B != zero_zero_int )
% 5.01/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.01/5.24 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_add_self1
% 5.01/5.24 thf(fact_3443_div__add__self2,axiom,
% 5.01/5.24 ! [B: nat,A: nat] :
% 5.01/5.24 ( ( B != zero_zero_nat )
% 5.01/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.01/5.24 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_add_self2
% 5.01/5.24 thf(fact_3444_div__add__self2,axiom,
% 5.01/5.24 ! [B: int,A: int] :
% 5.01/5.24 ( ( B != zero_zero_int )
% 5.01/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.01/5.24 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_add_self2
% 5.01/5.24 thf(fact_3445_divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_diff_eq_iff
% 5.01/5.24 thf(fact_3446_divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_diff_eq_iff
% 5.01/5.24 thf(fact_3447_divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_diff_eq_iff
% 5.01/5.24 thf(fact_3448_diff__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_divide_eq_iff
% 5.01/5.24 thf(fact_3449_diff__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_divide_eq_iff
% 5.01/5.24 thf(fact_3450_diff__divide__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_divide_eq_iff
% 5.01/5.24 thf(fact_3451_diff__frac__eq,axiom,
% 5.01/5.24 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 5.01/5.24 ( ( Y != zero_zero_complex )
% 5.01/5.24 => ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_frac_eq
% 5.01/5.24 thf(fact_3452_diff__frac__eq,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real,W: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_frac_eq
% 5.01/5.24 thf(fact_3453_diff__frac__eq,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_frac_eq
% 5.01/5.24 thf(fact_3454_add__divide__eq__if__simps_I4_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(4)
% 5.01/5.24 thf(fact_3455_add__divide__eq__if__simps_I4_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(4)
% 5.01/5.24 thf(fact_3456_add__divide__eq__if__simps_I4_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.01/5.24 = A ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(4)
% 5.01/5.24 thf(fact_3457_power__le__imp__le__base,axiom,
% 5.01/5.24 ! [A: real,N: nat,B: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.24 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_imp_le_base
% 5.01/5.24 thf(fact_3458_power__le__imp__le__base,axiom,
% 5.01/5.24 ! [A: rat,N: nat,B: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_imp_le_base
% 5.01/5.24 thf(fact_3459_power__le__imp__le__base,axiom,
% 5.01/5.24 ! [A: nat,N: nat,B: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.24 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_imp_le_base
% 5.01/5.24 thf(fact_3460_power__le__imp__le__base,axiom,
% 5.01/5.24 ! [A: int,N: nat,B: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.24 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_le_imp_le_base
% 5.01/5.24 thf(fact_3461_power__inject__base,axiom,
% 5.01/5.24 ! [A: real,N: nat,B: real] :
% 5.01/5.24 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.01/5.24 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.24 => ( A = B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_inject_base
% 5.01/5.24 thf(fact_3462_power__inject__base,axiom,
% 5.01/5.24 ! [A: rat,N: nat,B: rat] :
% 5.01/5.24 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.01/5.24 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.24 => ( A = B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_inject_base
% 5.01/5.24 thf(fact_3463_power__inject__base,axiom,
% 5.01/5.24 ! [A: nat,N: nat,B: nat] :
% 5.01/5.24 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.01/5.24 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.01/5.24 => ( A = B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_inject_base
% 5.01/5.24 thf(fact_3464_power__inject__base,axiom,
% 5.01/5.24 ! [A: int,N: nat,B: int] :
% 5.01/5.24 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.01/5.24 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.24 => ( A = B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_inject_base
% 5.01/5.24 thf(fact_3465_eq__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( A
% 5.01/5.24 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( ( times_times_real @ A @ C )
% 5.01/5.24 = ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_minus_divide_eq
% 5.01/5.24 thf(fact_3466_eq__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: complex,B: complex,C: complex] :
% 5.01/5.24 ( ( A
% 5.01/5.24 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( ( times_times_complex @ A @ C )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_minus_divide_eq
% 5.01/5.24 thf(fact_3467_eq__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( A
% 5.01/5.24 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( ( times_times_rat @ A @ C )
% 5.01/5.24 = ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_minus_divide_eq
% 5.01/5.24 thf(fact_3468_minus__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = A )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( ( uminus_uminus_real @ B )
% 5.01/5.24 = ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( A = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_eq_eq
% 5.01/5.24 thf(fact_3469_minus__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: complex,C: complex,A: complex] :
% 5.01/5.24 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.24 = A )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( ( uminus1482373934393186551omplex @ B )
% 5.01/5.24 = ( times_times_complex @ A @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( A = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_eq_eq
% 5.01/5.24 thf(fact_3470_minus__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = A )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( ( uminus_uminus_rat @ B )
% 5.01/5.24 = ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( A = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_eq_eq
% 5.01/5.24 thf(fact_3471_nonzero__neg__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: real,A: real,C: real] :
% 5.01/5.24 ( ( B != zero_zero_real )
% 5.01/5.24 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.24 = C )
% 5.01/5.24 = ( ( uminus_uminus_real @ A )
% 5.01/5.24 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq
% 5.01/5.24 thf(fact_3472_nonzero__neg__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: complex,A: complex,C: complex] :
% 5.01/5.24 ( ( B != zero_zero_complex )
% 5.01/5.24 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.24 = C )
% 5.01/5.24 = ( ( uminus1482373934393186551omplex @ A )
% 5.01/5.24 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq
% 5.01/5.24 thf(fact_3473_nonzero__neg__divide__eq__eq,axiom,
% 5.01/5.24 ! [B: rat,A: rat,C: rat] :
% 5.01/5.24 ( ( B != zero_zero_rat )
% 5.01/5.24 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.24 = C )
% 5.01/5.24 = ( ( uminus_uminus_rat @ A )
% 5.01/5.24 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq
% 5.01/5.24 thf(fact_3474_nonzero__neg__divide__eq__eq2,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( B != zero_zero_real )
% 5.01/5.24 => ( ( C
% 5.01/5.24 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.01/5.24 = ( ( times_times_real @ C @ B )
% 5.01/5.24 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq2
% 5.01/5.24 thf(fact_3475_nonzero__neg__divide__eq__eq2,axiom,
% 5.01/5.24 ! [B: complex,C: complex,A: complex] :
% 5.01/5.24 ( ( B != zero_zero_complex )
% 5.01/5.24 => ( ( C
% 5.01/5.24 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.24 = ( ( times_times_complex @ C @ B )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq2
% 5.01/5.24 thf(fact_3476_nonzero__neg__divide__eq__eq2,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( B != zero_zero_rat )
% 5.01/5.24 => ( ( C
% 5.01/5.24 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.01/5.24 = ( ( times_times_rat @ C @ B )
% 5.01/5.24 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nonzero_neg_divide_eq_eq2
% 5.01/5.24 thf(fact_3477_divide__eq__minus__1__iff,axiom,
% 5.01/5.24 ! [A: real,B: real] :
% 5.01/5.24 ( ( ( divide_divide_real @ A @ B )
% 5.01/5.24 = ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.24 = ( ( B != zero_zero_real )
% 5.01/5.24 & ( A
% 5.01/5.24 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_minus_1_iff
% 5.01/5.24 thf(fact_3478_divide__eq__minus__1__iff,axiom,
% 5.01/5.24 ! [A: complex,B: complex] :
% 5.01/5.24 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.01/5.24 = ( ( B != zero_zero_complex )
% 5.01/5.24 & ( A
% 5.01/5.24 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_minus_1_iff
% 5.01/5.24 thf(fact_3479_divide__eq__minus__1__iff,axiom,
% 5.01/5.24 ! [A: rat,B: rat] :
% 5.01/5.24 ( ( ( divide_divide_rat @ A @ B )
% 5.01/5.24 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.24 = ( ( B != zero_zero_rat )
% 5.01/5.24 & ( A
% 5.01/5.24 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_minus_1_iff
% 5.01/5.24 thf(fact_3480_mod__double__modulus,axiom,
% 5.01/5.24 ! [M: code_integer,X2: code_integer] :
% 5.01/5.24 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.01/5.24 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.01/5.24 => ( ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( modulo364778990260209775nteger @ X2 @ M ) )
% 5.01/5.24 | ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_double_modulus
% 5.01/5.24 thf(fact_3481_mod__double__modulus,axiom,
% 5.01/5.24 ! [M: nat,X2: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.01/5.24 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.01/5.24 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_double_modulus
% 5.01/5.24 thf(fact_3482_mod__double__modulus,axiom,
% 5.01/5.24 ! [M: int,X2: int] :
% 5.01/5.24 ( ( ord_less_int @ zero_zero_int @ M )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.24 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( modulo_modulo_int @ X2 @ M ) )
% 5.01/5.24 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_double_modulus
% 5.01/5.24 thf(fact_3483_divmod__digit__1_I2_J,axiom,
% 5.01/5.24 ! [A: code_integer,B: code_integer] :
% 5.01/5.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.24 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.24 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.24 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(2)
% 5.01/5.24 thf(fact_3484_divmod__digit__1_I2_J,axiom,
% 5.01/5.24 ! [A: nat,B: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.24 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.24 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(2)
% 5.01/5.24 thf(fact_3485_divmod__digit__1_I2_J,axiom,
% 5.01/5.24 ! [A: int,B: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.24 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.01/5.24 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(2)
% 5.01/5.24 thf(fact_3486_bounded__Max__nat,axiom,
% 5.01/5.24 ! [P: nat > $o,X2: nat,M7: nat] :
% 5.01/5.24 ( ( P @ X2 )
% 5.01/5.24 => ( ! [X4: nat] :
% 5.01/5.24 ( ( P @ X4 )
% 5.01/5.24 => ( ord_less_eq_nat @ X4 @ M7 ) )
% 5.01/5.24 => ~ ! [M4: nat] :
% 5.01/5.24 ( ( P @ M4 )
% 5.01/5.24 => ~ ! [X: nat] :
% 5.01/5.24 ( ( P @ X )
% 5.01/5.24 => ( ord_less_eq_nat @ X @ M4 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % bounded_Max_nat
% 5.01/5.24 thf(fact_3487_numeral__1__eq__Suc__0,axiom,
% 5.01/5.24 ( ( numeral_numeral_nat @ one )
% 5.01/5.24 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.24
% 5.01/5.24 % numeral_1_eq_Suc_0
% 5.01/5.24 thf(fact_3488_num_Osize_I5_J,axiom,
% 5.01/5.24 ! [X23: num] :
% 5.01/5.24 ( ( size_size_num @ ( bit0 @ X23 ) )
% 5.01/5.24 = ( plus_plus_nat @ ( size_size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % num.size(5)
% 5.01/5.24 thf(fact_3489_ex__least__nat__less,axiom,
% 5.01/5.24 ! [P: nat > $o,N: nat] :
% 5.01/5.24 ( ( P @ N )
% 5.01/5.24 => ( ~ ( P @ zero_zero_nat )
% 5.01/5.24 => ? [K3: nat] :
% 5.01/5.24 ( ( ord_less_nat @ K3 @ N )
% 5.01/5.24 & ! [I2: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ I2 @ K3 )
% 5.01/5.24 => ~ ( P @ I2 ) )
% 5.01/5.24 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % ex_least_nat_less
% 5.01/5.24 thf(fact_3490_num_Osize_I6_J,axiom,
% 5.01/5.24 ! [X33: num] :
% 5.01/5.24 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.01/5.24 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % num.size(6)
% 5.01/5.24 thf(fact_3491_diff__Suc__less,axiom,
% 5.01/5.24 ! [N: nat,I: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.01/5.24
% 5.01/5.24 % diff_Suc_less
% 5.01/5.24 thf(fact_3492_n__less__n__mult__m,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.01/5.24 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % n_less_n_mult_m
% 5.01/5.24 thf(fact_3493_n__less__m__mult__n,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.01/5.24 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % n_less_m_mult_n
% 5.01/5.24 thf(fact_3494_one__less__mult,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.24 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.01/5.24 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % one_less_mult
% 5.01/5.24 thf(fact_3495_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: real,Xs: list_real] :
% 5.01/5.24 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3496_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: complex,Xs: list_complex] :
% 5.01/5.24 ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3497_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: set_nat,Xs: list_set_nat] :
% 5.01/5.24 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3498_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.01/5.24 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3499_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: $o,Xs: list_o] :
% 5.01/5.24 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3500_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: nat,Xs: list_nat] :
% 5.01/5.24 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3501_length__pos__if__in__set,axiom,
% 5.01/5.24 ! [X2: int,Xs: list_int] :
% 5.01/5.24 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 5.01/5.24 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % length_pos_if_in_set
% 5.01/5.24 thf(fact_3502_nat__induct__non__zero,axiom,
% 5.01/5.24 ! [N: nat,P: nat > $o] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( P @ one_one_nat )
% 5.01/5.24 => ( ! [N3: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.24 => ( ( P @ N3 )
% 5.01/5.24 => ( P @ ( suc @ N3 ) ) ) )
% 5.01/5.24 => ( P @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_induct_non_zero
% 5.01/5.24 thf(fact_3503_nat__mult__le__cancel1,axiom,
% 5.01/5.24 ! [K: nat,M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.24 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.24 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_mult_le_cancel1
% 5.01/5.24 thf(fact_3504_nat__diff__split__asm,axiom,
% 5.01/5.24 ! [P: nat > $o,A: nat,B: nat] :
% 5.01/5.24 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.01/5.24 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.01/5.24 & ~ ( P @ zero_zero_nat ) )
% 5.01/5.24 | ? [D3: nat] :
% 5.01/5.24 ( ( A
% 5.01/5.24 = ( plus_plus_nat @ B @ D3 ) )
% 5.01/5.24 & ~ ( P @ D3 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_diff_split_asm
% 5.01/5.24 thf(fact_3505_nat__diff__split,axiom,
% 5.01/5.24 ! [P: nat > $o,A: nat,B: nat] :
% 5.01/5.24 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.01/5.24 = ( ( ( ord_less_nat @ A @ B )
% 5.01/5.24 => ( P @ zero_zero_nat ) )
% 5.01/5.24 & ! [D3: nat] :
% 5.01/5.24 ( ( A
% 5.01/5.24 = ( plus_plus_nat @ B @ D3 ) )
% 5.01/5.24 => ( P @ D3 ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_diff_split
% 5.01/5.24 thf(fact_3506_power__gt__expt,axiom,
% 5.01/5.24 ! [N: nat,K: nat] :
% 5.01/5.24 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.24 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_gt_expt
% 5.01/5.24 thf(fact_3507_nat__one__le__power,axiom,
% 5.01/5.24 ! [I: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.01/5.24 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_one_le_power
% 5.01/5.24 thf(fact_3508_div__greater__zero__iff,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_greater_zero_iff
% 5.01/5.24 thf(fact_3509_div__le__mono2,axiom,
% 5.01/5.24 ! [M: nat,N: nat,K: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.24 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.24 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_le_mono2
% 5.01/5.24 thf(fact_3510_div__less__iff__less__mult,axiom,
% 5.01/5.24 ! [Q2: nat,M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.01/5.24 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.01/5.24 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_less_iff_less_mult
% 5.01/5.24 thf(fact_3511_nat__mult__div__cancel1,axiom,
% 5.01/5.24 ! [K: nat,M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.24 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_mult_div_cancel1
% 5.01/5.24 thf(fact_3512_div__eq__dividend__iff,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.24 => ( ( ( divide_divide_nat @ M @ N )
% 5.01/5.24 = M )
% 5.01/5.24 = ( N = one_one_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_eq_dividend_iff
% 5.01/5.24 thf(fact_3513_div__less__dividend,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ one_one_nat @ N )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.24 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_less_dividend
% 5.01/5.24 thf(fact_3514_prod__decode__aux_Ocases,axiom,
% 5.01/5.24 ! [X2: product_prod_nat_nat] :
% 5.01/5.24 ~ ! [K3: nat,M4: nat] :
% 5.01/5.24 ( X2
% 5.01/5.24 != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 5.01/5.24
% 5.01/5.24 % prod_decode_aux.cases
% 5.01/5.24 thf(fact_3515_mod__mult2__eq_H,axiom,
% 5.01/5.24 ! [A: int,M: nat,N: nat] :
% 5.01/5.24 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.24 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_mult2_eq'
% 5.01/5.24 thf(fact_3516_mod__mult2__eq_H,axiom,
% 5.01/5.24 ! [A: nat,M: nat,N: nat] :
% 5.01/5.24 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.01/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_mult2_eq'
% 5.01/5.24 thf(fact_3517_mod__mult2__eq_H,axiom,
% 5.01/5.24 ! [A: code_integer,M: nat,N: nat] :
% 5.01/5.24 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.01/5.24 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mod_mult2_eq'
% 5.01/5.24 thf(fact_3518_field__char__0__class_Oof__nat__div,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % field_char_0_class.of_nat_div
% 5.01/5.24 thf(fact_3519_field__char__0__class_Oof__nat__div,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % field_char_0_class.of_nat_div
% 5.01/5.24 thf(fact_3520_field__char__0__class_Oof__nat__div,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % field_char_0_class.of_nat_div
% 5.01/5.24 thf(fact_3521_dbl__inc__def,axiom,
% 5.01/5.24 ( neg_nu8557863876264182079omplex
% 5.01/5.24 = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_inc_def
% 5.01/5.24 thf(fact_3522_dbl__inc__def,axiom,
% 5.01/5.24 ( neg_nu8295874005876285629c_real
% 5.01/5.24 = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_inc_def
% 5.01/5.24 thf(fact_3523_dbl__inc__def,axiom,
% 5.01/5.24 ( neg_nu5219082963157363817nc_rat
% 5.01/5.24 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_inc_def
% 5.01/5.24 thf(fact_3524_dbl__inc__def,axiom,
% 5.01/5.24 ( neg_nu5851722552734809277nc_int
% 5.01/5.24 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_inc_def
% 5.01/5.24 thf(fact_3525_real__of__nat__div__aux,axiom,
% 5.01/5.24 ! [X2: nat,D: nat] :
% 5.01/5.24 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.01/5.24 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % real_of_nat_div_aux
% 5.01/5.24 thf(fact_3526_field__le__mult__one__interval,axiom,
% 5.01/5.24 ! [X2: real,Y: real] :
% 5.01/5.24 ( ! [Z3: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 5.01/5.24 => ( ( ord_less_real @ Z3 @ one_one_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X2 ) @ Y ) ) )
% 5.01/5.24 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.24
% 5.01/5.24 % field_le_mult_one_interval
% 5.01/5.24 thf(fact_3527_field__le__mult__one__interval,axiom,
% 5.01/5.24 ! [X2: rat,Y: rat] :
% 5.01/5.24 ( ! [Z3: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 5.01/5.24 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X2 ) @ Y ) ) )
% 5.01/5.24 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.01/5.24
% 5.01/5.24 % field_le_mult_one_interval
% 5.01/5.24 thf(fact_3528_mult__less__cancel__right2,axiom,
% 5.01/5.24 ! [A: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ A @ one_one_real ) )
% 5.01/5.24 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right2
% 5.01/5.24 thf(fact_3529_mult__less__cancel__right2,axiom,
% 5.01/5.24 ! [A: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.01/5.24 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right2
% 5.01/5.24 thf(fact_3530_mult__less__cancel__right2,axiom,
% 5.01/5.24 ! [A: int,C: int] :
% 5.01/5.24 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_int @ A @ one_one_int ) )
% 5.01/5.24 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right2
% 5.01/5.24 thf(fact_3531_mult__less__cancel__right1,axiom,
% 5.01/5.24 ! [C: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ one_one_real @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right1
% 5.01/5.24 thf(fact_3532_mult__less__cancel__right1,axiom,
% 5.01/5.24 ! [C: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right1
% 5.01/5.24 thf(fact_3533_mult__less__cancel__right1,axiom,
% 5.01/5.24 ! [C: int,B: int] :
% 5.01/5.24 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_int @ one_one_int @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_right1
% 5.01/5.24 thf(fact_3534_mult__less__cancel__left2,axiom,
% 5.01/5.24 ! [C: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ A @ one_one_real ) )
% 5.01/5.24 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left2
% 5.01/5.24 thf(fact_3535_mult__less__cancel__left2,axiom,
% 5.01/5.24 ! [C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.01/5.24 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left2
% 5.01/5.24 thf(fact_3536_mult__less__cancel__left2,axiom,
% 5.01/5.24 ! [C: int,A: int] :
% 5.01/5.24 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_int @ A @ one_one_int ) )
% 5.01/5.24 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left2
% 5.01/5.24 thf(fact_3537_mult__less__cancel__left1,axiom,
% 5.01/5.24 ! [C: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ one_one_real @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left1
% 5.01/5.24 thf(fact_3538_mult__less__cancel__left1,axiom,
% 5.01/5.24 ! [C: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left1
% 5.01/5.24 thf(fact_3539_mult__less__cancel__left1,axiom,
% 5.01/5.24 ! [C: int,B: int] :
% 5.01/5.24 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_int @ one_one_int @ B ) )
% 5.01/5.24 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_less_cancel_left1
% 5.01/5.24 thf(fact_3540_mult__le__cancel__right2,axiom,
% 5.01/5.24 ! [A: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.01/5.24 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right2
% 5.01/5.24 thf(fact_3541_mult__le__cancel__right2,axiom,
% 5.01/5.24 ! [A: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.01/5.24 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right2
% 5.01/5.24 thf(fact_3542_mult__le__cancel__right2,axiom,
% 5.01/5.24 ! [A: int,C: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.01/5.24 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.01/5.24 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right2
% 5.01/5.24 thf(fact_3543_mult__le__cancel__right1,axiom,
% 5.01/5.24 ! [C: real,B: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.01/5.24 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right1
% 5.01/5.24 thf(fact_3544_mult__le__cancel__right1,axiom,
% 5.01/5.24 ! [C: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.01/5.24 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right1
% 5.01/5.24 thf(fact_3545_mult__le__cancel__right1,axiom,
% 5.01/5.24 ! [C: int,B: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.01/5.24 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_right1
% 5.01/5.24 thf(fact_3546_mult__le__cancel__left2,axiom,
% 5.01/5.24 ! [C: real,A: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.01/5.24 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left2
% 5.01/5.24 thf(fact_3547_mult__le__cancel__left2,axiom,
% 5.01/5.24 ! [C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.01/5.24 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left2
% 5.01/5.24 thf(fact_3548_mult__le__cancel__left2,axiom,
% 5.01/5.24 ! [C: int,A: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.01/5.24 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.01/5.24 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left2
% 5.01/5.24 thf(fact_3549_mult__le__cancel__left1,axiom,
% 5.01/5.24 ! [C: real,B: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.01/5.24 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left1
% 5.01/5.24 thf(fact_3550_mult__le__cancel__left1,axiom,
% 5.01/5.24 ! [C: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.01/5.24 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left1
% 5.01/5.24 thf(fact_3551_mult__le__cancel__left1,axiom,
% 5.01/5.24 ! [C: int,B: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.01/5.24 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.01/5.24 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.01/5.24 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.01/5.24 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_le_cancel_left1
% 5.01/5.24 thf(fact_3552_divide__left__mono__neg,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.24 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.24 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_left_mono_neg
% 5.01/5.24 thf(fact_3553_divide__left__mono__neg,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.24 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.24 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_left_mono_neg
% 5.01/5.24 thf(fact_3554_mult__imp__le__div__pos,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X2 )
% 5.01/5.24 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_le_div_pos
% 5.01/5.24 thf(fact_3555_mult__imp__le__div__pos,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X2 )
% 5.01/5.24 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_le_div_pos
% 5.01/5.24 thf(fact_3556_mult__imp__div__pos__le,axiom,
% 5.01/5.24 ! [Y: real,X2: real,Z: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y ) )
% 5.01/5.24 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_div_pos_le
% 5.01/5.24 thf(fact_3557_mult__imp__div__pos__le,axiom,
% 5.01/5.24 ! [Y: rat,X2: rat,Z: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y ) )
% 5.01/5.24 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_imp_div_pos_le
% 5.01/5.24 thf(fact_3558_pos__le__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_le_divide_eq
% 5.01/5.24 thf(fact_3559_pos__le__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_le_divide_eq
% 5.01/5.24 thf(fact_3560_pos__divide__le__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_divide_le_eq
% 5.01/5.24 thf(fact_3561_pos__divide__le__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_divide_le_eq
% 5.01/5.24 thf(fact_3562_neg__le__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_le_divide_eq
% 5.01/5.24 thf(fact_3563_neg__le__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_le_divide_eq
% 5.01/5.24 thf(fact_3564_neg__divide__le__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_divide_le_eq
% 5.01/5.24 thf(fact_3565_neg__divide__le__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_divide_le_eq
% 5.01/5.24 thf(fact_3566_divide__left__mono,axiom,
% 5.01/5.24 ! [B: real,A: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ B @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.24 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_left_mono
% 5.01/5.24 thf(fact_3567_divide__left__mono,axiom,
% 5.01/5.24 ! [B: rat,A: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.24 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_left_mono
% 5.01/5.24 thf(fact_3568_le__divide__eq,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq
% 5.01/5.24 thf(fact_3569_le__divide__eq,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq
% 5.01/5.24 thf(fact_3570_divide__le__eq,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq
% 5.01/5.24 thf(fact_3571_divide__le__eq,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq
% 5.01/5.24 thf(fact_3572_convex__bound__le,axiom,
% 5.01/5.24 ! [X2: real,A: real,Y: real,U: real,V: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.01/5.24 => ( ( ( plus_plus_real @ U @ V )
% 5.01/5.24 = one_one_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_le
% 5.01/5.24 thf(fact_3573_convex__bound__le,axiom,
% 5.01/5.24 ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.01/5.24 => ( ( ( plus_plus_rat @ U @ V )
% 5.01/5.24 = one_one_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_le
% 5.01/5.24 thf(fact_3574_convex__bound__le,axiom,
% 5.01/5.24 ! [X2: int,A: int,Y: int,U: int,V: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.01/5.24 => ( ( ( plus_plus_int @ U @ V )
% 5.01/5.24 = one_one_int )
% 5.01/5.24 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_le
% 5.01/5.24 thf(fact_3575_divide__le__eq__1,axiom,
% 5.01/5.24 ! [B: real,A: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 & ( ord_less_eq_real @ B @ A ) )
% 5.01/5.24 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.24 & ( ord_less_eq_real @ A @ B ) )
% 5.01/5.24 | ( A = zero_zero_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_1
% 5.01/5.24 thf(fact_3576_divide__le__eq__1,axiom,
% 5.01/5.24 ! [B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 & ( ord_less_eq_rat @ B @ A ) )
% 5.01/5.24 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.24 & ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.24 | ( A = zero_zero_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_1
% 5.01/5.24 thf(fact_3577_le__divide__eq__1,axiom,
% 5.01/5.24 ! [B: real,A: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 & ( ord_less_eq_real @ A @ B ) )
% 5.01/5.24 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.24 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_1
% 5.01/5.24 thf(fact_3578_le__divide__eq__1,axiom,
% 5.01/5.24 ! [B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 & ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.24 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.24 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_1
% 5.01/5.24 thf(fact_3579_less__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3580_less__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3581_divide__less__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_numeral(1)
% 5.01/5.24 thf(fact_3582_divide__less__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_numeral(1)
% 5.01/5.24 thf(fact_3583_frac__le__eq,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real,W: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.01/5.24 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % frac_le_eq
% 5.01/5.24 thf(fact_3584_frac__le__eq,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.01/5.24 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % frac_le_eq
% 5.01/5.24 thf(fact_3585_divmod__digit__1_I1_J,axiom,
% 5.01/5.24 ! [A: code_integer,B: code_integer] :
% 5.01/5.24 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.24 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.24 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.01/5.24 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(1)
% 5.01/5.24 thf(fact_3586_divmod__digit__1_I1_J,axiom,
% 5.01/5.24 ! [A: nat,B: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.01/5.24 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.01/5.24 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(1)
% 5.01/5.24 thf(fact_3587_divmod__digit__1_I1_J,axiom,
% 5.01/5.24 ! [A: int,B: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.24 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.01/5.24 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.01/5.24 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divmod_digit_1(1)
% 5.01/5.24 thf(fact_3588_frac__less__eq,axiom,
% 5.01/5.24 ! [Y: real,Z: real,X2: real,W: real] :
% 5.01/5.24 ( ( Y != zero_zero_real )
% 5.01/5.24 => ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.01/5.24 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % frac_less_eq
% 5.01/5.24 thf(fact_3589_frac__less__eq,axiom,
% 5.01/5.24 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.01/5.24 ( ( Y != zero_zero_rat )
% 5.01/5.24 => ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.01/5.24 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % frac_less_eq
% 5.01/5.24 thf(fact_3590_power__Suc__less,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less
% 5.01/5.24 thf(fact_3591_power__Suc__less,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less
% 5.01/5.24 thf(fact_3592_power__Suc__less,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less
% 5.01/5.24 thf(fact_3593_power__Suc__less,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less
% 5.01/5.24 thf(fact_3594_less__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_divide_eq
% 5.01/5.24 thf(fact_3595_less__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_minus_divide_eq
% 5.01/5.24 thf(fact_3596_minus__divide__less__eq,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_less_eq
% 5.01/5.24 thf(fact_3597_minus__divide__less__eq,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_less_eq
% 5.01/5.24 thf(fact_3598_neg__less__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_less_minus_divide_eq
% 5.01/5.24 thf(fact_3599_neg__less__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_less_minus_divide_eq
% 5.01/5.24 thf(fact_3600_neg__minus__divide__less__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_minus_divide_less_eq
% 5.01/5.24 thf(fact_3601_neg__minus__divide__less__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_minus_divide_less_eq
% 5.01/5.24 thf(fact_3602_pos__less__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_less_minus_divide_eq
% 5.01/5.24 thf(fact_3603_pos__less__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_less_minus_divide_eq
% 5.01/5.24 thf(fact_3604_pos__minus__divide__less__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_minus_divide_less_eq
% 5.01/5.24 thf(fact_3605_pos__minus__divide__less__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_minus_divide_less_eq
% 5.01/5.24 thf(fact_3606_eq__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.24 = ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.24 = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3607_eq__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: complex,C: complex] :
% 5.01/5.24 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.24 = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3608_eq__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % eq_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3609_divide__eq__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ( divide_divide_real @ B @ C )
% 5.01/5.24 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_real )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_real )
% 5.01/5.24 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.24 = zero_zero_real ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(2)
% 5.01/5.24 thf(fact_3610_divide__eq__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: complex,C: complex,W: num] :
% 5.01/5.24 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_complex )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_complex )
% 5.01/5.24 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.24 = zero_zero_complex ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(2)
% 5.01/5.24 thf(fact_3611_divide__eq__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ( divide_divide_rat @ B @ C )
% 5.01/5.24 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.24 = ( ( ( C != zero_zero_rat )
% 5.01/5.24 => ( B
% 5.01/5.24 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ( C = zero_zero_rat )
% 5.01/5.24 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = zero_zero_rat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_eq_eq_numeral(2)
% 5.01/5.24 thf(fact_3612_power__Suc__le__self,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_le_self
% 5.01/5.24 thf(fact_3613_power__Suc__le__self,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_le_self
% 5.01/5.24 thf(fact_3614_power__Suc__le__self,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_le_self
% 5.01/5.24 thf(fact_3615_power__Suc__le__self,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_le_self
% 5.01/5.24 thf(fact_3616_add__divide__eq__if__simps_I3_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(3)
% 5.01/5.24 thf(fact_3617_add__divide__eq__if__simps_I3_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(3)
% 5.01/5.24 thf(fact_3618_add__divide__eq__if__simps_I3_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.01/5.24 = B ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(3)
% 5.01/5.24 thf(fact_3619_minus__divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_add_eq_iff
% 5.01/5.24 thf(fact_3620_minus__divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_add_eq_iff
% 5.01/5.24 thf(fact_3621_minus__divide__add__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_add_eq_iff
% 5.01/5.24 thf(fact_3622_power__Suc__less__one,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less_one
% 5.01/5.24 thf(fact_3623_power__Suc__less__one,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less_one
% 5.01/5.24 thf(fact_3624_power__Suc__less__one,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less_one
% 5.01/5.24 thf(fact_3625_power__Suc__less__one,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_Suc_less_one
% 5.01/5.24 thf(fact_3626_minus__divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: real,X2: real,Y: real] :
% 5.01/5.24 ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_diff_eq_iff
% 5.01/5.24 thf(fact_3627_minus__divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: complex,X2: complex,Y: complex] :
% 5.01/5.24 ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_diff_eq_iff
% 5.01/5.24 thf(fact_3628_minus__divide__diff__eq__iff,axiom,
% 5.01/5.24 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.24 ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_diff_eq_iff
% 5.01/5.24 thf(fact_3629_add__divide__eq__if__simps_I5_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.01/5.24 = ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(5)
% 5.01/5.24 thf(fact_3630_add__divide__eq__if__simps_I5_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(5)
% 5.01/5.24 thf(fact_3631_add__divide__eq__if__simps_I5_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.01/5.24 = ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(5)
% 5.01/5.24 thf(fact_3632_add__divide__eq__if__simps_I6_J,axiom,
% 5.01/5.24 ! [Z: real,A: real,B: real] :
% 5.01/5.24 ( ( ( Z = zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.01/5.24 = ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_real )
% 5.01/5.24 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(6)
% 5.01/5.24 thf(fact_3633_add__divide__eq__if__simps_I6_J,axiom,
% 5.01/5.24 ! [Z: complex,A: complex,B: complex] :
% 5.01/5.24 ( ( ( Z = zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.01/5.24 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_complex )
% 5.01/5.24 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(6)
% 5.01/5.24 thf(fact_3634_add__divide__eq__if__simps_I6_J,axiom,
% 5.01/5.24 ! [Z: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ( Z = zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.01/5.24 = ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ( Z != zero_zero_rat )
% 5.01/5.24 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.01/5.24 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_divide_eq_if_simps(6)
% 5.01/5.24 thf(fact_3635_power__strict__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: real] :
% 5.01/5.24 ( ( ord_less_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_strict_decreasing
% 5.01/5.24 thf(fact_3636_power__strict__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: rat] :
% 5.01/5.24 ( ( ord_less_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_strict_decreasing
% 5.01/5.24 thf(fact_3637_power__strict__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: nat] :
% 5.01/5.24 ( ( ord_less_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_strict_decreasing
% 5.01/5.24 thf(fact_3638_power__strict__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: int] :
% 5.01/5.24 ( ( ord_less_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_strict_decreasing
% 5.01/5.24 thf(fact_3639_power__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: real] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_decreasing
% 5.01/5.24 thf(fact_3640_power__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_decreasing
% 5.01/5.24 thf(fact_3641_power__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.01/5.24 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.01/5.24 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_decreasing
% 5.01/5.24 thf(fact_3642_power__decreasing,axiom,
% 5.01/5.24 ! [N: nat,N2: nat,A: int] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.01/5.24 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_decreasing
% 5.01/5.24 thf(fact_3643_zero__power2,axiom,
% 5.01/5.24 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = zero_zero_rat ) ).
% 5.01/5.24
% 5.01/5.24 % zero_power2
% 5.01/5.24 thf(fact_3644_zero__power2,axiom,
% 5.01/5.24 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = zero_zero_real ) ).
% 5.01/5.24
% 5.01/5.24 % zero_power2
% 5.01/5.24 thf(fact_3645_zero__power2,axiom,
% 5.01/5.24 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = zero_zero_nat ) ).
% 5.01/5.24
% 5.01/5.24 % zero_power2
% 5.01/5.24 thf(fact_3646_zero__power2,axiom,
% 5.01/5.24 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = zero_zero_int ) ).
% 5.01/5.24
% 5.01/5.24 % zero_power2
% 5.01/5.24 thf(fact_3647_zero__power2,axiom,
% 5.01/5.24 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = zero_zero_complex ) ).
% 5.01/5.24
% 5.01/5.24 % zero_power2
% 5.01/5.24 thf(fact_3648_self__le__power,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % self_le_power
% 5.01/5.24 thf(fact_3649_self__le__power,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % self_le_power
% 5.01/5.24 thf(fact_3650_self__le__power,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % self_le_power
% 5.01/5.24 thf(fact_3651_self__le__power,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % self_le_power
% 5.01/5.24 thf(fact_3652_one__less__power,axiom,
% 5.01/5.24 ! [A: real,N: nat] :
% 5.01/5.24 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % one_less_power
% 5.01/5.24 thf(fact_3653_one__less__power,axiom,
% 5.01/5.24 ! [A: rat,N: nat] :
% 5.01/5.24 ( ( ord_less_rat @ one_one_rat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % one_less_power
% 5.01/5.24 thf(fact_3654_one__less__power,axiom,
% 5.01/5.24 ! [A: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ one_one_nat @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % one_less_power
% 5.01/5.24 thf(fact_3655_one__less__power,axiom,
% 5.01/5.24 ! [A: int,N: nat] :
% 5.01/5.24 ( ( ord_less_int @ one_one_int @ A )
% 5.01/5.24 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % one_less_power
% 5.01/5.24 thf(fact_3656_numeral__2__eq__2,axiom,
% 5.01/5.24 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.01/5.24 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % numeral_2_eq_2
% 5.01/5.24 thf(fact_3657_pos2,axiom,
% 5.01/5.24 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos2
% 5.01/5.24 thf(fact_3658_power__diff,axiom,
% 5.01/5.24 ! [A: complex,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_complex )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.24 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff
% 5.01/5.24 thf(fact_3659_power__diff,axiom,
% 5.01/5.24 ! [A: real,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff
% 5.01/5.24 thf(fact_3660_power__diff,axiom,
% 5.01/5.24 ! [A: rat,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff
% 5.01/5.24 thf(fact_3661_power__diff,axiom,
% 5.01/5.24 ! [A: nat,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_nat )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff
% 5.01/5.24 thf(fact_3662_power__diff,axiom,
% 5.01/5.24 ! [A: int,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_int )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.24 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff
% 5.01/5.24 thf(fact_3663_numeral__3__eq__3,axiom,
% 5.01/5.24 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.01/5.24 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % numeral_3_eq_3
% 5.01/5.24 thf(fact_3664_Suc__diff__eq__diff__pred,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.01/5.24 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % Suc_diff_eq_diff_pred
% 5.01/5.24 thf(fact_3665_Suc__pred_H,axiom,
% 5.01/5.24 ! [N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( N
% 5.01/5.24 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % Suc_pred'
% 5.01/5.24 thf(fact_3666_div__if,axiom,
% 5.01/5.24 ( divide_divide_nat
% 5.01/5.24 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.24 ( if_nat
% 5.01/5.24 @ ( ( ord_less_nat @ M3 @ N4 )
% 5.01/5.24 | ( N4 = zero_zero_nat ) )
% 5.01/5.24 @ zero_zero_nat
% 5.01/5.24 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_if
% 5.01/5.24 thf(fact_3667_div__geq,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ~ ( ord_less_nat @ M @ N )
% 5.01/5.24 => ( ( divide_divide_nat @ M @ N )
% 5.01/5.24 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_geq
% 5.01/5.24 thf(fact_3668_add__eq__if,axiom,
% 5.01/5.24 ( plus_plus_nat
% 5.01/5.24 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % add_eq_if
% 5.01/5.24 thf(fact_3669_less__eq__div__iff__mult__less__eq,axiom,
% 5.01/5.24 ! [Q2: nat,M: nat,N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.01/5.24 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.01/5.24 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_eq_div_iff_mult_less_eq
% 5.01/5.24 thf(fact_3670_dividend__less__times__div,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dividend_less_times_div
% 5.01/5.24 thf(fact_3671_dividend__less__div__times,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dividend_less_div_times
% 5.01/5.24 thf(fact_3672_split__div,axiom,
% 5.01/5.24 ! [P: nat > $o,M: nat,N: nat] :
% 5.01/5.24 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( ( ( N = zero_zero_nat )
% 5.01/5.24 => ( P @ zero_zero_nat ) )
% 5.01/5.24 & ( ( N != zero_zero_nat )
% 5.01/5.24 => ! [I4: nat,J3: nat] :
% 5.01/5.24 ( ( ord_less_nat @ J3 @ N )
% 5.01/5.24 => ( ( M
% 5.01/5.24 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.01/5.24 => ( P @ I4 ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % split_div
% 5.01/5.24 thf(fact_3673_mult__eq__if,axiom,
% 5.01/5.24 ( times_times_nat
% 5.01/5.24 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % mult_eq_if
% 5.01/5.24 thf(fact_3674_Suc__mod__eq__add3__mod,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.01/5.24 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.01/5.24
% 5.01/5.24 % Suc_mod_eq_add3_mod
% 5.01/5.24 thf(fact_3675_convex__bound__lt,axiom,
% 5.01/5.24 ! [X2: real,A: real,Y: real,U: real,V: real] :
% 5.01/5.24 ( ( ord_less_real @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_real @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.01/5.24 => ( ( ( plus_plus_real @ U @ V )
% 5.01/5.24 = one_one_real )
% 5.01/5.24 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_lt
% 5.01/5.24 thf(fact_3676_convex__bound__lt,axiom,
% 5.01/5.24 ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.01/5.24 ( ( ord_less_rat @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_rat @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.01/5.24 => ( ( ( plus_plus_rat @ U @ V )
% 5.01/5.24 = one_one_rat )
% 5.01/5.24 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_lt
% 5.01/5.24 thf(fact_3677_convex__bound__lt,axiom,
% 5.01/5.24 ! [X2: int,A: int,Y: int,U: int,V: int] :
% 5.01/5.24 ( ( ord_less_int @ X2 @ A )
% 5.01/5.24 => ( ( ord_less_int @ Y @ A )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.01/5.24 => ( ( ( plus_plus_int @ U @ V )
% 5.01/5.24 = one_one_int )
% 5.01/5.24 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % convex_bound_lt
% 5.01/5.24 thf(fact_3678_le__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3679_le__divide__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_numeral(1)
% 5.01/5.24 thf(fact_3680_divide__le__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_numeral(1)
% 5.01/5.24 thf(fact_3681_divide__le__eq__numeral_I1_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_numeral(1)
% 5.01/5.24 thf(fact_3682_le__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: real,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_minus_divide_eq
% 5.01/5.24 thf(fact_3683_le__minus__divide__eq,axiom,
% 5.01/5.24 ! [A: rat,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_minus_divide_eq
% 5.01/5.24 thf(fact_3684_minus__divide__le__eq,axiom,
% 5.01/5.24 ! [B: real,C: real,A: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_le_eq
% 5.01/5.24 thf(fact_3685_minus__divide__le__eq,axiom,
% 5.01/5.24 ! [B: rat,C: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % minus_divide_le_eq
% 5.01/5.24 thf(fact_3686_neg__le__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_le_minus_divide_eq
% 5.01/5.24 thf(fact_3687_neg__le__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_le_minus_divide_eq
% 5.01/5.24 thf(fact_3688_neg__minus__divide__le__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_minus_divide_le_eq
% 5.01/5.24 thf(fact_3689_neg__minus__divide__le__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % neg_minus_divide_le_eq
% 5.01/5.24 thf(fact_3690_pos__le__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: real,A: real,B: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_le_minus_divide_eq
% 5.01/5.24 thf(fact_3691_pos__le__minus__divide__eq,axiom,
% 5.01/5.24 ! [C: rat,A: rat,B: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.01/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_le_minus_divide_eq
% 5.01/5.24 thf(fact_3692_pos__minus__divide__le__eq,axiom,
% 5.01/5.24 ! [C: real,B: real,A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_minus_divide_le_eq
% 5.01/5.24 thf(fact_3693_pos__minus__divide__le__eq,axiom,
% 5.01/5.24 ! [C: rat,B: rat,A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.01/5.24 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % pos_minus_divide_le_eq
% 5.01/5.24 thf(fact_3694_scaling__mono,axiom,
% 5.01/5.24 ! [U: real,V: real,R: real,S2: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ U @ V )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.01/5.24 => ( ( ord_less_eq_real @ R @ S2 )
% 5.01/5.24 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % scaling_mono
% 5.01/5.24 thf(fact_3695_scaling__mono,axiom,
% 5.01/5.24 ! [U: rat,V: rat,R: rat,S2: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ U @ V )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 5.01/5.24 => ( ( ord_less_eq_rat @ R @ S2 )
% 5.01/5.24 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % scaling_mono
% 5.01/5.24 thf(fact_3696_half__gt__zero__iff,axiom,
% 5.01/5.24 ! [A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.24 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.01/5.24
% 5.01/5.24 % half_gt_zero_iff
% 5.01/5.24 thf(fact_3697_half__gt__zero__iff,axiom,
% 5.01/5.24 ! [A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.24
% 5.01/5.24 % half_gt_zero_iff
% 5.01/5.24 thf(fact_3698_half__gt__zero,axiom,
% 5.01/5.24 ! [A: real] :
% 5.01/5.24 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.24 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % half_gt_zero
% 5.01/5.24 thf(fact_3699_half__gt__zero,axiom,
% 5.01/5.24 ! [A: rat] :
% 5.01/5.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.24 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % half_gt_zero
% 5.01/5.24 thf(fact_3700_divide__less__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_numeral(2)
% 5.01/5.24 thf(fact_3701_divide__less__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_less_eq_numeral(2)
% 5.01/5.24 thf(fact_3702_less__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3703_less__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3704_power2__le__imp__le,axiom,
% 5.01/5.24 ! [X2: real,Y: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_le_imp_le
% 5.01/5.24 thf(fact_3705_power2__le__imp__le,axiom,
% 5.01/5.24 ! [X2: rat,Y: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_le_imp_le
% 5.01/5.24 thf(fact_3706_power2__le__imp__le,axiom,
% 5.01/5.24 ! [X2: nat,Y: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.01/5.24 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_le_imp_le
% 5.01/5.24 thf(fact_3707_power2__le__imp__le,axiom,
% 5.01/5.24 ! [X2: int,Y: int] :
% 5.01/5.24 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.24 => ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_le_imp_le
% 5.01/5.24 thf(fact_3708_power2__eq__imp__eq,axiom,
% 5.01/5.24 ! [X2: real,Y: real] :
% 5.01/5.24 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( X2 = Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_eq_imp_eq
% 5.01/5.24 thf(fact_3709_power2__eq__imp__eq,axiom,
% 5.01/5.24 ! [X2: rat,Y: rat] :
% 5.01/5.24 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( X2 = Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_eq_imp_eq
% 5.01/5.24 thf(fact_3710_power2__eq__imp__eq,axiom,
% 5.01/5.24 ! [X2: nat,Y: nat] :
% 5.01/5.24 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.01/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.01/5.24 => ( X2 = Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_eq_imp_eq
% 5.01/5.24 thf(fact_3711_power2__eq__imp__eq,axiom,
% 5.01/5.24 ! [X2: int,Y: int] :
% 5.01/5.24 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.24 => ( X2 = Y ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_eq_imp_eq
% 5.01/5.24 thf(fact_3712_zero__le__power2,axiom,
% 5.01/5.24 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % zero_le_power2
% 5.01/5.24 thf(fact_3713_zero__le__power2,axiom,
% 5.01/5.24 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % zero_le_power2
% 5.01/5.24 thf(fact_3714_zero__le__power2,axiom,
% 5.01/5.24 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % zero_le_power2
% 5.01/5.24 thf(fact_3715_power2__less__0,axiom,
% 5.01/5.24 ! [A: real] :
% 5.01/5.24 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.01/5.24
% 5.01/5.24 % power2_less_0
% 5.01/5.24 thf(fact_3716_power2__less__0,axiom,
% 5.01/5.24 ! [A: rat] :
% 5.01/5.24 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.01/5.24
% 5.01/5.24 % power2_less_0
% 5.01/5.24 thf(fact_3717_power2__less__0,axiom,
% 5.01/5.24 ! [A: int] :
% 5.01/5.24 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.01/5.24
% 5.01/5.24 % power2_less_0
% 5.01/5.24 thf(fact_3718_exp__add__not__zero__imp__right,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.01/5.24 != zero_zero_nat )
% 5.01/5.24 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.24 != zero_zero_nat ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_add_not_zero_imp_right
% 5.01/5.24 thf(fact_3719_exp__add__not__zero__imp__right,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.01/5.24 != zero_zero_int )
% 5.01/5.24 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.24 != zero_zero_int ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_add_not_zero_imp_right
% 5.01/5.24 thf(fact_3720_exp__add__not__zero__imp__left,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.01/5.24 != zero_zero_nat )
% 5.01/5.24 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.01/5.24 != zero_zero_nat ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_add_not_zero_imp_left
% 5.01/5.24 thf(fact_3721_exp__add__not__zero__imp__left,axiom,
% 5.01/5.24 ! [M: nat,N: nat] :
% 5.01/5.24 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.01/5.24 != zero_zero_int )
% 5.01/5.24 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.01/5.24 != zero_zero_int ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_add_not_zero_imp_left
% 5.01/5.24 thf(fact_3722_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.24 != zero_zero_nat )
% 5.01/5.24 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.24 != zero_zero_nat ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_not_zero_imp_exp_diff_not_zero
% 5.01/5.24 thf(fact_3723_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.24 != zero_zero_int )
% 5.01/5.24 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.24 != zero_zero_int ) ) ).
% 5.01/5.24
% 5.01/5.24 % exp_not_zero_imp_exp_diff_not_zero
% 5.01/5.24 thf(fact_3724_power__diff__power__eq,axiom,
% 5.01/5.24 ! [A: nat,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_nat )
% 5.01/5.24 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.01/5.24 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.01/5.24 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.01/5.24 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff_power_eq
% 5.01/5.24 thf(fact_3725_power__diff__power__eq,axiom,
% 5.01/5.24 ! [A: int,N: nat,M: nat] :
% 5.01/5.24 ( ( A != zero_zero_int )
% 5.01/5.24 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.01/5.24 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.01/5.24 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.01/5.24 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_diff_power_eq
% 5.01/5.24 thf(fact_3726_inverse__of__nat__le,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( N != zero_zero_nat )
% 5.01/5.24 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % inverse_of_nat_le
% 5.01/5.24 thf(fact_3727_inverse__of__nat__le,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( N != zero_zero_nat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % inverse_of_nat_le
% 5.01/5.24 thf(fact_3728_less__2__cases,axiom,
% 5.01/5.24 ! [N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 => ( ( N = zero_zero_nat )
% 5.01/5.24 | ( N
% 5.01/5.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_2_cases
% 5.01/5.24 thf(fact_3729_less__2__cases__iff,axiom,
% 5.01/5.24 ! [N: nat] :
% 5.01/5.24 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.24 = ( ( N = zero_zero_nat )
% 5.01/5.24 | ( N
% 5.01/5.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % less_2_cases_iff
% 5.01/5.24 thf(fact_3730_power__eq__if,axiom,
% 5.01/5.24 ( power_power_real
% 5.01/5.24 = ( ^ [P5: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_eq_if
% 5.01/5.24 thf(fact_3731_power__eq__if,axiom,
% 5.01/5.24 ( power_power_rat
% 5.01/5.24 = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_eq_if
% 5.01/5.24 thf(fact_3732_power__eq__if,axiom,
% 5.01/5.24 ( power_power_nat
% 5.01/5.24 = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_eq_if
% 5.01/5.24 thf(fact_3733_power__eq__if,axiom,
% 5.01/5.24 ( power_power_int
% 5.01/5.24 = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_eq_if
% 5.01/5.24 thf(fact_3734_power__eq__if,axiom,
% 5.01/5.24 ( power_power_complex
% 5.01/5.24 = ( ^ [P5: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_eq_if
% 5.01/5.24 thf(fact_3735_nat__induct2,axiom,
% 5.01/5.24 ! [P: nat > $o,N: nat] :
% 5.01/5.24 ( ( P @ zero_zero_nat )
% 5.01/5.24 => ( ( P @ one_one_nat )
% 5.01/5.24 => ( ! [N3: nat] :
% 5.01/5.24 ( ( P @ N3 )
% 5.01/5.24 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.24 => ( P @ N ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % nat_induct2
% 5.01/5.24 thf(fact_3736_power__minus__mult,axiom,
% 5.01/5.24 ! [N: nat,A: real] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.01/5.24 = ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_minus_mult
% 5.01/5.24 thf(fact_3737_power__minus__mult,axiom,
% 5.01/5.24 ! [N: nat,A: rat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.01/5.24 = ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_minus_mult
% 5.01/5.24 thf(fact_3738_power__minus__mult,axiom,
% 5.01/5.24 ! [N: nat,A: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.01/5.24 = ( power_power_nat @ A @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_minus_mult
% 5.01/5.24 thf(fact_3739_power__minus__mult,axiom,
% 5.01/5.24 ! [N: nat,A: int] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.01/5.24 = ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_minus_mult
% 5.01/5.24 thf(fact_3740_power__minus__mult,axiom,
% 5.01/5.24 ! [N: nat,A: complex] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.01/5.24 = ( power_power_complex @ A @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power_minus_mult
% 5.01/5.24 thf(fact_3741_le__div__geq,axiom,
% 5.01/5.24 ! [N: nat,M: nat] :
% 5.01/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.24 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.24 => ( ( divide_divide_nat @ M @ N )
% 5.01/5.24 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_div_geq
% 5.01/5.24 thf(fact_3742_split__div_H,axiom,
% 5.01/5.24 ! [P: nat > $o,M: nat,N: nat] :
% 5.01/5.24 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.01/5.24 = ( ( ( N = zero_zero_nat )
% 5.01/5.24 & ( P @ zero_zero_nat ) )
% 5.01/5.24 | ? [Q4: nat] :
% 5.01/5.24 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.01/5.24 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.01/5.24 & ( P @ Q4 ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % split_div'
% 5.01/5.24 thf(fact_3743_div__exp__mod__exp__eq,axiom,
% 5.01/5.24 ! [A: nat,N: nat,M: nat] :
% 5.01/5.24 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_exp_mod_exp_eq
% 5.01/5.24 thf(fact_3744_div__exp__mod__exp__eq,axiom,
% 5.01/5.24 ! [A: int,N: nat,M: nat] :
% 5.01/5.24 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_exp_mod_exp_eq
% 5.01/5.24 thf(fact_3745_div__exp__mod__exp__eq,axiom,
% 5.01/5.24 ! [A: code_integer,N: nat,M: nat] :
% 5.01/5.24 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.01/5.24 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % div_exp_mod_exp_eq
% 5.01/5.24 thf(fact_3746_dbl__dec__def,axiom,
% 5.01/5.24 ( neg_nu6075765906172075777c_real
% 5.01/5.24 = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_dec_def
% 5.01/5.24 thf(fact_3747_dbl__dec__def,axiom,
% 5.01/5.24 ( neg_nu3179335615603231917ec_rat
% 5.01/5.24 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_dec_def
% 5.01/5.24 thf(fact_3748_dbl__dec__def,axiom,
% 5.01/5.24 ( neg_nu3811975205180677377ec_int
% 5.01/5.24 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_dec_def
% 5.01/5.24 thf(fact_3749_dbl__dec__def,axiom,
% 5.01/5.24 ( neg_nu6511756317524482435omplex
% 5.01/5.24 = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % dbl_dec_def
% 5.01/5.24 thf(fact_3750_le__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: real,C: real] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3751_le__divide__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [W: num,B: rat,C: rat] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % le_divide_eq_numeral(2)
% 5.01/5.24 thf(fact_3752_divide__le__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: real,C: real,W: num] :
% 5.01/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.24 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.24 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.01/5.24 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_numeral(2)
% 5.01/5.24 thf(fact_3753_divide__le__eq__numeral_I2_J,axiom,
% 5.01/5.24 ! [B: rat,C: rat,W: num] :
% 5.01/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.24 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.01/5.24 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.01/5.24 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.01/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % divide_le_eq_numeral(2)
% 5.01/5.24 thf(fact_3754_power2__less__imp__less,axiom,
% 5.01/5.24 ! [X2: real,Y: real] :
% 5.01/5.24 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.24 => ( ord_less_real @ X2 @ Y ) ) ) ).
% 5.01/5.24
% 5.01/5.24 % power2_less_imp_less
% 5.01/5.24 thf(fact_3755_power2__less__imp__less,axiom,
% 5.01/5.24 ! [X2: rat,Y: rat] :
% 5.01/5.24 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.24 => ( ord_less_rat @ X2 @ Y ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % power2_less_imp_less
% 5.01/5.25 thf(fact_3756_power2__less__imp__less,axiom,
% 5.01/5.25 ! [X2: nat,Y: nat] :
% 5.01/5.25 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.01/5.25 => ( ord_less_nat @ X2 @ Y ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % power2_less_imp_less
% 5.01/5.25 thf(fact_3757_power2__less__imp__less,axiom,
% 5.01/5.25 ! [X2: int,Y: int] :
% 5.01/5.25 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.25 => ( ord_less_int @ X2 @ Y ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % power2_less_imp_less
% 5.01/5.25 thf(fact_3758_sum__power2__le__zero__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.01/5.25 = ( ( X2 = zero_zero_real )
% 5.01/5.25 & ( Y = zero_zero_real ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_le_zero_iff
% 5.01/5.25 thf(fact_3759_sum__power2__le__zero__iff,axiom,
% 5.01/5.25 ! [X2: rat,Y: rat] :
% 5.01/5.25 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.01/5.25 = ( ( X2 = zero_zero_rat )
% 5.01/5.25 & ( Y = zero_zero_rat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_le_zero_iff
% 5.01/5.25 thf(fact_3760_sum__power2__le__zero__iff,axiom,
% 5.01/5.25 ! [X2: int,Y: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.01/5.25 = ( ( X2 = zero_zero_int )
% 5.01/5.25 & ( Y = zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_le_zero_iff
% 5.01/5.25 thf(fact_3761_sum__power2__ge__zero,axiom,
% 5.01/5.25 ! [X2: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_ge_zero
% 5.01/5.25 thf(fact_3762_sum__power2__ge__zero,axiom,
% 5.01/5.25 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_ge_zero
% 5.01/5.25 thf(fact_3763_sum__power2__ge__zero,axiom,
% 5.01/5.25 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_ge_zero
% 5.01/5.25 thf(fact_3764_sum__power2__gt__zero__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.25 = ( ( X2 != zero_zero_real )
% 5.01/5.25 | ( Y != zero_zero_real ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_gt_zero_iff
% 5.01/5.25 thf(fact_3765_sum__power2__gt__zero__iff,axiom,
% 5.01/5.25 ! [X2: rat,Y: rat] :
% 5.01/5.25 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.25 = ( ( X2 != zero_zero_rat )
% 5.01/5.25 | ( Y != zero_zero_rat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_gt_zero_iff
% 5.01/5.25 thf(fact_3766_sum__power2__gt__zero__iff,axiom,
% 5.01/5.25 ! [X2: int,Y: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.25 = ( ( X2 != zero_zero_int )
% 5.01/5.25 | ( Y != zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % sum_power2_gt_zero_iff
% 5.01/5.25 thf(fact_3767_not__sum__power2__lt__zero,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.01/5.25
% 5.01/5.25 % not_sum_power2_lt_zero
% 5.01/5.25 thf(fact_3768_not__sum__power2__lt__zero,axiom,
% 5.01/5.25 ! [X2: rat,Y: rat] :
% 5.01/5.25 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.01/5.25
% 5.01/5.25 % not_sum_power2_lt_zero
% 5.01/5.25 thf(fact_3769_not__sum__power2__lt__zero,axiom,
% 5.01/5.25 ! [X2: int,Y: int] :
% 5.01/5.25 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % not_sum_power2_lt_zero
% 5.01/5.25 thf(fact_3770_zero__le__even__power_H,axiom,
% 5.01/5.25 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zero_le_even_power'
% 5.01/5.25 thf(fact_3771_zero__le__even__power_H,axiom,
% 5.01/5.25 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zero_le_even_power'
% 5.01/5.25 thf(fact_3772_zero__le__even__power_H,axiom,
% 5.01/5.25 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zero_le_even_power'
% 5.01/5.25 thf(fact_3773_nat__bit__induct,axiom,
% 5.01/5.25 ! [P: nat > $o,N: nat] :
% 5.01/5.25 ( ( P @ zero_zero_nat )
% 5.01/5.25 => ( ! [N3: nat] :
% 5.01/5.25 ( ( P @ N3 )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.25 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.01/5.25 => ( ! [N3: nat] :
% 5.01/5.25 ( ( P @ N3 )
% 5.01/5.25 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.01/5.25 => ( P @ N ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_bit_induct
% 5.01/5.25 thf(fact_3774_mult__exp__mod__exp__eq,axiom,
% 5.01/5.25 ! [M: nat,N: nat,A: nat] :
% 5.01/5.25 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.25 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.25 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mult_exp_mod_exp_eq
% 5.01/5.25 thf(fact_3775_mult__exp__mod__exp__eq,axiom,
% 5.01/5.25 ! [M: nat,N: nat,A: int] :
% 5.01/5.25 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.25 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mult_exp_mod_exp_eq
% 5.01/5.25 thf(fact_3776_mult__exp__mod__exp__eq,axiom,
% 5.01/5.25 ! [M: nat,N: nat,A: code_integer] :
% 5.01/5.25 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.25 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.25 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mult_exp_mod_exp_eq
% 5.01/5.25 thf(fact_3777_div__2__gt__zero,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.25 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_2_gt_zero
% 5.01/5.25 thf(fact_3778_Suc__n__div__2__gt__zero,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % Suc_n_div_2_gt_zero
% 5.01/5.25 thf(fact_3779_odd__0__le__power__imp__0__le,axiom,
% 5.01/5.25 ! [A: real,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.01/5.25 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_0_le_power_imp_0_le
% 5.01/5.25 thf(fact_3780_odd__0__le__power__imp__0__le,axiom,
% 5.01/5.25 ! [A: rat,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.01/5.25 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_0_le_power_imp_0_le
% 5.01/5.25 thf(fact_3781_odd__0__le__power__imp__0__le,axiom,
% 5.01/5.25 ! [A: int,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.01/5.25 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_0_le_power_imp_0_le
% 5.01/5.25 thf(fact_3782_odd__power__less__zero,axiom,
% 5.01/5.25 ! [A: real,N: nat] :
% 5.01/5.25 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.25 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_power_less_zero
% 5.01/5.25 thf(fact_3783_odd__power__less__zero,axiom,
% 5.01/5.25 ! [A: rat,N: nat] :
% 5.01/5.25 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.25 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_power_less_zero
% 5.01/5.25 thf(fact_3784_odd__power__less__zero,axiom,
% 5.01/5.25 ! [A: int,N: nat] :
% 5.01/5.25 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_power_less_zero
% 5.01/5.25 thf(fact_3785_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.01/5.25 ! [X2: nat,N: nat,M: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.25 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % VEBT_internal.exp_split_high_low(1)
% 5.01/5.25 thf(fact_3786_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.01/5.25 ! [X2: nat,N: nat,M: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.25 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % VEBT_internal.exp_split_high_low(2)
% 5.01/5.25 thf(fact_3787_arith__geo__mean,axiom,
% 5.01/5.25 ! [U: real,X2: real,Y: real] :
% 5.01/5.25 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.25 = ( times_times_real @ X2 @ Y ) )
% 5.01/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.25 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % arith_geo_mean
% 5.01/5.25 thf(fact_3788_arith__geo__mean,axiom,
% 5.01/5.25 ! [U: rat,X2: rat,Y: rat] :
% 5.01/5.25 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.25 = ( times_times_rat @ X2 @ Y ) )
% 5.01/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.25 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % arith_geo_mean
% 5.01/5.25 thf(fact_3789_invar__vebt_Ocases,axiom,
% 5.01/5.25 ! [A12: vEBT_VEBT,A23: nat] :
% 5.01/5.25 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.01/5.25 => ( ( ? [A3: $o,B2: $o] :
% 5.01/5.25 ( A12
% 5.01/5.25 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.25 => ( A23
% 5.01/5.25 != ( suc @ zero_zero_nat ) ) )
% 5.01/5.25 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.01/5.25 ( ( A12
% 5.01/5.25 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.25 => ( ( A23 = Deg2 )
% 5.01/5.25 => ( ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.01/5.25 => ( ( vEBT_invar_vebt @ Summary3 @ M4 )
% 5.01/5.25 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.01/5.25 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( M4 = N3 )
% 5.01/5.25 => ( ( Deg2
% 5.01/5.25 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.01/5.25 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 5.01/5.25 => ~ ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.01/5.25 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.01/5.25 ( ( A12
% 5.01/5.25 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.25 => ( ( A23 = Deg2 )
% 5.01/5.25 => ( ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.01/5.25 => ( ( vEBT_invar_vebt @ Summary3 @ M4 )
% 5.01/5.25 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.01/5.25 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( M4
% 5.01/5.25 = ( suc @ N3 ) )
% 5.01/5.25 => ( ( Deg2
% 5.01/5.25 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.01/5.25 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X_1 )
% 5.01/5.25 => ~ ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.01/5.25 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M4: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 5.01/5.25 ( ( A12
% 5.01/5.25 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.25 => ( ( A23 = Deg2 )
% 5.01/5.25 => ( ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.01/5.25 => ( ( vEBT_invar_vebt @ Summary3 @ M4 )
% 5.01/5.25 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.01/5.25 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( M4 = N3 )
% 5.01/5.25 => ( ( Deg2
% 5.01/5.25 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.01/5.25 => ( ! [I2: nat] :
% 5.01/5.25 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X5 ) )
% 5.01/5.25 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.01/5.25 => ( ( ( Mi3 = Ma3 )
% 5.01/5.25 => ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) )
% 5.01/5.25 => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.01/5.25 => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.01/5.25 => ~ ( ( Mi3 != Ma3 )
% 5.01/5.25 => ! [I2: nat] :
% 5.01/5.25 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.01/5.25 = I2 )
% 5.01/5.25 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.01/5.25 & ! [X: nat] :
% 5.01/5.25 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.01/5.25 = I2 )
% 5.01/5.25 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.01/5.25 => ( ( ord_less_nat @ Mi3 @ X )
% 5.01/5.25 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.01/5.25 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M4: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 5.01/5.25 ( ( A12
% 5.01/5.25 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.25 => ( ( A23 = Deg2 )
% 5.01/5.25 => ( ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ( vEBT_invar_vebt @ X @ N3 ) )
% 5.01/5.25 => ( ( vEBT_invar_vebt @ Summary3 @ M4 )
% 5.01/5.25 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.01/5.25 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( M4
% 5.01/5.25 = ( suc @ N3 ) )
% 5.01/5.25 => ( ( Deg2
% 5.01/5.25 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.01/5.25 => ( ! [I2: nat] :
% 5.01/5.25 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X5 ) )
% 5.01/5.25 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.01/5.25 => ( ( ( Mi3 = Ma3 )
% 5.01/5.25 => ! [X: vEBT_VEBT] :
% 5.01/5.25 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.01/5.25 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X @ X_1 ) ) )
% 5.01/5.25 => ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.01/5.25 => ( ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.01/5.25 => ~ ( ( Mi3 != Ma3 )
% 5.01/5.25 => ! [I2: nat] :
% 5.01/5.25 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.01/5.25 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 5.01/5.25 = I2 )
% 5.01/5.25 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.01/5.25 & ! [X: nat] :
% 5.01/5.25 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 5.01/5.25 = I2 )
% 5.01/5.25 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 5.01/5.25 => ( ( ord_less_nat @ Mi3 @ X )
% 5.01/5.25 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % invar_vebt.cases
% 5.01/5.25 thf(fact_3790_buildup__gives__valid,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.01/5.25
% 5.01/5.25 % buildup_gives_valid
% 5.01/5.25 thf(fact_3791_zle__add1__eq__le,axiom,
% 5.01/5.25 ! [W: int,Z: int] :
% 5.01/5.25 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.01/5.25 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % zle_add1_eq_le
% 5.01/5.25 thf(fact_3792_verit__minus__simplify_I3_J,axiom,
% 5.01/5.25 ! [B: real] :
% 5.01/5.25 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.01/5.25 = ( uminus_uminus_real @ B ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(3)
% 5.01/5.25 thf(fact_3793_verit__minus__simplify_I3_J,axiom,
% 5.01/5.25 ! [B: int] :
% 5.01/5.25 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.01/5.25 = ( uminus_uminus_int @ B ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(3)
% 5.01/5.25 thf(fact_3794_verit__minus__simplify_I3_J,axiom,
% 5.01/5.25 ! [B: complex] :
% 5.01/5.25 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.01/5.25 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(3)
% 5.01/5.25 thf(fact_3795_verit__minus__simplify_I3_J,axiom,
% 5.01/5.25 ! [B: code_integer] :
% 5.01/5.25 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.25 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(3)
% 5.01/5.25 thf(fact_3796_verit__minus__simplify_I3_J,axiom,
% 5.01/5.25 ! [B: rat] :
% 5.01/5.25 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.01/5.25 = ( uminus_uminus_rat @ B ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(3)
% 5.01/5.25 thf(fact_3797_verit__le__mono__div,axiom,
% 5.01/5.25 ! [A2: nat,B4: nat,N: nat] :
% 5.01/5.25 ( ( ord_less_nat @ A2 @ B4 )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ord_less_eq_nat
% 5.01/5.25 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.01/5.25 @ ( if_nat
% 5.01/5.25 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.01/5.25 = zero_zero_nat )
% 5.01/5.25 @ one_one_nat
% 5.01/5.25 @ zero_zero_nat ) )
% 5.01/5.25 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_le_mono_div
% 5.01/5.25 thf(fact_3798_mod__exhaust__less__4,axiom,
% 5.01/5.25 ! [M: nat] :
% 5.01/5.25 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.25 = zero_zero_nat )
% 5.01/5.25 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.25 = one_one_nat )
% 5.01/5.25 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.25 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.25 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.25 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mod_exhaust_less_4
% 5.01/5.25 thf(fact_3799_nat__approx__posE,axiom,
% 5.01/5.25 ! [E: rat] :
% 5.01/5.25 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_approx_posE
% 5.01/5.25 thf(fact_3800_nat__approx__posE,axiom,
% 5.01/5.25 ! [E: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_approx_posE
% 5.01/5.25 thf(fact_3801_set__bit__0,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.01/5.25 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_0
% 5.01/5.25 thf(fact_3802_set__bit__0,axiom,
% 5.01/5.25 ! [A: nat] :
% 5.01/5.25 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.01/5.25 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_0
% 5.01/5.25 thf(fact_3803_negative__zle,axiom,
% 5.01/5.25 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.01/5.25
% 5.01/5.25 % negative_zle
% 5.01/5.25 thf(fact_3804_zle__diff1__eq,axiom,
% 5.01/5.25 ! [W: int,Z: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.01/5.25 = ( ord_less_int @ W @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % zle_diff1_eq
% 5.01/5.25 thf(fact_3805_negative__eq__positive,axiom,
% 5.01/5.25 ! [N: nat,M: nat] :
% 5.01/5.25 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.25 = ( semiri1314217659103216013at_int @ M ) )
% 5.01/5.25 = ( ( N = zero_zero_nat )
% 5.01/5.25 & ( M = zero_zero_nat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % negative_eq_positive
% 5.01/5.25 thf(fact_3806_verit__eq__simplify_I8_J,axiom,
% 5.01/5.25 ! [X23: num,Y22: num] :
% 5.01/5.25 ( ( ( bit0 @ X23 )
% 5.01/5.25 = ( bit0 @ Y22 ) )
% 5.01/5.25 = ( X23 = Y22 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_eq_simplify(8)
% 5.01/5.25 thf(fact_3807_verit__minus__simplify_I4_J,axiom,
% 5.01/5.25 ! [B: real] :
% 5.01/5.25 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 5.01/5.25 = B ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(4)
% 5.01/5.25 thf(fact_3808_verit__minus__simplify_I4_J,axiom,
% 5.01/5.25 ! [B: int] :
% 5.01/5.25 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 5.01/5.25 = B ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(4)
% 5.01/5.25 thf(fact_3809_verit__minus__simplify_I4_J,axiom,
% 5.01/5.25 ! [B: complex] :
% 5.01/5.25 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 5.01/5.25 = B ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(4)
% 5.01/5.25 thf(fact_3810_verit__minus__simplify_I4_J,axiom,
% 5.01/5.25 ! [B: code_integer] :
% 5.01/5.25 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 5.01/5.25 = B ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(4)
% 5.01/5.25 thf(fact_3811_verit__minus__simplify_I4_J,axiom,
% 5.01/5.25 ! [B: rat] :
% 5.01/5.25 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 5.01/5.25 = B ) ).
% 5.01/5.25
% 5.01/5.25 % verit_minus_simplify(4)
% 5.01/5.25 thf(fact_3812_verit__eq__simplify_I9_J,axiom,
% 5.01/5.25 ! [X33: num,Y32: num] :
% 5.01/5.25 ( ( ( bit1 @ X33 )
% 5.01/5.25 = ( bit1 @ Y32 ) )
% 5.01/5.25 = ( X33 = Y32 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_eq_simplify(9)
% 5.01/5.25 thf(fact_3813_set__bit__nonnegative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.01/5.25 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_nonnegative_int_iff
% 5.01/5.25 thf(fact_3814_set__bit__negative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_negative_int_iff
% 5.01/5.25 thf(fact_3815_i0__less,axiom,
% 5.01/5.25 ! [N: extended_enat] :
% 5.01/5.25 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.01/5.25 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.01/5.25
% 5.01/5.25 % i0_less
% 5.01/5.25 thf(fact_3816_idiff__0,axiom,
% 5.01/5.25 ! [N: extended_enat] :
% 5.01/5.25 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.01/5.25 = zero_z5237406670263579293d_enat ) ).
% 5.01/5.25
% 5.01/5.25 % idiff_0
% 5.01/5.25 thf(fact_3817_idiff__0__right,axiom,
% 5.01/5.25 ! [N: extended_enat] :
% 5.01/5.25 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.01/5.25 = N ) ).
% 5.01/5.25
% 5.01/5.25 % idiff_0_right
% 5.01/5.25 thf(fact_3818_double__eq__0__iff,axiom,
% 5.01/5.25 ! [A: real] :
% 5.01/5.25 ( ( ( plus_plus_real @ A @ A )
% 5.01/5.25 = zero_zero_real )
% 5.01/5.25 = ( A = zero_zero_real ) ) ).
% 5.01/5.25
% 5.01/5.25 % double_eq_0_iff
% 5.01/5.25 thf(fact_3819_double__eq__0__iff,axiom,
% 5.01/5.25 ! [A: rat] :
% 5.01/5.25 ( ( ( plus_plus_rat @ A @ A )
% 5.01/5.25 = zero_zero_rat )
% 5.01/5.25 = ( A = zero_zero_rat ) ) ).
% 5.01/5.25
% 5.01/5.25 % double_eq_0_iff
% 5.01/5.25 thf(fact_3820_double__eq__0__iff,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ( ( ( plus_plus_int @ A @ A )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 = ( A = zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % double_eq_0_iff
% 5.01/5.25 thf(fact_3821_not__real__square__gt__zero,axiom,
% 5.01/5.25 ! [X2: real] :
% 5.01/5.25 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 5.01/5.25 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.25
% 5.01/5.25 % not_real_square_gt_zero
% 5.01/5.25 thf(fact_3822_mod__pos__pos__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( ord_less_int @ K @ L )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 = K ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mod_pos_pos_trivial
% 5.01/5.25 thf(fact_3823_mod__neg__neg__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ L @ K )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 = K ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mod_neg_neg_trivial
% 5.01/5.25 thf(fact_3824_real__add__minus__iff,axiom,
% 5.01/5.25 ! [X2: real,A: real] :
% 5.01/5.25 ( ( ( plus_plus_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.01/5.25 = zero_zero_real )
% 5.01/5.25 = ( X2 = A ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_add_minus_iff
% 5.01/5.25 thf(fact_3825_zmod__numeral__Bit0,axiom,
% 5.01/5.25 ! [V: num,W: num] :
% 5.01/5.25 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.01/5.25 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_numeral_Bit0
% 5.01/5.25 thf(fact_3826_int__eq__iff__numeral,axiom,
% 5.01/5.25 ! [M: nat,V: num] :
% 5.01/5.25 ( ( ( semiri1314217659103216013at_int @ M )
% 5.01/5.25 = ( numeral_numeral_int @ V ) )
% 5.01/5.25 = ( M
% 5.01/5.25 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_eq_iff_numeral
% 5.01/5.25 thf(fact_3827_div__neg__neg__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ L @ K )
% 5.01/5.25 => ( ( divide_divide_int @ K @ L )
% 5.01/5.25 = zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_neg_neg_trivial
% 5.01/5.25 thf(fact_3828_div__pos__pos__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( ord_less_int @ K @ L )
% 5.01/5.25 => ( ( divide_divide_int @ K @ L )
% 5.01/5.25 = zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_pos_pos_trivial
% 5.01/5.25 thf(fact_3829_negative__zless,axiom,
% 5.01/5.25 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.01/5.25
% 5.01/5.25 % negative_zless
% 5.01/5.25 thf(fact_3830_half__nonnegative__int__iff,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.01/5.25 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % half_nonnegative_int_iff
% 5.01/5.25 thf(fact_3831_half__negative__int__iff,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % half_negative_int_iff
% 5.01/5.25 thf(fact_3832_zmod__numeral__Bit1,axiom,
% 5.01/5.25 ! [V: num,W: num] :
% 5.01/5.25 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_numeral_Bit1
% 5.01/5.25 thf(fact_3833_zdiv__mono__strict,axiom,
% 5.01/5.25 ! [A2: int,B4: int,N: int] :
% 5.01/5.25 ( ( ord_less_int @ A2 @ B4 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.01/5.25 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ( ( modulo_modulo_int @ B4 @ N )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono_strict
% 5.01/5.25 thf(fact_3834_zmult__zless__mono2,axiom,
% 5.01/5.25 ! [I: int,J: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ I @ J )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmult_zless_mono2
% 5.01/5.25 thf(fact_3835_Euclidean__Division_Opos__mod__bound,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.01/5.25
% 5.01/5.25 % Euclidean_Division.pos_mod_bound
% 5.01/5.25 thf(fact_3836_neg__mod__bound,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ L @ zero_zero_int )
% 5.01/5.25 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_mod_bound
% 5.01/5.25 thf(fact_3837_less__int__code_I1_J,axiom,
% 5.01/5.25 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % less_int_code(1)
% 5.01/5.25 thf(fact_3838_int__int__eq,axiom,
% 5.01/5.25 ! [M: nat,N: nat] :
% 5.01/5.25 ( ( ( semiri1314217659103216013at_int @ M )
% 5.01/5.25 = ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.25 = ( M = N ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_int_eq
% 5.01/5.25 thf(fact_3839_int__if,axiom,
% 5.01/5.25 ! [P: $o,A: nat,B: nat] :
% 5.01/5.25 ( ( P
% 5.01/5.25 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.01/5.25 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.01/5.25 & ( ~ P
% 5.01/5.25 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.01/5.25 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_if
% 5.01/5.25 thf(fact_3840_nat__int__comparison_I1_J,axiom,
% 5.01/5.25 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.01/5.25 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ A4 )
% 5.01/5.25 = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_int_comparison(1)
% 5.01/5.25 thf(fact_3841_int__diff__cases,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ~ ! [M4: nat,N3: nat] :
% 5.01/5.25 ( Z
% 5.01/5.25 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_diff_cases
% 5.01/5.25 thf(fact_3842_int__distrib_I4_J,axiom,
% 5.01/5.25 ! [W: int,Z1: int,Z22: int] :
% 5.01/5.25 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.01/5.25 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_distrib(4)
% 5.01/5.25 thf(fact_3843_int__distrib_I3_J,axiom,
% 5.01/5.25 ! [Z1: int,Z22: int,W: int] :
% 5.01/5.25 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.01/5.25 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_distrib(3)
% 5.01/5.25 thf(fact_3844_minus__int__code_I1_J,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.01/5.25 = K ) ).
% 5.01/5.25
% 5.01/5.25 % minus_int_code(1)
% 5.01/5.25 thf(fact_3845_zmod__le__nonneg__dividend,axiom,
% 5.01/5.25 ! [M: int,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.01/5.25 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_le_nonneg_dividend
% 5.01/5.25 thf(fact_3846_Euclidean__Division_Opos__mod__sign,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % Euclidean_Division.pos_mod_sign
% 5.01/5.25 thf(fact_3847_neg__mod__sign,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ L @ zero_zero_int )
% 5.01/5.25 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_mod_sign
% 5.01/5.25 thf(fact_3848_zmod__trivial__iff,axiom,
% 5.01/5.25 ! [I: int,K: int] :
% 5.01/5.25 ( ( ( modulo_modulo_int @ I @ K )
% 5.01/5.25 = I )
% 5.01/5.25 = ( ( K = zero_zero_int )
% 5.01/5.25 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.01/5.25 & ( ord_less_int @ I @ K ) )
% 5.01/5.25 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.01/5.25 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_trivial_iff
% 5.01/5.25 thf(fact_3849_pos__mod__conj,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.25 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_mod_conj
% 5.01/5.25 thf(fact_3850_neg__mod__conj,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.01/5.25 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_mod_conj
% 5.01/5.25 thf(fact_3851_mod__pos__geq,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ( ord_less_eq_int @ L @ K )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mod_pos_geq
% 5.01/5.25 thf(fact_3852_zmod__zminus1__eq__if,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.25 = zero_zero_int ) )
% 5.01/5.25 & ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.25 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_zminus1_eq_if
% 5.01/5.25 thf(fact_3853_zmod__zminus2__eq__if,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.25 = zero_zero_int ) )
% 5.01/5.25 & ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.25 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_zminus2_eq_if
% 5.01/5.25 thf(fact_3854_zmod__zminus2__not__zero,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 != zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_zminus2_not_zero
% 5.01/5.25 thf(fact_3855_zmod__zminus1__not__zero,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 != zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_zminus1_not_zero
% 5.01/5.25 thf(fact_3856_int__ops_I1_J,axiom,
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.01/5.25 = zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(1)
% 5.01/5.25 thf(fact_3857_int__ops_I6_J,axiom,
% 5.01/5.25 ! [A: nat,B: nat] :
% 5.01/5.25 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.01/5.25 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.01/5.25 = zero_zero_int ) )
% 5.01/5.25 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.01/5.25 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.01/5.25 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(6)
% 5.01/5.25 thf(fact_3858_zero__le__imp__eq__int,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.25 => ? [N3: nat] :
% 5.01/5.25 ( K
% 5.01/5.25 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zero_le_imp_eq_int
% 5.01/5.25 thf(fact_3859_nonneg__int__cases,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( K
% 5.01/5.25 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nonneg_int_cases
% 5.01/5.25 thf(fact_3860_less__eq__int__code_I1_J,axiom,
% 5.01/5.25 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.01/5.25
% 5.01/5.25 % less_eq_int_code(1)
% 5.01/5.25 thf(fact_3861_pos__zmult__eq__1__iff,axiom,
% 5.01/5.25 ! [M: int,N: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ M )
% 5.01/5.25 => ( ( ( times_times_int @ M @ N )
% 5.01/5.25 = one_one_int )
% 5.01/5.25 = ( ( M = one_one_int )
% 5.01/5.25 & ( N = one_one_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_zmult_eq_1_iff
% 5.01/5.25 thf(fact_3862_minus__int__code_I2_J,axiom,
% 5.01/5.25 ! [L: int] :
% 5.01/5.25 ( ( minus_minus_int @ zero_zero_int @ L )
% 5.01/5.25 = ( uminus_uminus_int @ L ) ) ).
% 5.01/5.25
% 5.01/5.25 % minus_int_code(2)
% 5.01/5.25 thf(fact_3863_uminus__int__code_I1_J,axiom,
% 5.01/5.25 ( ( uminus_uminus_int @ zero_zero_int )
% 5.01/5.25 = zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % uminus_int_code(1)
% 5.01/5.25 thf(fact_3864_plus__int__code_I1_J,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.01/5.25 = K ) ).
% 5.01/5.25
% 5.01/5.25 % plus_int_code(1)
% 5.01/5.25 thf(fact_3865_plus__int__code_I2_J,axiom,
% 5.01/5.25 ! [L: int] :
% 5.01/5.25 ( ( plus_plus_int @ zero_zero_int @ L )
% 5.01/5.25 = L ) ).
% 5.01/5.25
% 5.01/5.25 % plus_int_code(2)
% 5.01/5.25 thf(fact_3866_zmod__minus1,axiom,
% 5.01/5.25 ! [B: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.01/5.25 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_minus1
% 5.01/5.25 thf(fact_3867_mod__pos__neg__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.25 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % mod_pos_neg_trivial
% 5.01/5.25 thf(fact_3868_int__mod__pos__eq,axiom,
% 5.01/5.25 ! [A: int,B: int,Q2: int,R: int] :
% 5.01/5.25 ( ( A
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.01/5.25 => ( ( ord_less_int @ R @ B )
% 5.01/5.25 => ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = R ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_mod_pos_eq
% 5.01/5.25 thf(fact_3869_int__mod__neg__eq,axiom,
% 5.01/5.25 ! [A: int,B: int,Q2: int,R: int] :
% 5.01/5.25 ( ( A
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ B @ R )
% 5.01/5.25 => ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = R ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_mod_neg_eq
% 5.01/5.25 thf(fact_3870_split__zmod,axiom,
% 5.01/5.25 ! [P: int > $o,N: int,K: int] :
% 5.01/5.25 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.01/5.25 = ( ( ( K = zero_zero_int )
% 5.01/5.25 => ( P @ N ) )
% 5.01/5.25 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.01/5.25 & ( ord_less_int @ J3 @ K )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ J3 ) ) )
% 5.01/5.25 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.25 => ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_int @ K @ J3 )
% 5.01/5.25 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ J3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % split_zmod
% 5.01/5.25 thf(fact_3871_zmod__int,axiom,
% 5.01/5.25 ! [A: nat,B: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.25 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_int
% 5.01/5.25 thf(fact_3872_div__neg__pos__less0,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_neg_pos_less0
% 5.01/5.25 thf(fact_3873_neg__imp__zdiv__neg__iff,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_imp_zdiv_neg_iff
% 5.01/5.25 thf(fact_3874_pos__imp__zdiv__neg__iff,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_imp_zdiv_neg_iff
% 5.01/5.25 thf(fact_3875_div__mod__decomp__int,axiom,
% 5.01/5.25 ! [A2: int,N: int] :
% 5.01/5.25 ( A2
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_mod_decomp_int
% 5.01/5.25 thf(fact_3876_pos__int__cases,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( ( K
% 5.01/5.25 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_int_cases
% 5.01/5.25 thf(fact_3877_zero__less__imp__eq__int,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ? [N3: nat] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.25 & ( K
% 5.01/5.25 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zero_less_imp_eq_int
% 5.01/5.25 thf(fact_3878_negative__zless__0,axiom,
% 5.01/5.25 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % negative_zless_0
% 5.01/5.25 thf(fact_3879_negD,axiom,
% 5.01/5.25 ! [X2: int] :
% 5.01/5.25 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.01/5.25 => ? [N3: nat] :
% 5.01/5.25 ( X2
% 5.01/5.25 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % negD
% 5.01/5.25 thf(fact_3880_int__one__le__iff__zero__less,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.01/5.25 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_one_le_iff_zero_less
% 5.01/5.25 thf(fact_3881_nonpos__int__cases,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( K
% 5.01/5.25 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nonpos_int_cases
% 5.01/5.25 thf(fact_3882_negative__zle__0,axiom,
% 5.01/5.25 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % negative_zle_0
% 5.01/5.25 thf(fact_3883_enat__0__less__mult__iff,axiom,
% 5.01/5.25 ! [M: extended_enat,N: extended_enat] :
% 5.01/5.25 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.01/5.25 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.01/5.25 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % enat_0_less_mult_iff
% 5.01/5.25 thf(fact_3884_not__iless0,axiom,
% 5.01/5.25 ! [N: extended_enat] :
% 5.01/5.25 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.01/5.25
% 5.01/5.25 % not_iless0
% 5.01/5.25 thf(fact_3885_odd__nonzero,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.01/5.25 != zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % odd_nonzero
% 5.01/5.25 thf(fact_3886_odd__less__0__iff,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % odd_less_0_iff
% 5.01/5.25 thf(fact_3887_iadd__is__0,axiom,
% 5.01/5.25 ! [M: extended_enat,N: extended_enat] :
% 5.01/5.25 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.01/5.25 = zero_z5237406670263579293d_enat )
% 5.01/5.25 = ( ( M = zero_z5237406670263579293d_enat )
% 5.01/5.25 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % iadd_is_0
% 5.01/5.25 thf(fact_3888_i0__lb,axiom,
% 5.01/5.25 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.01/5.25
% 5.01/5.25 % i0_lb
% 5.01/5.25 thf(fact_3889_ile0__eq,axiom,
% 5.01/5.25 ! [N: extended_enat] :
% 5.01/5.25 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.01/5.25 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.01/5.25
% 5.01/5.25 % ile0_eq
% 5.01/5.25 thf(fact_3890_minus__mod__int__eq,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.01/5.25 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minus_mod_int_eq
% 5.01/5.25 thf(fact_3891_zdiv__zminus1__eq__if,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( B != zero_zero_int )
% 5.01/5.25 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.25 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.01/5.25 & ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.25 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_zminus1_eq_if
% 5.01/5.25 thf(fact_3892_zdiv__zminus2__eq__if,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( B != zero_zero_int )
% 5.01/5.25 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.25 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.01/5.25 & ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.25 != zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.25 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_zminus2_eq_if
% 5.01/5.25 thf(fact_3893_split__neg__lemma,axiom,
% 5.01/5.25 ! [K: int,P: int > int > $o,N: int] :
% 5.01/5.25 ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.25 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.01/5.25 = ( ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_int @ K @ J3 )
% 5.01/5.25 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % split_neg_lemma
% 5.01/5.25 thf(fact_3894_split__pos__lemma,axiom,
% 5.01/5.25 ! [K: int,P: int > int > $o,N: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.01/5.25 = ( ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.01/5.25 & ( ord_less_int @ J3 @ K )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % split_pos_lemma
% 5.01/5.25 thf(fact_3895_zmod__zmult2__eq,axiom,
% 5.01/5.25 ! [C: int,A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.25 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_zmult2_eq
% 5.01/5.25 thf(fact_3896_verit__le__mono__div__int,axiom,
% 5.01/5.25 ! [A2: int,B4: int,N: int] :
% 5.01/5.25 ( ( ord_less_int @ A2 @ B4 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.01/5.25 => ( ord_less_eq_int
% 5.01/5.25 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.01/5.25 @ ( if_int
% 5.01/5.25 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 @ one_one_int
% 5.01/5.25 @ zero_zero_int ) )
% 5.01/5.25 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_le_mono_div_int
% 5.01/5.25 thf(fact_3897_set__bit__greater__eq,axiom,
% 5.01/5.25 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_greater_eq
% 5.01/5.25 thf(fact_3898_int__cases3,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( K != zero_zero_int )
% 5.01/5.25 => ( ! [N3: nat] :
% 5.01/5.25 ( ( K
% 5.01/5.25 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( ( K
% 5.01/5.25 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.01/5.25 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_cases3
% 5.01/5.25 thf(fact_3899_neg__int__cases,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( ( K
% 5.01/5.25 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.01/5.25 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_int_cases
% 5.01/5.25 thf(fact_3900_not__zle__0__negative,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % not_zle_0_negative
% 5.01/5.25 thf(fact_3901_le__imp__0__less,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.25 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % le_imp_0_less
% 5.01/5.25 thf(fact_3902_verit__less__mono__div__int2,axiom,
% 5.01/5.25 ! [A2: int,B4: int,N: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A2 @ B4 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_less_mono_div_int2
% 5.01/5.25 thf(fact_3903_unique__quotient__lemma__neg,axiom,
% 5.01/5.25 ! [B: int,Q5: int,R3: int,Q2: int,R: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ B @ R )
% 5.01/5.25 => ( ( ord_less_int @ B @ R3 )
% 5.01/5.25 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unique_quotient_lemma_neg
% 5.01/5.25 thf(fact_3904_unique__quotient__lemma,axiom,
% 5.01/5.25 ! [B: int,Q5: int,R3: int,Q2: int,R: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.01/5.25 => ( ( ord_less_int @ R3 @ B )
% 5.01/5.25 => ( ( ord_less_int @ R @ B )
% 5.01/5.25 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unique_quotient_lemma
% 5.01/5.25 thf(fact_3905_zdiv__mono2__neg__lemma,axiom,
% 5.01/5.25 ! [B: int,Q2: int,R: int,B5: int,Q5: int,R3: int] :
% 5.01/5.25 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R3 ) )
% 5.01/5.25 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R3 ) @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ R @ B )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.01/5.25 => ( ( ord_less_eq_int @ B5 @ B )
% 5.01/5.25 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono2_neg_lemma
% 5.01/5.25 thf(fact_3906_zdiv__mono2__lemma,axiom,
% 5.01/5.25 ! [B: int,Q2: int,R: int,B5: int,Q5: int,R3: int] :
% 5.01/5.25 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R3 ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R3 ) )
% 5.01/5.25 => ( ( ord_less_int @ R3 @ B5 )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.01/5.25 => ( ( ord_less_eq_int @ B5 @ B )
% 5.01/5.25 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono2_lemma
% 5.01/5.25 thf(fact_3907_q__pos__lemma,axiom,
% 5.01/5.25 ! [B5: int,Q5: int,R3: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B5 @ Q5 ) @ R3 ) )
% 5.01/5.25 => ( ( ord_less_int @ R3 @ B5 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.01/5.25 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % q_pos_lemma
% 5.01/5.25 thf(fact_3908_zdiv__mono1,axiom,
% 5.01/5.25 ! [A: int,A5: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ A5 )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A5 @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono1
% 5.01/5.25 thf(fact_3909_zdiv__mono2,axiom,
% 5.01/5.25 ! [A: int,B5: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.01/5.25 => ( ( ord_less_eq_int @ B5 @ B )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B5 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono2
% 5.01/5.25 thf(fact_3910_zdiv__eq__0__iff,axiom,
% 5.01/5.25 ! [I: int,K: int] :
% 5.01/5.25 ( ( ( divide_divide_int @ I @ K )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 = ( ( K = zero_zero_int )
% 5.01/5.25 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.01/5.25 & ( ord_less_int @ I @ K ) )
% 5.01/5.25 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.01/5.25 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_eq_0_iff
% 5.01/5.25 thf(fact_3911_zdiv__mono1__neg,axiom,
% 5.01/5.25 ! [A: int,A5: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ A5 )
% 5.01/5.25 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A5 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono1_neg
% 5.01/5.25 thf(fact_3912_zdiv__mono2__neg,axiom,
% 5.01/5.25 ! [A: int,B5: int,B: int] :
% 5.01/5.25 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.01/5.25 => ( ( ord_less_eq_int @ B5 @ B )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B5 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_mono2_neg
% 5.01/5.25 thf(fact_3913_div__int__pos__iff,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.01/5.25 = ( ( K = zero_zero_int )
% 5.01/5.25 | ( L = zero_zero_int )
% 5.01/5.25 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.25 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.01/5.25 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.25 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_int_pos_iff
% 5.01/5.25 thf(fact_3914_div__positive__int,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ L @ K )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_positive_int
% 5.01/5.25 thf(fact_3915_div__nonneg__neg__le0,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.25 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_nonneg_neg_le0
% 5.01/5.25 thf(fact_3916_div__nonpos__pos__le0,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_nonpos_pos_le0
% 5.01/5.25 thf(fact_3917_pos__imp__zdiv__pos__iff,axiom,
% 5.01/5.25 ! [K: int,I: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.01/5.25 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_imp_zdiv_pos_iff
% 5.01/5.25 thf(fact_3918_neg__imp__zdiv__nonneg__iff,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ B @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.01/5.25 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_imp_zdiv_nonneg_iff
% 5.01/5.25 thf(fact_3919_pos__imp__zdiv__nonneg__iff,axiom,
% 5.01/5.25 ! [B: int,A: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.01/5.25 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_imp_zdiv_nonneg_iff
% 5.01/5.25 thf(fact_3920_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.01/5.25 = ( ( ord_less_eq_int @ B @ A )
% 5.01/5.25 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nonneg1_imp_zdiv_pos_iff
% 5.01/5.25 thf(fact_3921_zdiv__zmult2__eq,axiom,
% 5.01/5.25 ! [C: int,A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.01/5.25 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.25 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiv_zmult2_eq
% 5.01/5.25 thf(fact_3922_int__div__less__self,axiom,
% 5.01/5.25 ! [X2: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.01/5.25 => ( ( ord_less_int @ one_one_int @ K )
% 5.01/5.25 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_div_less_self
% 5.01/5.25 thf(fact_3923_pos__zmod__mult__2,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.25 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_zmod_mult_2
% 5.01/5.25 thf(fact_3924_neg__zmod__mult__2,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.25 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_zmod_mult_2
% 5.01/5.25 thf(fact_3925_vebt__buildup_Osimps_I1_J,axiom,
% 5.01/5.25 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.01/5.25 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.01/5.25
% 5.01/5.25 % vebt_buildup.simps(1)
% 5.01/5.25 thf(fact_3926_verit__comp__simplify1_I2_J,axiom,
% 5.01/5.25 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(2)
% 5.01/5.25 thf(fact_3927_verit__comp__simplify1_I2_J,axiom,
% 5.01/5.25 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(2)
% 5.01/5.25 thf(fact_3928_verit__comp__simplify1_I2_J,axiom,
% 5.01/5.25 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(2)
% 5.01/5.25 thf(fact_3929_verit__comp__simplify1_I2_J,axiom,
% 5.01/5.25 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(2)
% 5.01/5.25 thf(fact_3930_verit__comp__simplify1_I2_J,axiom,
% 5.01/5.25 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(2)
% 5.01/5.25 thf(fact_3931_verit__la__disequality,axiom,
% 5.01/5.25 ! [A: rat,B: rat] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 | ~ ( ord_less_eq_rat @ A @ B )
% 5.01/5.25 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_la_disequality
% 5.01/5.25 thf(fact_3932_verit__la__disequality,axiom,
% 5.01/5.25 ! [A: num,B: num] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 | ~ ( ord_less_eq_num @ A @ B )
% 5.01/5.25 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_la_disequality
% 5.01/5.25 thf(fact_3933_verit__la__disequality,axiom,
% 5.01/5.25 ! [A: nat,B: nat] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 | ~ ( ord_less_eq_nat @ A @ B )
% 5.01/5.25 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_la_disequality
% 5.01/5.25 thf(fact_3934_verit__la__disequality,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 | ~ ( ord_less_eq_int @ A @ B )
% 5.01/5.25 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_la_disequality
% 5.01/5.25 thf(fact_3935_verit__comp__simplify1_I1_J,axiom,
% 5.01/5.25 ! [A: real] :
% 5.01/5.25 ~ ( ord_less_real @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(1)
% 5.01/5.25 thf(fact_3936_verit__comp__simplify1_I1_J,axiom,
% 5.01/5.25 ! [A: rat] :
% 5.01/5.25 ~ ( ord_less_rat @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(1)
% 5.01/5.25 thf(fact_3937_verit__comp__simplify1_I1_J,axiom,
% 5.01/5.25 ! [A: num] :
% 5.01/5.25 ~ ( ord_less_num @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(1)
% 5.01/5.25 thf(fact_3938_verit__comp__simplify1_I1_J,axiom,
% 5.01/5.25 ! [A: nat] :
% 5.01/5.25 ~ ( ord_less_nat @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(1)
% 5.01/5.25 thf(fact_3939_verit__comp__simplify1_I1_J,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ~ ( ord_less_int @ A @ A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(1)
% 5.01/5.25 thf(fact_3940_verit__negate__coefficient_I3_J,axiom,
% 5.01/5.25 ! [A: real,B: real] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 => ( ( uminus_uminus_real @ A )
% 5.01/5.25 = ( uminus_uminus_real @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(3)
% 5.01/5.25 thf(fact_3941_verit__negate__coefficient_I3_J,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 => ( ( uminus_uminus_int @ A )
% 5.01/5.25 = ( uminus_uminus_int @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(3)
% 5.01/5.25 thf(fact_3942_verit__negate__coefficient_I3_J,axiom,
% 5.01/5.25 ! [A: code_integer,B: code_integer] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 => ( ( uminus1351360451143612070nteger @ A )
% 5.01/5.25 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(3)
% 5.01/5.25 thf(fact_3943_verit__negate__coefficient_I3_J,axiom,
% 5.01/5.25 ! [A: rat,B: rat] :
% 5.01/5.25 ( ( A = B )
% 5.01/5.25 => ( ( uminus_uminus_rat @ A )
% 5.01/5.25 = ( uminus_uminus_rat @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(3)
% 5.01/5.25 thf(fact_3944_nat__int__comparison_I2_J,axiom,
% 5.01/5.25 ( ord_less_nat
% 5.01/5.25 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_int_comparison(2)
% 5.01/5.25 thf(fact_3945_realpow__pos__nth2,axiom,
% 5.01/5.25 ! [A: real,N: nat] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.25 => ? [R4: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.01/5.25 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 5.01/5.25 = A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % realpow_pos_nth2
% 5.01/5.25 thf(fact_3946_int__ops_I7_J,axiom,
% 5.01/5.25 ! [A: nat,B: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.01/5.25 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(7)
% 5.01/5.25 thf(fact_3947_verit__la__generic,axiom,
% 5.01/5.25 ! [A: int,X2: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ X2 )
% 5.01/5.25 | ( A = X2 )
% 5.01/5.25 | ( ord_less_eq_int @ X2 @ A ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_la_generic
% 5.01/5.25 thf(fact_3948_int__less__induct,axiom,
% 5.01/5.25 ! [I: int,K: int,P: int > $o] :
% 5.01/5.25 ( ( ord_less_int @ I @ K )
% 5.01/5.25 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_int @ I3 @ K )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( P @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_less_induct
% 5.01/5.25 thf(fact_3949_real__arch__pow__inv,axiom,
% 5.01/5.25 ! [Y: real,X2: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.25 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.25 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N3 ) @ Y ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_arch_pow_inv
% 5.01/5.25 thf(fact_3950_not__int__zless__negative,axiom,
% 5.01/5.25 ! [N: nat,M: nat] :
% 5.01/5.25 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % not_int_zless_negative
% 5.01/5.25 thf(fact_3951_int__cases2,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ! [N3: nat] :
% 5.01/5.25 ( Z
% 5.01/5.25 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( Z
% 5.01/5.25 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_cases2
% 5.01/5.25 thf(fact_3952_real__0__less__add__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.25 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_0_less_add_iff
% 5.01/5.25 thf(fact_3953_real__add__less__0__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 5.01/5.25 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_add_less_0_iff
% 5.01/5.25 thf(fact_3954_reals__Archimedean3,axiom,
% 5.01/5.25 ! [X2: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.25 => ! [Y4: real] :
% 5.01/5.25 ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % reals_Archimedean3
% 5.01/5.25 thf(fact_3955_int__distrib_I1_J,axiom,
% 5.01/5.25 ! [Z1: int,Z22: int,W: int] :
% 5.01/5.25 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_distrib(1)
% 5.01/5.25 thf(fact_3956_int__distrib_I2_J,axiom,
% 5.01/5.25 ! [W: int,Z1: int,Z22: int] :
% 5.01/5.25 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_distrib(2)
% 5.01/5.25 thf(fact_3957_real__add__le__0__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 5.01/5.25 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_add_le_0_iff
% 5.01/5.25 thf(fact_3958_real__0__le__add__iff,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.25 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_0_le_add_iff
% 5.01/5.25 thf(fact_3959_div__eq__minus1,axiom,
% 5.01/5.25 ! [B: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.25 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_eq_minus1
% 5.01/5.25 thf(fact_3960_split__zdiv,axiom,
% 5.01/5.25 ! [P: int > $o,N: int,K: int] :
% 5.01/5.25 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.01/5.25 = ( ( ( K = zero_zero_int )
% 5.01/5.25 => ( P @ zero_zero_int ) )
% 5.01/5.25 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.01/5.25 & ( ord_less_int @ J3 @ K )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ I4 ) ) )
% 5.01/5.25 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.25 => ! [I4: int,J3: int] :
% 5.01/5.25 ( ( ( ord_less_int @ K @ J3 )
% 5.01/5.25 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.01/5.25 => ( P @ I4 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % split_zdiv
% 5.01/5.25 thf(fact_3961_int__div__neg__eq,axiom,
% 5.01/5.25 ! [A: int,B: int,Q2: int,R: int] :
% 5.01/5.25 ( ( A
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.01/5.25 => ( ( ord_less_int @ B @ R )
% 5.01/5.25 => ( ( divide_divide_int @ A @ B )
% 5.01/5.25 = Q2 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_div_neg_eq
% 5.01/5.25 thf(fact_3962_int__div__pos__eq,axiom,
% 5.01/5.25 ! [A: int,B: int,Q2: int,R: int] :
% 5.01/5.25 ( ( A
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.01/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.01/5.25 => ( ( ord_less_int @ R @ B )
% 5.01/5.25 => ( ( divide_divide_int @ A @ B )
% 5.01/5.25 = Q2 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_div_pos_eq
% 5.01/5.25 thf(fact_3963_vebt__buildup_Osimps_I2_J,axiom,
% 5.01/5.25 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.01/5.25 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.01/5.25
% 5.01/5.25 % vebt_buildup.simps(2)
% 5.01/5.25 thf(fact_3964_realpow__pos__nth,axiom,
% 5.01/5.25 ! [N: nat,A: real] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.25 => ? [R4: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.01/5.25 & ( ( power_power_real @ R4 @ N )
% 5.01/5.25 = A ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % realpow_pos_nth
% 5.01/5.25 thf(fact_3965_realpow__pos__nth__unique,axiom,
% 5.01/5.25 ! [N: nat,A: real] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.25 => ? [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.01/5.25 & ( ( power_power_real @ X4 @ N )
% 5.01/5.25 = A )
% 5.01/5.25 & ! [Y4: real] :
% 5.01/5.25 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.01/5.25 & ( ( power_power_real @ Y4 @ N )
% 5.01/5.25 = A ) )
% 5.01/5.25 => ( Y4 = X4 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % realpow_pos_nth_unique
% 5.01/5.25 thf(fact_3966_div__pos__geq,axiom,
% 5.01/5.25 ! [L: int,K: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.25 => ( ( ord_less_eq_int @ L @ K )
% 5.01/5.25 => ( ( divide_divide_int @ K @ L )
% 5.01/5.25 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_pos_geq
% 5.01/5.25 thf(fact_3967_real__archimedian__rdiv__eq__0,axiom,
% 5.01/5.25 ! [X2: real,C: real] :
% 5.01/5.25 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.01/5.25 => ( ! [M4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.01/5.25 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X2 ) @ C ) )
% 5.01/5.25 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_archimedian_rdiv_eq_0
% 5.01/5.25 thf(fact_3968_not__exp__less__eq__0__int,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % not_exp_less_eq_0_int
% 5.01/5.25 thf(fact_3969_div__pos__neg__trivial,axiom,
% 5.01/5.25 ! [K: int,L: int] :
% 5.01/5.25 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ K @ L )
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_pos_neg_trivial
% 5.01/5.25 thf(fact_3970_real__of__nat__div2,axiom,
% 5.01/5.25 ! [N: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_of_nat_div2
% 5.01/5.25 thf(fact_3971_verit__comp__simplify1_I3_J,axiom,
% 5.01/5.25 ! [B5: real,A5: real] :
% 5.01/5.25 ( ( ~ ( ord_less_eq_real @ B5 @ A5 ) )
% 5.01/5.25 = ( ord_less_real @ A5 @ B5 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(3)
% 5.01/5.25 thf(fact_3972_verit__comp__simplify1_I3_J,axiom,
% 5.01/5.25 ! [B5: rat,A5: rat] :
% 5.01/5.25 ( ( ~ ( ord_less_eq_rat @ B5 @ A5 ) )
% 5.01/5.25 = ( ord_less_rat @ A5 @ B5 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(3)
% 5.01/5.25 thf(fact_3973_verit__comp__simplify1_I3_J,axiom,
% 5.01/5.25 ! [B5: num,A5: num] :
% 5.01/5.25 ( ( ~ ( ord_less_eq_num @ B5 @ A5 ) )
% 5.01/5.25 = ( ord_less_num @ A5 @ B5 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(3)
% 5.01/5.25 thf(fact_3974_verit__comp__simplify1_I3_J,axiom,
% 5.01/5.25 ! [B5: nat,A5: nat] :
% 5.01/5.25 ( ( ~ ( ord_less_eq_nat @ B5 @ A5 ) )
% 5.01/5.25 = ( ord_less_nat @ A5 @ B5 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(3)
% 5.01/5.25 thf(fact_3975_verit__comp__simplify1_I3_J,axiom,
% 5.01/5.25 ! [B5: int,A5: int] :
% 5.01/5.25 ( ( ~ ( ord_less_eq_int @ B5 @ A5 ) )
% 5.01/5.25 = ( ord_less_int @ A5 @ B5 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_comp_simplify1(3)
% 5.01/5.25 thf(fact_3976_verit__sum__simplify,axiom,
% 5.01/5.25 ! [A: complex] :
% 5.01/5.25 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.01/5.25 = A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_sum_simplify
% 5.01/5.25 thf(fact_3977_verit__sum__simplify,axiom,
% 5.01/5.25 ! [A: real] :
% 5.01/5.25 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.01/5.25 = A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_sum_simplify
% 5.01/5.25 thf(fact_3978_verit__sum__simplify,axiom,
% 5.01/5.25 ! [A: rat] :
% 5.01/5.25 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.01/5.25 = A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_sum_simplify
% 5.01/5.25 thf(fact_3979_verit__sum__simplify,axiom,
% 5.01/5.25 ! [A: nat] :
% 5.01/5.25 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.01/5.25 = A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_sum_simplify
% 5.01/5.25 thf(fact_3980_verit__sum__simplify,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.01/5.25 = A ) ).
% 5.01/5.25
% 5.01/5.25 % verit_sum_simplify
% 5.01/5.25 thf(fact_3981_verit__negate__coefficient_I2_J,axiom,
% 5.01/5.25 ! [A: real,B: real] :
% 5.01/5.25 ( ( ord_less_real @ A @ B )
% 5.01/5.25 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(2)
% 5.01/5.25 thf(fact_3982_verit__negate__coefficient_I2_J,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_int @ A @ B )
% 5.01/5.25 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(2)
% 5.01/5.25 thf(fact_3983_verit__negate__coefficient_I2_J,axiom,
% 5.01/5.25 ! [A: code_integer,B: code_integer] :
% 5.01/5.25 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.01/5.25 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(2)
% 5.01/5.25 thf(fact_3984_verit__negate__coefficient_I2_J,axiom,
% 5.01/5.25 ! [A: rat,B: rat] :
% 5.01/5.25 ( ( ord_less_rat @ A @ B )
% 5.01/5.25 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_negate_coefficient(2)
% 5.01/5.25 thf(fact_3985_int__bit__induct,axiom,
% 5.01/5.25 ! [P: int > $o,K: int] :
% 5.01/5.25 ( ( P @ zero_zero_int )
% 5.01/5.25 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.25 => ( ! [K3: int] :
% 5.01/5.25 ( ( P @ K3 )
% 5.01/5.25 => ( ( K3 != zero_zero_int )
% 5.01/5.25 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.25 => ( ! [K3: int] :
% 5.01/5.25 ( ( P @ K3 )
% 5.01/5.25 => ( ( K3
% 5.01/5.25 != ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.25 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.01/5.25 => ( P @ K ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_bit_induct
% 5.01/5.25 thf(fact_3986_verit__eq__simplify_I10_J,axiom,
% 5.01/5.25 ! [X23: num] :
% 5.01/5.25 ( one
% 5.01/5.25 != ( bit0 @ X23 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_eq_simplify(10)
% 5.01/5.25 thf(fact_3987_real__arch__simple,axiom,
% 5.01/5.25 ! [X2: real] :
% 5.01/5.25 ? [N3: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_arch_simple
% 5.01/5.25 thf(fact_3988_real__arch__simple,axiom,
% 5.01/5.25 ! [X2: rat] :
% 5.01/5.25 ? [N3: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.01/5.25
% 5.01/5.25 % real_arch_simple
% 5.01/5.25 thf(fact_3989_reals__Archimedean2,axiom,
% 5.01/5.25 ! [X2: rat] :
% 5.01/5.25 ? [N3: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.01/5.25
% 5.01/5.25 % reals_Archimedean2
% 5.01/5.25 thf(fact_3990_reals__Archimedean2,axiom,
% 5.01/5.25 ! [X2: real] :
% 5.01/5.25 ? [N3: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.01/5.25
% 5.01/5.25 % reals_Archimedean2
% 5.01/5.25 thf(fact_3991_int__power__div__base,axiom,
% 5.01/5.25 ! [M: nat,K: int] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.25 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.25 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.01/5.25 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_power_div_base
% 5.01/5.25 thf(fact_3992_exists__least__lemma,axiom,
% 5.01/5.25 ! [P: nat > $o] :
% 5.01/5.25 ( ~ ( P @ zero_zero_nat )
% 5.01/5.25 => ( ? [X_1: nat] : ( P @ X_1 )
% 5.01/5.25 => ? [N3: nat] :
% 5.01/5.25 ( ~ ( P @ N3 )
% 5.01/5.25 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % exists_least_lemma
% 5.01/5.25 thf(fact_3993_verit__eq__simplify_I14_J,axiom,
% 5.01/5.25 ! [X23: num,X33: num] :
% 5.01/5.25 ( ( bit0 @ X23 )
% 5.01/5.25 != ( bit1 @ X33 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_eq_simplify(14)
% 5.01/5.25 thf(fact_3994_verit__eq__simplify_I12_J,axiom,
% 5.01/5.25 ! [X33: num] :
% 5.01/5.25 ( one
% 5.01/5.25 != ( bit1 @ X33 ) ) ).
% 5.01/5.25
% 5.01/5.25 % verit_eq_simplify(12)
% 5.01/5.25 thf(fact_3995_zmult__zless__mono2__lemma,axiom,
% 5.01/5.25 ! [I: int,J: int,K: nat] :
% 5.01/5.25 ( ( ord_less_int @ I @ J )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.25 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmult_zless_mono2_lemma
% 5.01/5.25 thf(fact_3996_int__ops_I3_J,axiom,
% 5.01/5.25 ! [N: num] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.01/5.25 = ( numeral_numeral_int @ N ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(3)
% 5.01/5.25 thf(fact_3997_int__of__nat__induct,axiom,
% 5.01/5.25 ! [P: int > $o,Z: int] :
% 5.01/5.25 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.01/5.25 => ( P @ Z ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_of_nat_induct
% 5.01/5.25 thf(fact_3998_int__cases,axiom,
% 5.01/5.25 ! [Z: int] :
% 5.01/5.25 ( ! [N3: nat] :
% 5.01/5.25 ( Z
% 5.01/5.25 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( Z
% 5.01/5.25 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_cases
% 5.01/5.25 thf(fact_3999_zle__int,axiom,
% 5.01/5.25 ! [M: nat,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.25 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.01/5.25
% 5.01/5.25 % zle_int
% 5.01/5.25 thf(fact_4000_nat__int__comparison_I3_J,axiom,
% 5.01/5.25 ( ord_less_eq_nat
% 5.01/5.25 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % nat_int_comparison(3)
% 5.01/5.25 thf(fact_4001_zless__iff__Suc__zadd,axiom,
% 5.01/5.25 ( ord_less_int
% 5.01/5.25 = ( ^ [W2: int,Z5: int] :
% 5.01/5.25 ? [N4: nat] :
% 5.01/5.25 ( Z5
% 5.01/5.25 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zless_iff_Suc_zadd
% 5.01/5.25 thf(fact_4002_zadd__int__left,axiom,
% 5.01/5.25 ! [M: nat,N: nat,Z: int] :
% 5.01/5.25 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.01/5.25 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % zadd_int_left
% 5.01/5.25 thf(fact_4003_int__plus,axiom,
% 5.01/5.25 ! [N: nat,M: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.25 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_plus
% 5.01/5.25 thf(fact_4004_int__ops_I5_J,axiom,
% 5.01/5.25 ! [A: nat,B: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.01/5.25 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(5)
% 5.01/5.25 thf(fact_4005_int__le__induct,axiom,
% 5.01/5.25 ! [I: int,K: int,P: int > $o] :
% 5.01/5.25 ( ( ord_less_eq_int @ I @ K )
% 5.01/5.25 => ( ( P @ K )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ I3 @ K )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( P @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_le_induct
% 5.01/5.25 thf(fact_4006_int__ops_I2_J,axiom,
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.01/5.25 = one_one_int ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(2)
% 5.01/5.25 thf(fact_4007_zmult__eq__1__iff,axiom,
% 5.01/5.25 ! [M: int,N: int] :
% 5.01/5.25 ( ( ( times_times_int @ M @ N )
% 5.01/5.25 = one_one_int )
% 5.01/5.25 = ( ( ( M = one_one_int )
% 5.01/5.25 & ( N = one_one_int ) )
% 5.01/5.25 | ( ( M
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.25 & ( N
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmult_eq_1_iff
% 5.01/5.25 thf(fact_4008_pos__zmult__eq__1__iff__lemma,axiom,
% 5.01/5.25 ! [M: int,N: int] :
% 5.01/5.25 ( ( ( times_times_int @ M @ N )
% 5.01/5.25 = one_one_int )
% 5.01/5.25 => ( ( M = one_one_int )
% 5.01/5.25 | ( M
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_zmult_eq_1_iff_lemma
% 5.01/5.25 thf(fact_4009_zle__iff__zadd,axiom,
% 5.01/5.25 ( ord_less_eq_int
% 5.01/5.25 = ( ^ [W2: int,Z5: int] :
% 5.01/5.25 ? [N4: nat] :
% 5.01/5.25 ( Z5
% 5.01/5.25 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zle_iff_zadd
% 5.01/5.25 thf(fact_4010_int__gr__induct,axiom,
% 5.01/5.25 ! [K: int,I: int,P: int > $o] :
% 5.01/5.25 ( ( ord_less_int @ K @ I )
% 5.01/5.25 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_int @ K @ I3 )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( P @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_gr_induct
% 5.01/5.25 thf(fact_4011_zless__add1__eq,axiom,
% 5.01/5.25 ! [W: int,Z: int] :
% 5.01/5.25 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.01/5.25 = ( ( ord_less_int @ W @ Z )
% 5.01/5.25 | ( W = Z ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zless_add1_eq
% 5.01/5.25 thf(fact_4012_eq__diff__eq_H,axiom,
% 5.01/5.25 ! [X2: real,Y: real,Z: real] :
% 5.01/5.25 ( ( X2
% 5.01/5.25 = ( minus_minus_real @ Y @ Z ) )
% 5.01/5.25 = ( Y
% 5.01/5.25 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % eq_diff_eq'
% 5.01/5.25 thf(fact_4013_pos__zdiv__mult__2,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.25 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.25 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pos_zdiv_mult_2
% 5.01/5.25 thf(fact_4014_neg__zdiv__mult__2,axiom,
% 5.01/5.25 ! [A: int,B: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.25 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.25 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % neg_zdiv_mult_2
% 5.01/5.25 thf(fact_4015_int__cases4,axiom,
% 5.01/5.25 ! [M: int] :
% 5.01/5.25 ( ! [N3: nat] :
% 5.01/5.25 ( M
% 5.01/5.25 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.01/5.25 => ~ ! [N3: nat] :
% 5.01/5.25 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.25 => ( M
% 5.01/5.25 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_cases4
% 5.01/5.25 thf(fact_4016_int__zle__neg,axiom,
% 5.01/5.25 ! [N: nat,M: nat] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.01/5.25 = ( ( N = zero_zero_nat )
% 5.01/5.25 & ( M = zero_zero_nat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_zle_neg
% 5.01/5.25 thf(fact_4017_int__ops_I4_J,axiom,
% 5.01/5.25 ! [A: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.01/5.25 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ops(4)
% 5.01/5.25 thf(fact_4018_int__Suc,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.01/5.25 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_Suc
% 5.01/5.25 thf(fact_4019_int__induct,axiom,
% 5.01/5.25 ! [P: int > $o,K: int,I: int] :
% 5.01/5.25 ( ( P @ K )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ I3 )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ I3 @ K )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( P @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_induct
% 5.01/5.25 thf(fact_4020_add1__zle__eq,axiom,
% 5.01/5.25 ! [W: int,Z: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.01/5.25 = ( ord_less_int @ W @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % add1_zle_eq
% 5.01/5.25 thf(fact_4021_int__ge__induct,axiom,
% 5.01/5.25 ! [K: int,I: int,P: int > $o] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ I )
% 5.01/5.25 => ( ( P @ K )
% 5.01/5.25 => ( ! [I3: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ I3 )
% 5.01/5.25 => ( ( P @ I3 )
% 5.01/5.25 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.01/5.25 => ( P @ I ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % int_ge_induct
% 5.01/5.25 thf(fact_4022_zless__imp__add1__zle,axiom,
% 5.01/5.25 ! [W: int,Z: int] :
% 5.01/5.25 ( ( ord_less_int @ W @ Z )
% 5.01/5.25 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.01/5.25
% 5.01/5.25 % zless_imp_add1_zle
% 5.01/5.25 thf(fact_4023_ex__less__of__nat__mult,axiom,
% 5.01/5.25 ! [X2: rat,Y: rat] :
% 5.01/5.25 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.25 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % ex_less_of_nat_mult
% 5.01/5.25 thf(fact_4024_ex__less__of__nat__mult,axiom,
% 5.01/5.25 ! [X2: real,Y: real] :
% 5.01/5.25 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.25 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % ex_less_of_nat_mult
% 5.01/5.25 thf(fact_4025_set__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: code_integer] :
% 5.01/5.25 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_Suc
% 5.01/5.25 thf(fact_4026_set__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: int] :
% 5.01/5.25 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_Suc
% 5.01/5.25 thf(fact_4027_set__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: nat] :
% 5.01/5.25 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % set_bit_Suc
% 5.01/5.25 thf(fact_4028_div__less__mono,axiom,
% 5.01/5.25 ! [A2: nat,B4: nat,N: nat] :
% 5.01/5.25 ( ( ord_less_nat @ A2 @ B4 )
% 5.01/5.25 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.25 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.01/5.25 = zero_zero_nat )
% 5.01/5.25 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.01/5.25 = zero_zero_nat )
% 5.01/5.25 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_less_mono
% 5.01/5.25 thf(fact_4029_div__mod__decomp,axiom,
% 5.01/5.25 ! [A2: nat,N: nat] :
% 5.01/5.25 ( A2
% 5.01/5.25 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % div_mod_decomp
% 5.01/5.25 thf(fact_4030_linear__plus__1__le__power,axiom,
% 5.01/5.25 ! [X2: real,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.25 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % linear_plus_1_le_power
% 5.01/5.25 thf(fact_4031_zdiff__int__split,axiom,
% 5.01/5.25 ! [P: int > $o,X2: nat,Y: nat] :
% 5.01/5.25 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y ) ) )
% 5.01/5.25 = ( ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.25 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.01/5.25 & ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.25 => ( P @ zero_zero_int ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zdiff_int_split
% 5.01/5.25 thf(fact_4032_buildup__nothing__in__leaf,axiom,
% 5.01/5.25 ! [N: nat,X2: nat] :
% 5.01/5.25 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.01/5.25
% 5.01/5.25 % buildup_nothing_in_leaf
% 5.01/5.25 thf(fact_4033_unset__bit__0,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.01/5.25 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_0
% 5.01/5.25 thf(fact_4034_unset__bit__0,axiom,
% 5.01/5.25 ! [A: nat] :
% 5.01/5.25 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.01/5.25 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_0
% 5.01/5.25 thf(fact_4035_flip__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: code_integer] :
% 5.01/5.25 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % flip_bit_Suc
% 5.01/5.25 thf(fact_4036_flip__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: int] :
% 5.01/5.25 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % flip_bit_Suc
% 5.01/5.25 thf(fact_4037_flip__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: nat] :
% 5.01/5.25 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % flip_bit_Suc
% 5.01/5.25 thf(fact_4038_unset__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: code_integer] :
% 5.01/5.25 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_Suc
% 5.01/5.25 thf(fact_4039_unset__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: int] :
% 5.01/5.25 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_Suc
% 5.01/5.25 thf(fact_4040_unset__bit__Suc,axiom,
% 5.01/5.25 ! [N: nat,A: nat] :
% 5.01/5.25 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.01/5.25 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_Suc
% 5.01/5.25 thf(fact_4041_signed__take__bit__rec,axiom,
% 5.01/5.25 ( bit_ri6519982836138164636nteger
% 5.01/5.25 = ( ^ [N4: nat,A4: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_rec
% 5.01/5.25 thf(fact_4042_signed__take__bit__rec,axiom,
% 5.01/5.25 ( bit_ri631733984087533419it_int
% 5.01/5.25 = ( ^ [N4: nat,A4: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_rec
% 5.01/5.25 thf(fact_4043_unset__bit__nonnegative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.01/5.25 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_nonnegative_int_iff
% 5.01/5.25 thf(fact_4044_flip__bit__nonnegative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.01/5.25 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % flip_bit_nonnegative_int_iff
% 5.01/5.25 thf(fact_4045_unset__bit__negative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_negative_int_iff
% 5.01/5.25 thf(fact_4046_flip__bit__negative__int__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.25 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % flip_bit_negative_int_iff
% 5.01/5.25 thf(fact_4047_signed__take__bit__of__0,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.01/5.25 = zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_of_0
% 5.01/5.25 thf(fact_4048_signed__take__bit__of__minus__1,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.25 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_of_minus_1
% 5.01/5.25 thf(fact_4049_signed__take__bit__of__minus__1,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.25 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_of_minus_1
% 5.01/5.25 thf(fact_4050_signed__take__bit__Suc__1,axiom,
% 5.01/5.25 ! [N: nat] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.01/5.25 = one_one_int ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_Suc_1
% 5.01/5.25 thf(fact_4051_signed__take__bit__numeral__of__1,axiom,
% 5.01/5.25 ! [K: num] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.01/5.25 = one_one_int ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_numeral_of_1
% 5.01/5.25 thf(fact_4052_signed__take__bit__Suc__bit0,axiom,
% 5.01/5.25 ! [N: nat,K: num] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.01/5.25 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_Suc_bit0
% 5.01/5.25 thf(fact_4053_signed__take__bit__Suc__minus__bit0,axiom,
% 5.01/5.25 ! [N: nat,K: num] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.25 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_Suc_minus_bit0
% 5.01/5.25 thf(fact_4054_signed__take__bit__0,axiom,
% 5.01/5.25 ! [A: code_integer] :
% 5.01/5.25 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.01/5.25 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_0
% 5.01/5.25 thf(fact_4055_signed__take__bit__0,axiom,
% 5.01/5.25 ! [A: int] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.01/5.25 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_0
% 5.01/5.25 thf(fact_4056_signed__take__bit__Suc__bit1,axiom,
% 5.01/5.25 ! [N: nat,K: num] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_Suc_bit1
% 5.01/5.25 thf(fact_4057_signed__take__bit__Suc__minus__bit1,axiom,
% 5.01/5.25 ! [N: nat,K: num] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.25 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_Suc_minus_bit1
% 5.01/5.25 thf(fact_4058_zero__one__enat__neq_I1_J,axiom,
% 5.01/5.25 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.01/5.25
% 5.01/5.25 % zero_one_enat_neq(1)
% 5.01/5.25 thf(fact_4059_imult__is__0,axiom,
% 5.01/5.25 ! [M: extended_enat,N: extended_enat] :
% 5.01/5.25 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.01/5.25 = zero_z5237406670263579293d_enat )
% 5.01/5.25 = ( ( M = zero_z5237406670263579293d_enat )
% 5.01/5.25 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % imult_is_0
% 5.01/5.25 thf(fact_4060_zmod__eq__0__iff,axiom,
% 5.01/5.25 ! [M: int,D: int] :
% 5.01/5.25 ( ( ( modulo_modulo_int @ M @ D )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 = ( ? [Q4: int] :
% 5.01/5.25 ( M
% 5.01/5.25 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_eq_0_iff
% 5.01/5.25 thf(fact_4061_zmod__eq__0D,axiom,
% 5.01/5.25 ! [M: int,D: int] :
% 5.01/5.25 ( ( ( modulo_modulo_int @ M @ D )
% 5.01/5.25 = zero_zero_int )
% 5.01/5.25 => ? [Q3: int] :
% 5.01/5.25 ( M
% 5.01/5.25 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % zmod_eq_0D
% 5.01/5.25 thf(fact_4062_times__int__code_I2_J,axiom,
% 5.01/5.25 ! [L: int] :
% 5.01/5.25 ( ( times_times_int @ zero_zero_int @ L )
% 5.01/5.25 = zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % times_int_code(2)
% 5.01/5.25 thf(fact_4063_times__int__code_I1_J,axiom,
% 5.01/5.25 ! [K: int] :
% 5.01/5.25 ( ( times_times_int @ K @ zero_zero_int )
% 5.01/5.25 = zero_zero_int ) ).
% 5.01/5.25
% 5.01/5.25 % times_int_code(1)
% 5.01/5.25 thf(fact_4064_signed__take__bit__mult,axiom,
% 5.01/5.25 ! [N: nat,K: int,L: int] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.01/5.25 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_mult
% 5.01/5.25 thf(fact_4065_signed__take__bit__minus,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.01/5.25 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_minus
% 5.01/5.25 thf(fact_4066_signed__take__bit__add,axiom,
% 5.01/5.25 ! [N: nat,K: int,L: int] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.01/5.25 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_add
% 5.01/5.25 thf(fact_4067_signed__take__bit__diff,axiom,
% 5.01/5.25 ! [N: nat,K: int,L: int] :
% 5.01/5.25 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.01/5.25 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_diff
% 5.01/5.25 thf(fact_4068_unset__bit__less__eq,axiom,
% 5.01/5.25 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.01/5.25
% 5.01/5.25 % unset_bit_less_eq
% 5.01/5.25 thf(fact_4069_minf_I7_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ~ ( ord_less_real @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(7)
% 5.01/5.25 thf(fact_4070_minf_I7_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ~ ( ord_less_rat @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(7)
% 5.01/5.25 thf(fact_4071_minf_I7_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ~ ( ord_less_num @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(7)
% 5.01/5.25 thf(fact_4072_minf_I7_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ~ ( ord_less_nat @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(7)
% 5.01/5.25 thf(fact_4073_minf_I7_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ~ ( ord_less_int @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(7)
% 5.01/5.25 thf(fact_4074_minf_I5_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ( ord_less_real @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(5)
% 5.01/5.25 thf(fact_4075_minf_I5_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ( ord_less_rat @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(5)
% 5.01/5.25 thf(fact_4076_minf_I5_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ( ord_less_num @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(5)
% 5.01/5.25 thf(fact_4077_minf_I5_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ( ord_less_nat @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(5)
% 5.01/5.25 thf(fact_4078_minf_I5_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ( ord_less_int @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(5)
% 5.01/5.25 thf(fact_4079_minf_I4_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(4)
% 5.01/5.25 thf(fact_4080_minf_I4_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(4)
% 5.01/5.25 thf(fact_4081_minf_I4_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(4)
% 5.01/5.25 thf(fact_4082_minf_I4_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(4)
% 5.01/5.25 thf(fact_4083_minf_I4_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(4)
% 5.01/5.25 thf(fact_4084_minf_I3_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(3)
% 5.01/5.25 thf(fact_4085_minf_I3_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(3)
% 5.01/5.25 thf(fact_4086_minf_I3_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(3)
% 5.01/5.25 thf(fact_4087_minf_I3_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(3)
% 5.01/5.25 thf(fact_4088_minf_I3_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(3)
% 5.01/5.25 thf(fact_4089_minf_I2_J,axiom,
% 5.01/5.25 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.01/5.25 ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(2)
% 5.01/5.25 thf(fact_4090_minf_I2_J,axiom,
% 5.01/5.25 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.01/5.25 ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(2)
% 5.01/5.25 thf(fact_4091_minf_I2_J,axiom,
% 5.01/5.25 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.01/5.25 ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(2)
% 5.01/5.25 thf(fact_4092_minf_I2_J,axiom,
% 5.01/5.25 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.01/5.25 ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(2)
% 5.01/5.25 thf(fact_4093_minf_I2_J,axiom,
% 5.01/5.25 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.01/5.25 ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(2)
% 5.01/5.25 thf(fact_4094_minf_I1_J,axiom,
% 5.01/5.25 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.01/5.25 ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(1)
% 5.01/5.25 thf(fact_4095_minf_I1_J,axiom,
% 5.01/5.25 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.01/5.25 ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(1)
% 5.01/5.25 thf(fact_4096_minf_I1_J,axiom,
% 5.01/5.25 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.01/5.25 ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(1)
% 5.01/5.25 thf(fact_4097_minf_I1_J,axiom,
% 5.01/5.25 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.01/5.25 ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(1)
% 5.01/5.25 thf(fact_4098_minf_I1_J,axiom,
% 5.01/5.25 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.01/5.25 ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % minf(1)
% 5.01/5.25 thf(fact_4099_pinf_I7_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ( ord_less_real @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(7)
% 5.01/5.25 thf(fact_4100_pinf_I7_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ( ord_less_rat @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(7)
% 5.01/5.25 thf(fact_4101_pinf_I7_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ( ord_less_num @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(7)
% 5.01/5.25 thf(fact_4102_pinf_I7_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ( ord_less_nat @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(7)
% 5.01/5.25 thf(fact_4103_pinf_I7_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ( ord_less_int @ T @ X ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(7)
% 5.01/5.25 thf(fact_4104_pinf_I5_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ~ ( ord_less_real @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(5)
% 5.01/5.25 thf(fact_4105_pinf_I5_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ~ ( ord_less_rat @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(5)
% 5.01/5.25 thf(fact_4106_pinf_I5_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ~ ( ord_less_num @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(5)
% 5.01/5.25 thf(fact_4107_pinf_I5_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ~ ( ord_less_nat @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(5)
% 5.01/5.25 thf(fact_4108_pinf_I5_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ~ ( ord_less_int @ X @ T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(5)
% 5.01/5.25 thf(fact_4109_pinf_I4_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(4)
% 5.01/5.25 thf(fact_4110_pinf_I4_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(4)
% 5.01/5.25 thf(fact_4111_pinf_I4_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(4)
% 5.01/5.25 thf(fact_4112_pinf_I4_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(4)
% 5.01/5.25 thf(fact_4113_pinf_I4_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(4)
% 5.01/5.25 thf(fact_4114_pinf_I3_J,axiom,
% 5.01/5.25 ! [T: real] :
% 5.01/5.25 ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(3)
% 5.01/5.25 thf(fact_4115_pinf_I3_J,axiom,
% 5.01/5.25 ! [T: rat] :
% 5.01/5.25 ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(3)
% 5.01/5.25 thf(fact_4116_pinf_I3_J,axiom,
% 5.01/5.25 ! [T: num] :
% 5.01/5.25 ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(3)
% 5.01/5.25 thf(fact_4117_pinf_I3_J,axiom,
% 5.01/5.25 ! [T: nat] :
% 5.01/5.25 ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(3)
% 5.01/5.25 thf(fact_4118_pinf_I3_J,axiom,
% 5.01/5.25 ! [T: int] :
% 5.01/5.25 ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ( X != T ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(3)
% 5.01/5.25 thf(fact_4119_pinf_I2_J,axiom,
% 5.01/5.25 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.01/5.25 ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(2)
% 5.01/5.25 thf(fact_4120_pinf_I2_J,axiom,
% 5.01/5.25 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.01/5.25 ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(2)
% 5.01/5.25 thf(fact_4121_pinf_I2_J,axiom,
% 5.01/5.25 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.01/5.25 ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(2)
% 5.01/5.25 thf(fact_4122_pinf_I2_J,axiom,
% 5.01/5.25 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.01/5.25 ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(2)
% 5.01/5.25 thf(fact_4123_pinf_I2_J,axiom,
% 5.01/5.25 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.01/5.25 ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 | ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 | ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(2)
% 5.01/5.25 thf(fact_4124_pinf_I1_J,axiom,
% 5.01/5.25 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.01/5.25 ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: real] :
% 5.01/5.25 ! [X4: real] :
% 5.01/5.25 ( ( ord_less_real @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: real] :
% 5.01/5.25 ! [X: real] :
% 5.01/5.25 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(1)
% 5.01/5.25 thf(fact_4125_pinf_I1_J,axiom,
% 5.01/5.25 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.01/5.25 ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: rat] :
% 5.01/5.25 ! [X4: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: rat] :
% 5.01/5.25 ! [X: rat] :
% 5.01/5.25 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(1)
% 5.01/5.25 thf(fact_4126_pinf_I1_J,axiom,
% 5.01/5.25 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.01/5.25 ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: num] :
% 5.01/5.25 ! [X4: num] :
% 5.01/5.25 ( ( ord_less_num @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: num] :
% 5.01/5.25 ! [X: num] :
% 5.01/5.25 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(1)
% 5.01/5.25 thf(fact_4127_pinf_I1_J,axiom,
% 5.01/5.25 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.01/5.25 ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: nat] :
% 5.01/5.25 ! [X4: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: nat] :
% 5.01/5.25 ! [X: nat] :
% 5.01/5.25 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(1)
% 5.01/5.25 thf(fact_4128_pinf_I1_J,axiom,
% 5.01/5.25 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.01/5.25 ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.25 => ( ( P @ X4 )
% 5.01/5.25 = ( P6 @ X4 ) ) )
% 5.01/5.25 => ( ? [Z2: int] :
% 5.01/5.25 ! [X4: int] :
% 5.01/5.25 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.25 => ( ( Q @ X4 )
% 5.01/5.25 = ( Q6 @ X4 ) ) )
% 5.01/5.25 => ? [Z3: int] :
% 5.01/5.25 ! [X: int] :
% 5.01/5.25 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.25 => ( ( ( P @ X )
% 5.01/5.25 & ( Q @ X ) )
% 5.01/5.25 = ( ( P6 @ X )
% 5.01/5.25 & ( Q6 @ X ) ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % pinf(1)
% 5.01/5.25 thf(fact_4129_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.01/5.25 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.01/5.25 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) ).
% 5.01/5.25
% 5.01/5.25 % VEBT_internal.naive_member.simps(2)
% 5.01/5.25 thf(fact_4130_imp__le__cong,axiom,
% 5.01/5.25 ! [X2: int,X7: int,P: $o,P6: $o] :
% 5.01/5.25 ( ( X2 = X7 )
% 5.01/5.25 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.01/5.25 => ( P = P6 ) )
% 5.01/5.25 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.25 => P )
% 5.01/5.25 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.01/5.25 => P6 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % imp_le_cong
% 5.01/5.25 thf(fact_4131_conj__le__cong,axiom,
% 5.01/5.25 ! [X2: int,X7: int,P: $o,P6: $o] :
% 5.01/5.25 ( ( X2 = X7 )
% 5.01/5.25 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.01/5.25 => ( P = P6 ) )
% 5.01/5.25 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.25 & P )
% 5.01/5.25 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.01/5.25 & P6 ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % conj_le_cong
% 5.01/5.25 thf(fact_4132_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.01/5.25 ! [A: $o,B: $o,X2: nat] :
% 5.01/5.25 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.01/5.25 = ( ( ( X2 = zero_zero_nat )
% 5.01/5.25 => A )
% 5.01/5.25 & ( ( X2 != zero_zero_nat )
% 5.01/5.25 => ( ( ( X2 = one_one_nat )
% 5.01/5.25 => B )
% 5.01/5.25 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % VEBT_internal.naive_member.simps(1)
% 5.01/5.25 thf(fact_4133_signed__take__bit__int__less__exp,axiom,
% 5.01/5.25 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_int_less_exp
% 5.01/5.25 thf(fact_4134_signed__take__bit__int__less__self__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.01/5.25 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_int_less_self_iff
% 5.01/5.25 thf(fact_4135_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.01/5.25 ! [K: int,N: nat] :
% 5.01/5.25 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.01/5.25 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.25
% 5.01/5.25 % signed_take_bit_int_greater_eq_self_iff
% 5.01/5.25 thf(fact_4136_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.01/5.25 ! [N: nat,K: int] :
% 5.01/5.25 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.01/5.26 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_less_eq_self_iff
% 5.01/5.26 thf(fact_4137_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.01/5.26 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_greater_eq_minus_exp
% 5.01/5.26 thf(fact_4138_signed__take__bit__int__greater__self__iff,axiom,
% 5.01/5.26 ! [K: int,N: nat] :
% 5.01/5.26 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.01/5.26 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_greater_self_iff
% 5.01/5.26 thf(fact_4139_pinf_I6_J,axiom,
% 5.01/5.26 ! [T: real] :
% 5.01/5.26 ? [Z3: real] :
% 5.01/5.26 ! [X: real] :
% 5.01/5.26 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.26 => ~ ( ord_less_eq_real @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(6)
% 5.01/5.26 thf(fact_4140_pinf_I6_J,axiom,
% 5.01/5.26 ! [T: rat] :
% 5.01/5.26 ? [Z3: rat] :
% 5.01/5.26 ! [X: rat] :
% 5.01/5.26 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.26 => ~ ( ord_less_eq_rat @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(6)
% 5.01/5.26 thf(fact_4141_pinf_I6_J,axiom,
% 5.01/5.26 ! [T: num] :
% 5.01/5.26 ? [Z3: num] :
% 5.01/5.26 ! [X: num] :
% 5.01/5.26 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.26 => ~ ( ord_less_eq_num @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(6)
% 5.01/5.26 thf(fact_4142_pinf_I6_J,axiom,
% 5.01/5.26 ! [T: nat] :
% 5.01/5.26 ? [Z3: nat] :
% 5.01/5.26 ! [X: nat] :
% 5.01/5.26 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.26 => ~ ( ord_less_eq_nat @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(6)
% 5.01/5.26 thf(fact_4143_pinf_I6_J,axiom,
% 5.01/5.26 ! [T: int] :
% 5.01/5.26 ? [Z3: int] :
% 5.01/5.26 ! [X: int] :
% 5.01/5.26 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.26 => ~ ( ord_less_eq_int @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(6)
% 5.01/5.26 thf(fact_4144_pinf_I8_J,axiom,
% 5.01/5.26 ! [T: real] :
% 5.01/5.26 ? [Z3: real] :
% 5.01/5.26 ! [X: real] :
% 5.01/5.26 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.26 => ( ord_less_eq_real @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(8)
% 5.01/5.26 thf(fact_4145_pinf_I8_J,axiom,
% 5.01/5.26 ! [T: rat] :
% 5.01/5.26 ? [Z3: rat] :
% 5.01/5.26 ! [X: rat] :
% 5.01/5.26 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.26 => ( ord_less_eq_rat @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(8)
% 5.01/5.26 thf(fact_4146_pinf_I8_J,axiom,
% 5.01/5.26 ! [T: num] :
% 5.01/5.26 ? [Z3: num] :
% 5.01/5.26 ! [X: num] :
% 5.01/5.26 ( ( ord_less_num @ Z3 @ X )
% 5.01/5.26 => ( ord_less_eq_num @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(8)
% 5.01/5.26 thf(fact_4147_pinf_I8_J,axiom,
% 5.01/5.26 ! [T: nat] :
% 5.01/5.26 ? [Z3: nat] :
% 5.01/5.26 ! [X: nat] :
% 5.01/5.26 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.26 => ( ord_less_eq_nat @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(8)
% 5.01/5.26 thf(fact_4148_pinf_I8_J,axiom,
% 5.01/5.26 ! [T: int] :
% 5.01/5.26 ? [Z3: int] :
% 5.01/5.26 ! [X: int] :
% 5.01/5.26 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.26 => ( ord_less_eq_int @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % pinf(8)
% 5.01/5.26 thf(fact_4149_minf_I6_J,axiom,
% 5.01/5.26 ! [T: real] :
% 5.01/5.26 ? [Z3: real] :
% 5.01/5.26 ! [X: real] :
% 5.01/5.26 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.26 => ( ord_less_eq_real @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(6)
% 5.01/5.26 thf(fact_4150_minf_I6_J,axiom,
% 5.01/5.26 ! [T: rat] :
% 5.01/5.26 ? [Z3: rat] :
% 5.01/5.26 ! [X: rat] :
% 5.01/5.26 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.26 => ( ord_less_eq_rat @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(6)
% 5.01/5.26 thf(fact_4151_minf_I6_J,axiom,
% 5.01/5.26 ! [T: num] :
% 5.01/5.26 ? [Z3: num] :
% 5.01/5.26 ! [X: num] :
% 5.01/5.26 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.26 => ( ord_less_eq_num @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(6)
% 5.01/5.26 thf(fact_4152_minf_I6_J,axiom,
% 5.01/5.26 ! [T: nat] :
% 5.01/5.26 ? [Z3: nat] :
% 5.01/5.26 ! [X: nat] :
% 5.01/5.26 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.26 => ( ord_less_eq_nat @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(6)
% 5.01/5.26 thf(fact_4153_minf_I6_J,axiom,
% 5.01/5.26 ! [T: int] :
% 5.01/5.26 ? [Z3: int] :
% 5.01/5.26 ! [X: int] :
% 5.01/5.26 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.26 => ( ord_less_eq_int @ X @ T ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(6)
% 5.01/5.26 thf(fact_4154_minf_I8_J,axiom,
% 5.01/5.26 ! [T: real] :
% 5.01/5.26 ? [Z3: real] :
% 5.01/5.26 ! [X: real] :
% 5.01/5.26 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.26 => ~ ( ord_less_eq_real @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(8)
% 5.01/5.26 thf(fact_4155_minf_I8_J,axiom,
% 5.01/5.26 ! [T: rat] :
% 5.01/5.26 ? [Z3: rat] :
% 5.01/5.26 ! [X: rat] :
% 5.01/5.26 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.26 => ~ ( ord_less_eq_rat @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(8)
% 5.01/5.26 thf(fact_4156_minf_I8_J,axiom,
% 5.01/5.26 ! [T: num] :
% 5.01/5.26 ? [Z3: num] :
% 5.01/5.26 ! [X: num] :
% 5.01/5.26 ( ( ord_less_num @ X @ Z3 )
% 5.01/5.26 => ~ ( ord_less_eq_num @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(8)
% 5.01/5.26 thf(fact_4157_minf_I8_J,axiom,
% 5.01/5.26 ! [T: nat] :
% 5.01/5.26 ? [Z3: nat] :
% 5.01/5.26 ! [X: nat] :
% 5.01/5.26 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.26 => ~ ( ord_less_eq_nat @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(8)
% 5.01/5.26 thf(fact_4158_minf_I8_J,axiom,
% 5.01/5.26 ! [T: int] :
% 5.01/5.26 ? [Z3: int] :
% 5.01/5.26 ! [X: int] :
% 5.01/5.26 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.26 => ~ ( ord_less_eq_int @ T @ X ) ) ).
% 5.01/5.26
% 5.01/5.26 % minf(8)
% 5.01/5.26 thf(fact_4159_inf__period_I1_J,axiom,
% 5.01/5.26 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.01/5.26 ( ! [X4: real,K3: real] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: real,K3: real] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: real,K4: real] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 & ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) )
% 5.01/5.26 & ( Q @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(1)
% 5.01/5.26 thf(fact_4160_inf__period_I1_J,axiom,
% 5.01/5.26 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.01/5.26 ( ! [X4: rat,K3: rat] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: rat,K3: rat] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: rat,K4: rat] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 & ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.01/5.26 & ( Q @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(1)
% 5.01/5.26 thf(fact_4161_inf__period_I1_J,axiom,
% 5.01/5.26 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.01/5.26 ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: int,K4: int] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 & ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) )
% 5.01/5.26 & ( Q @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(1)
% 5.01/5.26 thf(fact_4162_inf__period_I1_J,axiom,
% 5.01/5.26 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.01/5.26 ( ! [X4: complex,K3: complex] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: complex,K3: complex] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: complex,K4: complex] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 & ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.01/5.26 & ( Q @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(1)
% 5.01/5.26 thf(fact_4163_inf__period_I2_J,axiom,
% 5.01/5.26 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.01/5.26 ( ! [X4: real,K3: real] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: real,K3: real] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: real,K4: real] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 | ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) )
% 5.01/5.26 | ( Q @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(2)
% 5.01/5.26 thf(fact_4164_inf__period_I2_J,axiom,
% 5.01/5.26 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.01/5.26 ( ! [X4: rat,K3: rat] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: rat,K3: rat] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: rat,K4: rat] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 | ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.01/5.26 | ( Q @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(2)
% 5.01/5.26 thf(fact_4165_inf__period_I2_J,axiom,
% 5.01/5.26 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.01/5.26 ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: int,K4: int] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 | ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) )
% 5.01/5.26 | ( Q @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(2)
% 5.01/5.26 thf(fact_4166_inf__period_I2_J,axiom,
% 5.01/5.26 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 5.01/5.26 ( ! [X4: complex,K3: complex] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 = ( P @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ( ! [X4: complex,K3: complex] :
% 5.01/5.26 ( ( Q @ X4 )
% 5.01/5.26 = ( Q @ ( minus_minus_complex @ X4 @ ( times_times_complex @ K3 @ D4 ) ) ) )
% 5.01/5.26 => ! [X: complex,K4: complex] :
% 5.01/5.26 ( ( ( P @ X )
% 5.01/5.26 | ( Q @ X ) )
% 5.01/5.26 = ( ( P @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) )
% 5.01/5.26 | ( Q @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % inf_period(2)
% 5.01/5.26 thf(fact_4167_signed__take__bit__int__less__eq,axiom,
% 5.01/5.26 ! [N: nat,K: int] :
% 5.01/5.26 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.01/5.26 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_less_eq
% 5.01/5.26 thf(fact_4168_signed__take__bit__int__eq__self,axiom,
% 5.01/5.26 ! [N: nat,K: int] :
% 5.01/5.26 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.01/5.26 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.26 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.01/5.26 = K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_eq_self
% 5.01/5.26 thf(fact_4169_signed__take__bit__int__eq__self__iff,axiom,
% 5.01/5.26 ! [N: nat,K: int] :
% 5.01/5.26 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.01/5.26 = K )
% 5.01/5.26 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.01/5.26 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_eq_self_iff
% 5.01/5.26 thf(fact_4170_minusinfinity,axiom,
% 5.01/5.26 ! [D: int,P1: int > $o,P: int > $o] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.26 => ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( P1 @ X4 )
% 5.01/5.26 = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.01/5.26 => ( ? [Z2: int] :
% 5.01/5.26 ! [X4: int] :
% 5.01/5.26 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.26 => ( ( P @ X4 )
% 5.01/5.26 = ( P1 @ X4 ) ) )
% 5.01/5.26 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.01/5.26 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % minusinfinity
% 5.01/5.26 thf(fact_4171_plusinfinity,axiom,
% 5.01/5.26 ! [D: int,P6: int > $o,P: int > $o] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.26 => ( ! [X4: int,K3: int] :
% 5.01/5.26 ( ( P6 @ X4 )
% 5.01/5.26 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.01/5.26 => ( ? [Z2: int] :
% 5.01/5.26 ! [X4: int] :
% 5.01/5.26 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.26 => ( ( P @ X4 )
% 5.01/5.26 = ( P6 @ X4 ) ) )
% 5.01/5.26 => ( ? [X_1: int] : ( P6 @ X_1 )
% 5.01/5.26 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % plusinfinity
% 5.01/5.26 thf(fact_4172_signed__take__bit__int__greater__eq,axiom,
% 5.01/5.26 ! [K: int,N: nat] :
% 5.01/5.26 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.26 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_int_greater_eq
% 5.01/5.26 thf(fact_4173_signed__take__bit__Suc,axiom,
% 5.01/5.26 ! [N: nat,A: code_integer] :
% 5.01/5.26 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.01/5.26 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_Suc
% 5.01/5.26 thf(fact_4174_signed__take__bit__Suc,axiom,
% 5.01/5.26 ! [N: nat,A: int] :
% 5.01/5.26 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.01/5.26 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_Suc
% 5.01/5.26 thf(fact_4175_Bolzano,axiom,
% 5.01/5.26 ! [A: real,B: real,P: real > real > $o] :
% 5.01/5.26 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.26 => ( ! [A3: real,B2: real,C3: real] :
% 5.01/5.26 ( ( P @ A3 @ B2 )
% 5.01/5.26 => ( ( P @ B2 @ C3 )
% 5.01/5.26 => ( ( ord_less_eq_real @ A3 @ B2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ B2 @ C3 )
% 5.01/5.26 => ( P @ A3 @ C3 ) ) ) ) )
% 5.01/5.26 => ( ! [X4: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.26 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.26 => ? [D5: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.01/5.26 & ! [A3: real,B2: real] :
% 5.01/5.26 ( ( ( ord_less_eq_real @ A3 @ X4 )
% 5.01/5.26 & ( ord_less_eq_real @ X4 @ B2 )
% 5.01/5.26 & ( ord_less_real @ ( minus_minus_real @ B2 @ A3 ) @ D5 ) )
% 5.01/5.26 => ( P @ A3 @ B2 ) ) ) ) )
% 5.01/5.26 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Bolzano
% 5.01/5.26 thf(fact_4176_incr__mult__lemma,axiom,
% 5.01/5.26 ! [D: int,P: int > $o,K: int] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.26 => ( ! [X4: int] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 5.01/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.26 => ! [X: int] :
% 5.01/5.26 ( ( P @ X )
% 5.01/5.26 => ( P @ ( plus_plus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % incr_mult_lemma
% 5.01/5.26 thf(fact_4177_decr__mult__lemma,axiom,
% 5.01/5.26 ! [D: int,P: int > $o,K: int] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.26 => ( ! [X4: int] :
% 5.01/5.26 ( ( P @ X4 )
% 5.01/5.26 => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 5.01/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.26 => ! [X: int] :
% 5.01/5.26 ( ( P @ X )
% 5.01/5.26 => ( P @ ( minus_minus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % decr_mult_lemma
% 5.01/5.26 thf(fact_4178_both__member__options__def,axiom,
% 5.01/5.26 ( vEBT_V8194947554948674370ptions
% 5.01/5.26 = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 5.01/5.26 ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 5.01/5.26 | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % both_member_options_def
% 5.01/5.26 thf(fact_4179_divmod__algorithm__code_I8_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(8)
% 5.01/5.26 thf(fact_4180_divmod__algorithm__code_I8_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(8)
% 5.01/5.26 thf(fact_4181_divmod__algorithm__code_I8_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_num @ M @ N )
% 5.01/5.26 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(8)
% 5.01/5.26 thf(fact_4182_divmod__algorithm__code_I7_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(7)
% 5.01/5.26 thf(fact_4183_divmod__algorithm__code_I7_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(7)
% 5.01/5.26 thf(fact_4184_divmod__algorithm__code_I7_J,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.01/5.26 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.01/5.26 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.01/5.26 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(7)
% 5.01/5.26 thf(fact_4185_mult__le__cancel__iff2,axiom,
% 5.01/5.26 ! [Z: real,X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y ) )
% 5.01/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff2
% 5.01/5.26 thf(fact_4186_mult__le__cancel__iff2,axiom,
% 5.01/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.01/5.26 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y ) )
% 5.01/5.26 = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff2
% 5.01/5.26 thf(fact_4187_mult__le__cancel__iff2,axiom,
% 5.01/5.26 ! [Z: int,X2: int,Y: int] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.26 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y ) )
% 5.01/5.26 = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff2
% 5.01/5.26 thf(fact_4188_mult__le__cancel__iff1,axiom,
% 5.01/5.26 ! [Z: real,X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff1
% 5.01/5.26 thf(fact_4189_mult__le__cancel__iff1,axiom,
% 5.01/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.01/5.26 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff1
% 5.01/5.26 thf(fact_4190_mult__le__cancel__iff1,axiom,
% 5.01/5.26 ! [Z: int,X2: int,Y: int] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.26 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_le_cancel_iff1
% 5.01/5.26 thf(fact_4191_divides__aux__eq,axiom,
% 5.01/5.26 ! [Q2: nat,R: nat] :
% 5.01/5.26 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.01/5.26 = ( R = zero_zero_nat ) ) ).
% 5.01/5.26
% 5.01/5.26 % divides_aux_eq
% 5.01/5.26 thf(fact_4192_divides__aux__eq,axiom,
% 5.01/5.26 ! [Q2: int,R: int] :
% 5.01/5.26 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 = ( R = zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % divides_aux_eq
% 5.01/5.26 thf(fact_4193_signed__take__bit__numeral__minus__bit1,axiom,
% 5.01/5.26 ! [L: num,K: num] :
% 5.01/5.26 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.26 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_numeral_minus_bit1
% 5.01/5.26 thf(fact_4194_buildup__nothing__in__min__max,axiom,
% 5.01/5.26 ! [N: nat,X2: nat] :
% 5.01/5.26 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.01/5.26
% 5.01/5.26 % buildup_nothing_in_min_max
% 5.01/5.26 thf(fact_4195_pred__numeral__simps_I1_J,axiom,
% 5.01/5.26 ( ( pred_numeral @ one )
% 5.01/5.26 = zero_zero_nat ) ).
% 5.01/5.26
% 5.01/5.26 % pred_numeral_simps(1)
% 5.01/5.26 thf(fact_4196_eq__numeral__Suc,axiom,
% 5.01/5.26 ! [K: num,N: nat] :
% 5.01/5.26 ( ( ( numeral_numeral_nat @ K )
% 5.01/5.26 = ( suc @ N ) )
% 5.01/5.26 = ( ( pred_numeral @ K )
% 5.01/5.26 = N ) ) ).
% 5.01/5.26
% 5.01/5.26 % eq_numeral_Suc
% 5.01/5.26 thf(fact_4197_Suc__eq__numeral,axiom,
% 5.01/5.26 ! [N: nat,K: num] :
% 5.01/5.26 ( ( ( suc @ N )
% 5.01/5.26 = ( numeral_numeral_nat @ K ) )
% 5.01/5.26 = ( N
% 5.01/5.26 = ( pred_numeral @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Suc_eq_numeral
% 5.01/5.26 thf(fact_4198_pred__numeral__simps_I3_J,axiom,
% 5.01/5.26 ! [K: num] :
% 5.01/5.26 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.01/5.26 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pred_numeral_simps(3)
% 5.01/5.26 thf(fact_4199_less__Suc__numeral,axiom,
% 5.01/5.26 ! [N: nat,K: num] :
% 5.01/5.26 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.26 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % less_Suc_numeral
% 5.01/5.26 thf(fact_4200_less__numeral__Suc,axiom,
% 5.01/5.26 ! [K: num,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.01/5.26 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % less_numeral_Suc
% 5.01/5.26 thf(fact_4201_le__numeral__Suc,axiom,
% 5.01/5.26 ! [K: num,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.01/5.26 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % le_numeral_Suc
% 5.01/5.26 thf(fact_4202_le__Suc__numeral,axiom,
% 5.01/5.26 ! [N: nat,K: num] :
% 5.01/5.26 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.26 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % le_Suc_numeral
% 5.01/5.26 thf(fact_4203_diff__numeral__Suc,axiom,
% 5.01/5.26 ! [K: num,N: nat] :
% 5.01/5.26 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.01/5.26 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % diff_numeral_Suc
% 5.01/5.26 thf(fact_4204_diff__Suc__numeral,axiom,
% 5.01/5.26 ! [N: nat,K: num] :
% 5.01/5.26 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.26 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % diff_Suc_numeral
% 5.01/5.26 thf(fact_4205_divmod__algorithm__code_I2_J,axiom,
% 5.01/5.26 ! [M: num] :
% 5.01/5.26 ( ( unique5052692396658037445od_int @ M @ one )
% 5.01/5.26 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(2)
% 5.01/5.26 thf(fact_4206_divmod__algorithm__code_I2_J,axiom,
% 5.01/5.26 ! [M: num] :
% 5.01/5.26 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.01/5.26 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(2)
% 5.01/5.26 thf(fact_4207_divmod__algorithm__code_I2_J,axiom,
% 5.01/5.26 ! [M: num] :
% 5.01/5.26 ( ( unique3479559517661332726nteger @ M @ one )
% 5.01/5.26 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(2)
% 5.01/5.26 thf(fact_4208_divmod__algorithm__code_I3_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.01/5.26 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(3)
% 5.01/5.26 thf(fact_4209_divmod__algorithm__code_I3_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.01/5.26 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(3)
% 5.01/5.26 thf(fact_4210_divmod__algorithm__code_I3_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.01/5.26 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(3)
% 5.01/5.26 thf(fact_4211_divmod__algorithm__code_I4_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(4)
% 5.01/5.26 thf(fact_4212_divmod__algorithm__code_I4_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.01/5.26 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(4)
% 5.01/5.26 thf(fact_4213_divmod__algorithm__code_I4_J,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.01/5.26 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_algorithm_code(4)
% 5.01/5.26 thf(fact_4214_signed__take__bit__numeral__bit0,axiom,
% 5.01/5.26 ! [L: num,K: num] :
% 5.01/5.26 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.01/5.26 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_numeral_bit0
% 5.01/5.26 thf(fact_4215_signed__take__bit__numeral__minus__bit0,axiom,
% 5.01/5.26 ! [L: num,K: num] :
% 5.01/5.26 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.26 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_numeral_minus_bit0
% 5.01/5.26 thf(fact_4216_signed__take__bit__numeral__bit1,axiom,
% 5.01/5.26 ! [L: num,K: num] :
% 5.01/5.26 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.01/5.26 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % signed_take_bit_numeral_bit1
% 5.01/5.26 thf(fact_4217_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.01/5.26 ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.01/5.26 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) ).
% 5.01/5.26
% 5.01/5.26 % VEBT_internal.membermima.simps(1)
% 5.01/5.26 thf(fact_4218_numeral__eq__Suc,axiom,
% 5.01/5.26 ( numeral_numeral_nat
% 5.01/5.26 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % numeral_eq_Suc
% 5.01/5.26 thf(fact_4219_pred__numeral__def,axiom,
% 5.01/5.26 ( pred_numeral
% 5.01/5.26 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pred_numeral_def
% 5.01/5.26 thf(fact_4220_divmod__int__def,axiom,
% 5.01/5.26 ( unique5052692396658037445od_int
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_int_def
% 5.01/5.26 thf(fact_4221_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.01/5.26 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.01/5.26 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) ).
% 5.01/5.26
% 5.01/5.26 % VEBT_internal.membermima.simps(2)
% 5.01/5.26 thf(fact_4222_divmod__def,axiom,
% 5.01/5.26 ( unique5052692396658037445od_int
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_def
% 5.01/5.26 thf(fact_4223_divmod__def,axiom,
% 5.01/5.26 ( unique5055182867167087721od_nat
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_def
% 5.01/5.26 thf(fact_4224_divmod__def,axiom,
% 5.01/5.26 ( unique3479559517661332726nteger
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_def
% 5.01/5.26 thf(fact_4225_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.01/5.26 ! [Mi: nat,Ma: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X2: nat] :
% 5.01/5.26 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X2 )
% 5.01/5.26 = ( ( X2 = Mi )
% 5.01/5.26 | ( X2 = Ma ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % VEBT_internal.membermima.simps(3)
% 5.01/5.26 thf(fact_4226_divmod_H__nat__def,axiom,
% 5.01/5.26 ( unique5055182867167087721od_nat
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod'_nat_def
% 5.01/5.26 thf(fact_4227_divmod__divmod__step,axiom,
% 5.01/5.26 ( unique5055182867167087721od_nat
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N4 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N4 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_divmod_step
% 5.01/5.26 thf(fact_4228_divmod__divmod__step,axiom,
% 5.01/5.26 ( unique5052692396658037445od_int
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N4 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N4 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_divmod_step
% 5.01/5.26 thf(fact_4229_divmod__divmod__step,axiom,
% 5.01/5.26 ( unique3479559517661332726nteger
% 5.01/5.26 = ( ^ [M3: num,N4: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N4 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N4 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N4 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_divmod_step
% 5.01/5.26 thf(fact_4230_mult__less__iff1,axiom,
% 5.01/5.26 ! [Z: real,X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.01/5.26 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_real @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_less_iff1
% 5.01/5.26 thf(fact_4231_mult__less__iff1,axiom,
% 5.01/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.01/5.26 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_rat @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_less_iff1
% 5.01/5.26 thf(fact_4232_mult__less__iff1,axiom,
% 5.01/5.26 ! [Z: int,X2: int,Y: int] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.26 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.01/5.26 = ( ord_less_int @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % mult_less_iff1
% 5.01/5.26 thf(fact_4233_one__div__minus__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.26 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % one_div_minus_numeral
% 5.01/5.26 thf(fact_4234_minus__one__div__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.26 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % minus_one_div_numeral
% 5.01/5.26 thf(fact_4235_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4236_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4237_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4238_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4239_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4240_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_o,Ys: list_o] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4241_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_o,Ys: list_nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4242_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_o,Ys: list_int] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4243_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4244_product__nth,axiom,
% 5.01/5.26 ! [N: nat,Xs: list_nat,Ys: list_o] :
% 5.01/5.26 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.01/5.26 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys ) @ N )
% 5.01/5.26 = ( product_Pair_nat_o @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % product_nth
% 5.01/5.26 thf(fact_4245_neg__eucl__rel__int__mult__2,axiom,
% 5.01/5.26 ! [B: int,A: int,Q2: int,R: int] :
% 5.01/5.26 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.01/5.26 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % neg_eucl_rel_int_mult_2
% 5.01/5.26 thf(fact_4246_lemma__termdiff3,axiom,
% 5.01/5.26 ! [H: real,Z: real,K5: real,N: nat] :
% 5.01/5.26 ( ( H != zero_zero_real )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K5 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % lemma_termdiff3
% 5.01/5.26 thf(fact_4247_lemma__termdiff3,axiom,
% 5.01/5.26 ! [H: complex,Z: complex,K5: real,N: nat] :
% 5.01/5.26 ( ( H != zero_zero_complex )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K5 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % lemma_termdiff3
% 5.01/5.26 thf(fact_4248_triangle__def,axiom,
% 5.01/5.26 ( nat_triangle
% 5.01/5.26 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % triangle_def
% 5.01/5.26 thf(fact_4249_old_Oprod_Oinject,axiom,
% 5.01/5.26 ! [A: int,B: int,A5: int,B5: int] :
% 5.01/5.26 ( ( ( product_Pair_int_int @ A @ B )
% 5.01/5.26 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.01/5.26 = ( ( A = A5 )
% 5.01/5.26 & ( B = B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.inject
% 5.01/5.26 thf(fact_4250_old_Oprod_Oinject,axiom,
% 5.01/5.26 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.01/5.26 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.01/5.26 = ( ( A = A5 )
% 5.01/5.26 & ( B = B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.inject
% 5.01/5.26 thf(fact_4251_old_Oprod_Oinject,axiom,
% 5.01/5.26 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.01/5.26 = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.01/5.26 = ( ( A = A5 )
% 5.01/5.26 & ( B = B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.inject
% 5.01/5.26 thf(fact_4252_old_Oprod_Oinject,axiom,
% 5.01/5.26 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.01/5.26 = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.01/5.26 = ( ( A = A5 )
% 5.01/5.26 & ( B = B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.inject
% 5.01/5.26 thf(fact_4253_old_Oprod_Oinject,axiom,
% 5.01/5.26 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.01/5.26 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.01/5.26 = ( ( A = A5 )
% 5.01/5.26 & ( B = B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.inject
% 5.01/5.26 thf(fact_4254_prod_Oinject,axiom,
% 5.01/5.26 ! [X1: int,X23: int,Y1: int,Y22: int] :
% 5.01/5.26 ( ( ( product_Pair_int_int @ X1 @ X23 )
% 5.01/5.26 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.01/5.26 = ( ( X1 = Y1 )
% 5.01/5.26 & ( X23 = Y22 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod.inject
% 5.01/5.26 thf(fact_4255_prod_Oinject,axiom,
% 5.01/5.26 ! [X1: code_integer > option6357759511663192854e_term,X23: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc6137756002093451184nteger @ X1 @ X23 )
% 5.01/5.26 = ( produc6137756002093451184nteger @ Y1 @ Y22 ) )
% 5.01/5.26 = ( ( X1 = Y1 )
% 5.01/5.26 & ( X23 = Y22 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod.inject
% 5.01/5.26 thf(fact_4256_prod_Oinject,axiom,
% 5.01/5.26 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X23: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc8603105652947943368nteger @ X1 @ X23 )
% 5.01/5.26 = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 5.01/5.26 = ( ( X1 = Y1 )
% 5.01/5.26 & ( X23 = Y22 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod.inject
% 5.01/5.26 thf(fact_4257_prod_Oinject,axiom,
% 5.01/5.26 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X23: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc5700946648718959541nt_int @ X1 @ X23 )
% 5.01/5.26 = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 5.01/5.26 = ( ( X1 = Y1 )
% 5.01/5.26 & ( X23 = Y22 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod.inject
% 5.01/5.26 thf(fact_4258_prod_Oinject,axiom,
% 5.01/5.26 ! [X1: int > option6357759511663192854e_term,X23: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc4305682042979456191nt_int @ X1 @ X23 )
% 5.01/5.26 = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 5.01/5.26 = ( ( X1 = Y1 )
% 5.01/5.26 & ( X23 = Y22 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod.inject
% 5.01/5.26 thf(fact_4259_triangle__0,axiom,
% 5.01/5.26 ( ( nat_triangle @ zero_zero_nat )
% 5.01/5.26 = zero_zero_nat ) ).
% 5.01/5.26
% 5.01/5.26 % triangle_0
% 5.01/5.26 thf(fact_4260_length__product,axiom,
% 5.01/5.26 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4261_length__product,axiom,
% 5.01/5.26 ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.01/5.26 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4262_length__product,axiom,
% 5.01/5.26 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.01/5.26 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4263_length__product,axiom,
% 5.01/5.26 ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.01/5.26 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4264_length__product,axiom,
% 5.01/5.26 ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4265_length__product,axiom,
% 5.01/5.26 ! [Xs: list_o,Ys: list_o] :
% 5.01/5.26 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4266_length__product,axiom,
% 5.01/5.26 ! [Xs: list_o,Ys: list_nat] :
% 5.01/5.26 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4267_length__product,axiom,
% 5.01/5.26 ! [Xs: list_o,Ys: list_int] :
% 5.01/5.26 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4268_length__product,axiom,
% 5.01/5.26 ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 5.01/5.26 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4269_length__product,axiom,
% 5.01/5.26 ! [Xs: list_nat,Ys: list_o] :
% 5.01/5.26 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 5.01/5.26 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % length_product
% 5.01/5.26 thf(fact_4270_triangle__Suc,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( nat_triangle @ ( suc @ N ) )
% 5.01/5.26 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % triangle_Suc
% 5.01/5.26 thf(fact_4271_numeral__div__minus__numeral,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.26 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % numeral_div_minus_numeral
% 5.01/5.26 thf(fact_4272_minus__numeral__div__numeral,axiom,
% 5.01/5.26 ! [M: num,N: num] :
% 5.01/5.26 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.26 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % minus_numeral_div_numeral
% 5.01/5.26 thf(fact_4273_unique__remainder,axiom,
% 5.01/5.26 ! [A: int,B: int,Q2: int,R: int,Q5: int,R3: int] :
% 5.01/5.26 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R3 ) )
% 5.01/5.26 => ( R = R3 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % unique_remainder
% 5.01/5.26 thf(fact_4274_unique__quotient,axiom,
% 5.01/5.26 ! [A: int,B: int,Q2: int,R: int,Q5: int,R3: int] :
% 5.01/5.26 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R3 ) )
% 5.01/5.26 => ( Q2 = Q5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % unique_quotient
% 5.01/5.26 thf(fact_4275_eucl__rel__int__by0,axiom,
% 5.01/5.26 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % eucl_rel_int_by0
% 5.01/5.26 thf(fact_4276_div__int__unique,axiom,
% 5.01/5.26 ! [K: int,L: int,Q2: int,R: int] :
% 5.01/5.26 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( ( divide_divide_int @ K @ L )
% 5.01/5.26 = Q2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % div_int_unique
% 5.01/5.26 thf(fact_4277_mod__int__unique,axiom,
% 5.01/5.26 ! [K: int,L: int,Q2: int,R: int] :
% 5.01/5.26 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( ( modulo_modulo_int @ K @ L )
% 5.01/5.26 = R ) ) ).
% 5.01/5.26
% 5.01/5.26 % mod_int_unique
% 5.01/5.26 thf(fact_4278_eucl__rel__int__dividesI,axiom,
% 5.01/5.26 ! [L: int,K: int,Q2: int] :
% 5.01/5.26 ( ( L != zero_zero_int )
% 5.01/5.26 => ( ( K
% 5.01/5.26 = ( times_times_int @ Q2 @ L ) )
% 5.01/5.26 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % eucl_rel_int_dividesI
% 5.01/5.26 thf(fact_4279_Pair__inject,axiom,
% 5.01/5.26 ! [A: int,B: int,A5: int,B5: int] :
% 5.01/5.26 ( ( ( product_Pair_int_int @ A @ B )
% 5.01/5.26 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.01/5.26 => ~ ( ( A = A5 )
% 5.01/5.26 => ( B != B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Pair_inject
% 5.01/5.26 thf(fact_4280_Pair__inject,axiom,
% 5.01/5.26 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.01/5.26 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.01/5.26 => ~ ( ( A = A5 )
% 5.01/5.26 => ( B != B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Pair_inject
% 5.01/5.26 thf(fact_4281_Pair__inject,axiom,
% 5.01/5.26 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.01/5.26 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.01/5.26 = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.01/5.26 => ~ ( ( A = A5 )
% 5.01/5.26 => ( B != B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Pair_inject
% 5.01/5.26 thf(fact_4282_Pair__inject,axiom,
% 5.01/5.26 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.01/5.26 = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.01/5.26 => ~ ( ( A = A5 )
% 5.01/5.26 => ( B != B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Pair_inject
% 5.01/5.26 thf(fact_4283_Pair__inject,axiom,
% 5.01/5.26 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.01/5.26 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.01/5.26 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.01/5.26 => ~ ( ( A = A5 )
% 5.01/5.26 => ( B != B5 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Pair_inject
% 5.01/5.26 thf(fact_4284_prod__cases,axiom,
% 5.01/5.26 ! [P: product_prod_int_int > $o,P4: product_prod_int_int] :
% 5.01/5.26 ( ! [A3: int,B2: int] : ( P @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.01/5.26 => ( P @ P4 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases
% 5.01/5.26 thf(fact_4285_prod__cases,axiom,
% 5.01/5.26 ! [P: produc8763457246119570046nteger > $o,P4: produc8763457246119570046nteger] :
% 5.01/5.26 ( ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A3 @ B2 ) )
% 5.01/5.26 => ( P @ P4 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases
% 5.01/5.26 thf(fact_4286_prod__cases,axiom,
% 5.01/5.26 ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 5.01/5.26 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A3 @ B2 ) )
% 5.01/5.26 => ( P @ P4 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases
% 5.01/5.26 thf(fact_4287_prod__cases,axiom,
% 5.01/5.26 ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 5.01/5.26 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ B2 ) )
% 5.01/5.26 => ( P @ P4 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases
% 5.01/5.26 thf(fact_4288_prod__cases,axiom,
% 5.01/5.26 ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 5.01/5.26 ( ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ B2 ) )
% 5.01/5.26 => ( P @ P4 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases
% 5.01/5.26 thf(fact_4289_surj__pair,axiom,
% 5.01/5.26 ! [P4: product_prod_int_int] :
% 5.01/5.26 ? [X4: int,Y3: int] :
% 5.01/5.26 ( P4
% 5.01/5.26 = ( product_Pair_int_int @ X4 @ Y3 ) ) ).
% 5.01/5.26
% 5.01/5.26 % surj_pair
% 5.01/5.26 thf(fact_4290_surj__pair,axiom,
% 5.01/5.26 ! [P4: produc8763457246119570046nteger] :
% 5.01/5.26 ? [X4: code_integer > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.01/5.26 ( P4
% 5.01/5.26 = ( produc6137756002093451184nteger @ X4 @ Y3 ) ) ).
% 5.01/5.26
% 5.01/5.26 % surj_pair
% 5.01/5.26 thf(fact_4291_surj__pair,axiom,
% 5.01/5.26 ! [P4: produc1908205239877642774nteger] :
% 5.01/5.26 ? [X4: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] :
% 5.01/5.26 ( P4
% 5.01/5.26 = ( produc8603105652947943368nteger @ X4 @ Y3 ) ) ).
% 5.01/5.26
% 5.01/5.26 % surj_pair
% 5.01/5.26 thf(fact_4292_surj__pair,axiom,
% 5.01/5.26 ! [P4: produc2285326912895808259nt_int] :
% 5.01/5.26 ? [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.01/5.26 ( P4
% 5.01/5.26 = ( produc5700946648718959541nt_int @ X4 @ Y3 ) ) ).
% 5.01/5.26
% 5.01/5.26 % surj_pair
% 5.01/5.26 thf(fact_4293_surj__pair,axiom,
% 5.01/5.26 ! [P4: produc7773217078559923341nt_int] :
% 5.01/5.26 ? [X4: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.01/5.26 ( P4
% 5.01/5.26 = ( produc4305682042979456191nt_int @ X4 @ Y3 ) ) ).
% 5.01/5.26
% 5.01/5.26 % surj_pair
% 5.01/5.26 thf(fact_4294_old_Oprod_Oexhaust,axiom,
% 5.01/5.26 ! [Y: product_prod_int_int] :
% 5.01/5.26 ~ ! [A3: int,B2: int] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( product_Pair_int_int @ A3 @ B2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.exhaust
% 5.01/5.26 thf(fact_4295_old_Oprod_Oexhaust,axiom,
% 5.01/5.26 ! [Y: produc8763457246119570046nteger] :
% 5.01/5.26 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc6137756002093451184nteger @ A3 @ B2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.exhaust
% 5.01/5.26 thf(fact_4296_old_Oprod_Oexhaust,axiom,
% 5.01/5.26 ! [Y: produc1908205239877642774nteger] :
% 5.01/5.26 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: produc8923325533196201883nteger] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc8603105652947943368nteger @ A3 @ B2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.exhaust
% 5.01/5.26 thf(fact_4297_old_Oprod_Oexhaust,axiom,
% 5.01/5.26 ! [Y: produc2285326912895808259nt_int] :
% 5.01/5.26 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc5700946648718959541nt_int @ A3 @ B2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.exhaust
% 5.01/5.26 thf(fact_4298_old_Oprod_Oexhaust,axiom,
% 5.01/5.26 ! [Y: produc7773217078559923341nt_int] :
% 5.01/5.26 ~ ! [A3: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc4305682042979456191nt_int @ A3 @ B2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % old.prod.exhaust
% 5.01/5.26 thf(fact_4299_eucl__rel__int,axiom,
% 5.01/5.26 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % eucl_rel_int
% 5.01/5.26 thf(fact_4300_zminus1__lemma,axiom,
% 5.01/5.26 ! [A: int,B: int,Q2: int,R: int] :
% 5.01/5.26 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( ( B != zero_zero_int )
% 5.01/5.26 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % zminus1_lemma
% 5.01/5.26 thf(fact_4301_prod__induct3,axiom,
% 5.01/5.26 ! [P: produc8763457246119570046nteger > $o,X2: produc8763457246119570046nteger] :
% 5.01/5.26 ( ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 5.01/5.26 => ( P @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_induct3
% 5.01/5.26 thf(fact_4302_prod__induct3,axiom,
% 5.01/5.26 ! [P: produc1908205239877642774nteger > $o,X2: produc1908205239877642774nteger] :
% 5.01/5.26 ( ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) )
% 5.01/5.26 => ( P @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_induct3
% 5.01/5.26 thf(fact_4303_prod__induct3,axiom,
% 5.01/5.26 ! [P: produc2285326912895808259nt_int > $o,X2: produc2285326912895808259nt_int] :
% 5.01/5.26 ( ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 5.01/5.26 => ( P @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_induct3
% 5.01/5.26 thf(fact_4304_prod__induct3,axiom,
% 5.01/5.26 ! [P: produc7773217078559923341nt_int > $o,X2: produc7773217078559923341nt_int] :
% 5.01/5.26 ( ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) )
% 5.01/5.26 => ( P @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_induct3
% 5.01/5.26 thf(fact_4305_prod__cases3,axiom,
% 5.01/5.26 ! [Y: produc8763457246119570046nteger] :
% 5.01/5.26 ~ ! [A3: code_integer > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc6137756002093451184nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases3
% 5.01/5.26 thf(fact_4306_prod__cases3,axiom,
% 5.01/5.26 ! [Y: produc1908205239877642774nteger] :
% 5.01/5.26 ~ ! [A3: produc6241069584506657477e_term > option6357759511663192854e_term,B2: code_integer,C3: code_integer] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc8603105652947943368nteger @ A3 @ ( produc1086072967326762835nteger @ B2 @ C3 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases3
% 5.01/5.26 thf(fact_4307_prod__cases3,axiom,
% 5.01/5.26 ! [Y: produc2285326912895808259nt_int] :
% 5.01/5.26 ~ ! [A3: produc8551481072490612790e_term > option6357759511663192854e_term,B2: int,C3: int] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc5700946648718959541nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases3
% 5.01/5.26 thf(fact_4308_prod__cases3,axiom,
% 5.01/5.26 ! [Y: produc7773217078559923341nt_int] :
% 5.01/5.26 ~ ! [A3: int > option6357759511663192854e_term,B2: int,C3: int] :
% 5.01/5.26 ( Y
% 5.01/5.26 != ( produc4305682042979456191nt_int @ A3 @ ( product_Pair_int_int @ B2 @ C3 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % prod_cases3
% 5.01/5.26 thf(fact_4309_eucl__rel__int__iff,axiom,
% 5.01/5.26 ! [K: int,L: int,Q2: int,R: int] :
% 5.01/5.26 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 = ( ( K
% 5.01/5.26 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R ) )
% 5.01/5.26 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.01/5.26 & ( ord_less_int @ R @ L ) ) )
% 5.01/5.26 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.01/5.26 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.01/5.26 => ( ( ord_less_int @ L @ R )
% 5.01/5.26 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 5.01/5.26 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.01/5.26 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % eucl_rel_int_iff
% 5.01/5.26 thf(fact_4310_pos__eucl__rel__int__mult__2,axiom,
% 5.01/5.26 ! [B: int,A: int,Q2: int,R: int] :
% 5.01/5.26 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.26 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.26 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pos_eucl_rel_int_mult_2
% 5.01/5.26 thf(fact_4311_norm__divide__numeral,axiom,
% 5.01/5.26 ! [A: real,W: num] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_divide_numeral
% 5.01/5.26 thf(fact_4312_norm__divide__numeral,axiom,
% 5.01/5.26 ! [A: complex,W: num] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_divide_numeral
% 5.01/5.26 thf(fact_4313_norm__mult__numeral2,axiom,
% 5.01/5.26 ! [A: real,W: num] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.26 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_numeral2
% 5.01/5.26 thf(fact_4314_norm__mult__numeral2,axiom,
% 5.01/5.26 ! [A: complex,W: num] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.26 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_numeral2
% 5.01/5.26 thf(fact_4315_norm__mult__numeral1,axiom,
% 5.01/5.26 ! [W: num,A: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.01/5.26 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_numeral1
% 5.01/5.26 thf(fact_4316_norm__mult__numeral1,axiom,
% 5.01/5.26 ! [W: num,A: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.01/5.26 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_numeral1
% 5.01/5.26 thf(fact_4317_norm__neg__numeral,axiom,
% 5.01/5.26 ! [W: num] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.26 = ( numeral_numeral_real @ W ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_neg_numeral
% 5.01/5.26 thf(fact_4318_norm__neg__numeral,axiom,
% 5.01/5.26 ! [W: num] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.26 = ( numeral_numeral_real @ W ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_neg_numeral
% 5.01/5.26 thf(fact_4319_norm__le__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ zero_zero_real )
% 5.01/5.26 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_le_zero_iff
% 5.01/5.26 thf(fact_4320_norm__le__zero__iff,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real )
% 5.01/5.26 = ( X2 = zero_zero_complex ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_le_zero_iff
% 5.01/5.26 thf(fact_4321_zero__less__norm__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.01/5.26 = ( X2 != zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % zero_less_norm_iff
% 5.01/5.26 thf(fact_4322_zero__less__norm__iff,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.01/5.26 = ( X2 != zero_zero_complex ) ) ).
% 5.01/5.26
% 5.01/5.26 % zero_less_norm_iff
% 5.01/5.26 thf(fact_4323_norm__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.26 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_of_nat
% 5.01/5.26 thf(fact_4324_norm__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( semiri8010041392384452111omplex @ N ) )
% 5.01/5.26 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_of_nat
% 5.01/5.26 thf(fact_4325_norm__minus__cancel,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.26 = ( real_V7735802525324610683m_real @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_minus_cancel
% 5.01/5.26 thf(fact_4326_norm__minus__cancel,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.26 = ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_minus_cancel
% 5.01/5.26 thf(fact_4327_norm__zero,axiom,
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % norm_zero
% 5.01/5.26 thf(fact_4328_norm__zero,axiom,
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % norm_zero
% 5.01/5.26 thf(fact_4329_norm__eq__zero,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ( real_V7735802525324610683m_real @ X2 )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_eq_zero
% 5.01/5.26 thf(fact_4330_norm__eq__zero,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( ( real_V1022390504157884413omplex @ X2 )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( X2 = zero_zero_complex ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_eq_zero
% 5.01/5.26 thf(fact_4331_norm__one,axiom,
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.01/5.26 = one_one_real ) ).
% 5.01/5.26
% 5.01/5.26 % norm_one
% 5.01/5.26 thf(fact_4332_norm__one,axiom,
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.01/5.26 = one_one_real ) ).
% 5.01/5.26
% 5.01/5.26 % norm_one
% 5.01/5.26 thf(fact_4333_norm__numeral,axiom,
% 5.01/5.26 ! [W: num] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.26 = ( numeral_numeral_real @ W ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_numeral
% 5.01/5.26 thf(fact_4334_norm__numeral,axiom,
% 5.01/5.26 ! [W: num] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.26 = ( numeral_numeral_real @ W ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_numeral
% 5.01/5.26 thf(fact_4335_norm__minus__commute,axiom,
% 5.01/5.26 ! [A: real,B: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 5.01/5.26 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_minus_commute
% 5.01/5.26 thf(fact_4336_norm__minus__commute,axiom,
% 5.01/5.26 ! [A: complex,B: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.01/5.26 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_minus_commute
% 5.01/5.26 thf(fact_4337_norm__not__less__zero,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % norm_not_less_zero
% 5.01/5.26 thf(fact_4338_norm__ge__zero,axiom,
% 5.01/5.26 ! [X2: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_ge_zero
% 5.01/5.26 thf(fact_4339_norm__mult,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.26 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult
% 5.01/5.26 thf(fact_4340_norm__mult,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) )
% 5.01/5.26 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult
% 5.01/5.26 thf(fact_4341_norm__divide,axiom,
% 5.01/5.26 ! [A: real,B: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_divide
% 5.01/5.26 thf(fact_4342_norm__divide,axiom,
% 5.01/5.26 ! [A: complex,B: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_divide
% 5.01/5.26 thf(fact_4343_norm__power,axiom,
% 5.01/5.26 ! [X2: real,N: nat] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) )
% 5.01/5.26 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power
% 5.01/5.26 thf(fact_4344_norm__power,axiom,
% 5.01/5.26 ! [X2: complex,N: nat] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) )
% 5.01/5.26 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power
% 5.01/5.26 thf(fact_4345_norm__uminus__minus,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ Y ) )
% 5.01/5.26 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_uminus_minus
% 5.01/5.26 thf(fact_4346_norm__uminus__minus,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex] :
% 5.01/5.26 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y ) )
% 5.01/5.26 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_uminus_minus
% 5.01/5.26 thf(fact_4347_nonzero__norm__divide,axiom,
% 5.01/5.26 ! [B: real,A: real] :
% 5.01/5.26 ( ( B != zero_zero_real )
% 5.01/5.26 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % nonzero_norm_divide
% 5.01/5.26 thf(fact_4348_nonzero__norm__divide,axiom,
% 5.01/5.26 ! [B: complex,A: complex] :
% 5.01/5.26 ( ( B != zero_zero_complex )
% 5.01/5.26 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.26 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % nonzero_norm_divide
% 5.01/5.26 thf(fact_4349_power__eq__imp__eq__norm,axiom,
% 5.01/5.26 ! [W: real,N: nat,Z: real] :
% 5.01/5.26 ( ( ( power_power_real @ W @ N )
% 5.01/5.26 = ( power_power_real @ Z @ N ) )
% 5.01/5.26 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.26 => ( ( real_V7735802525324610683m_real @ W )
% 5.01/5.26 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % power_eq_imp_eq_norm
% 5.01/5.26 thf(fact_4350_power__eq__imp__eq__norm,axiom,
% 5.01/5.26 ! [W: complex,N: nat,Z: complex] :
% 5.01/5.26 ( ( ( power_power_complex @ W @ N )
% 5.01/5.26 = ( power_power_complex @ Z @ N ) )
% 5.01/5.26 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.26 => ( ( real_V1022390504157884413omplex @ W )
% 5.01/5.26 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % power_eq_imp_eq_norm
% 5.01/5.26 thf(fact_4351_norm__mult__less,axiom,
% 5.01/5.26 ! [X2: real,R: real,Y: real,S2: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.01/5.26 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) ) @ ( times_times_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_less
% 5.01/5.26 thf(fact_4352_norm__mult__less,axiom,
% 5.01/5.26 ! [X2: complex,R: real,Y: complex,S2: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.01/5.26 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) ) @ ( times_times_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_less
% 5.01/5.26 thf(fact_4353_norm__mult__ineq,axiom,
% 5.01/5.26 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_ineq
% 5.01/5.26 thf(fact_4354_norm__mult__ineq,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_mult_ineq
% 5.01/5.26 thf(fact_4355_norm__triangle__lt,axiom,
% 5.01/5.26 ! [X2: real,Y: real,E: real] :
% 5.01/5.26 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_lt
% 5.01/5.26 thf(fact_4356_norm__triangle__lt,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex,E: real] :
% 5.01/5.26 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_lt
% 5.01/5.26 thf(fact_4357_norm__add__less,axiom,
% 5.01/5.26 ! [X2: real,R: real,Y: real,S2: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.01/5.26 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_add_less
% 5.01/5.26 thf(fact_4358_norm__add__less,axiom,
% 5.01/5.26 ! [X2: complex,R: real,Y: complex,S2: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.01/5.26 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( plus_plus_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_add_less
% 5.01/5.26 thf(fact_4359_norm__triangle__mono,axiom,
% 5.01/5.26 ! [A: real,R: real,B: real,S2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_mono
% 5.01/5.26 thf(fact_4360_norm__triangle__mono,axiom,
% 5.01/5.26 ! [A: complex,R: real,B: complex,S2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_mono
% 5.01/5.26 thf(fact_4361_norm__triangle__ineq,axiom,
% 5.01/5.26 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq
% 5.01/5.26 thf(fact_4362_norm__triangle__ineq,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq
% 5.01/5.26 thf(fact_4363_norm__triangle__le,axiom,
% 5.01/5.26 ! [X2: real,Y: real,E: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_le
% 5.01/5.26 thf(fact_4364_norm__triangle__le,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex,E: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_le
% 5.01/5.26 thf(fact_4365_norm__add__leD,axiom,
% 5.01/5.26 ! [A: real,B: real,C: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_add_leD
% 5.01/5.26 thf(fact_4366_norm__add__leD,axiom,
% 5.01/5.26 ! [A: complex,B: complex,C: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_add_leD
% 5.01/5.26 thf(fact_4367_norm__diff__triangle__less,axiom,
% 5.01/5.26 ! [X2: real,Y: real,E1: real,Z: real,E22: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E1 )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.01/5.26 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_less
% 5.01/5.26 thf(fact_4368_norm__diff__triangle__less,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.01/5.26 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E1 )
% 5.01/5.26 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.01/5.26 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_less
% 5.01/5.26 thf(fact_4369_norm__power__ineq,axiom,
% 5.01/5.26 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power_ineq
% 5.01/5.26 thf(fact_4370_norm__power__ineq,axiom,
% 5.01/5.26 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power_ineq
% 5.01/5.26 thf(fact_4371_norm__triangle__sub,axiom,
% 5.01/5.26 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_sub
% 5.01/5.26 thf(fact_4372_norm__triangle__sub,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_sub
% 5.01/5.26 thf(fact_4373_norm__triangle__ineq4,axiom,
% 5.01/5.26 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq4
% 5.01/5.26 thf(fact_4374_norm__triangle__ineq4,axiom,
% 5.01/5.26 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq4
% 5.01/5.26 thf(fact_4375_norm__diff__triangle__le,axiom,
% 5.01/5.26 ! [X2: real,Y: real,E1: real,Z: real,E22: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E1 )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_le
% 5.01/5.26 thf(fact_4376_norm__diff__triangle__le,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E1 )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_le
% 5.01/5.26 thf(fact_4377_norm__triangle__le__diff,axiom,
% 5.01/5.26 ! [X2: real,Y: real,E: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_le_diff
% 5.01/5.26 thf(fact_4378_norm__triangle__le__diff,axiom,
% 5.01/5.26 ! [X2: complex,Y: complex,E: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_le_diff
% 5.01/5.26 thf(fact_4379_norm__diff__ineq,axiom,
% 5.01/5.26 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_ineq
% 5.01/5.26 thf(fact_4380_norm__diff__ineq,axiom,
% 5.01/5.26 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_ineq
% 5.01/5.26 thf(fact_4381_norm__triangle__ineq2,axiom,
% 5.01/5.26 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq2
% 5.01/5.26 thf(fact_4382_norm__triangle__ineq2,axiom,
% 5.01/5.26 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_triangle_ineq2
% 5.01/5.26 thf(fact_4383_power__eq__1__iff,axiom,
% 5.01/5.26 ! [W: real,N: nat] :
% 5.01/5.26 ( ( ( power_power_real @ W @ N )
% 5.01/5.26 = one_one_real )
% 5.01/5.26 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.01/5.26 = one_one_real )
% 5.01/5.26 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % power_eq_1_iff
% 5.01/5.26 thf(fact_4384_power__eq__1__iff,axiom,
% 5.01/5.26 ! [W: complex,N: nat] :
% 5.01/5.26 ( ( ( power_power_complex @ W @ N )
% 5.01/5.26 = one_one_complex )
% 5.01/5.26 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.01/5.26 = one_one_real )
% 5.01/5.26 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % power_eq_1_iff
% 5.01/5.26 thf(fact_4385_norm__diff__triangle__ineq,axiom,
% 5.01/5.26 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_ineq
% 5.01/5.26 thf(fact_4386_norm__diff__triangle__ineq,axiom,
% 5.01/5.26 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_diff_triangle_ineq
% 5.01/5.26 thf(fact_4387_square__norm__one,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.26 = one_one_real )
% 5.01/5.26 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.01/5.26 = one_one_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % square_norm_one
% 5.01/5.26 thf(fact_4388_square__norm__one,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.26 = one_one_complex )
% 5.01/5.26 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.01/5.26 = one_one_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % square_norm_one
% 5.01/5.26 thf(fact_4389_norm__power__diff,axiom,
% 5.01/5.26 ! [Z: real,W: real,M: nat] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power_diff
% 5.01/5.26 thf(fact_4390_norm__power__diff,axiom,
% 5.01/5.26 ! [Z: complex,W: complex,M: nat] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.01/5.26 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % norm_power_diff
% 5.01/5.26 thf(fact_4391_arcosh__1,axiom,
% 5.01/5.26 ( ( arcosh_real @ one_one_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % arcosh_1
% 5.01/5.26 thf(fact_4392_artanh__0,axiom,
% 5.01/5.26 ( ( artanh_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % artanh_0
% 5.01/5.26 thf(fact_4393_arsinh__0,axiom,
% 5.01/5.26 ( ( arsinh_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % arsinh_0
% 5.01/5.26 thf(fact_4394_pochhammer__double,axiom,
% 5.01/5.26 ! [Z: rat,N: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.26 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_double
% 5.01/5.26 thf(fact_4395_pochhammer__double,axiom,
% 5.01/5.26 ! [Z: real,N: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.26 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_double
% 5.01/5.26 thf(fact_4396_pochhammer__double,axiom,
% 5.01/5.26 ! [Z: complex,N: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.26 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_double
% 5.01/5.26 thf(fact_4397_ln__one__minus__pos__lower__bound,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.26 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_one_minus_pos_lower_bound
% 5.01/5.26 thf(fact_4398_central__binomial__lower__bound,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.26 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % central_binomial_lower_bound
% 5.01/5.26 thf(fact_4399_arsinh__minus__real,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( arsinh_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.26 = ( uminus_uminus_real @ ( arsinh_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % arsinh_minus_real
% 5.01/5.26 thf(fact_4400_ln__one,axiom,
% 5.01/5.26 ( ( ln_ln_real @ one_one_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % ln_one
% 5.01/5.26 thf(fact_4401_ln__less__cancel__iff,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) )
% 5.01/5.26 = ( ord_less_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_less_cancel_iff
% 5.01/5.26 thf(fact_4402_ln__inj__iff,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ( ( ln_ln_real @ X2 )
% 5.01/5.26 = ( ln_ln_real @ Y ) )
% 5.01/5.26 = ( X2 = Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_inj_iff
% 5.01/5.26 thf(fact_4403_pochhammer__0,axiom,
% 5.01/5.26 ! [A: complex] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.01/5.26 = one_one_complex ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0
% 5.01/5.26 thf(fact_4404_pochhammer__0,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.01/5.26 = one_one_real ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0
% 5.01/5.26 thf(fact_4405_pochhammer__0,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.01/5.26 = one_one_rat ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0
% 5.01/5.26 thf(fact_4406_pochhammer__0,axiom,
% 5.01/5.26 ! [A: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.01/5.26 = one_one_nat ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0
% 5.01/5.26 thf(fact_4407_pochhammer__0,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.01/5.26 = one_one_int ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0
% 5.01/5.26 thf(fact_4408_ln__le__cancel__iff,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) )
% 5.01/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_le_cancel_iff
% 5.01/5.26 thf(fact_4409_ln__less__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.01/5.26 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_less_zero_iff
% 5.01/5.26 thf(fact_4410_ln__gt__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.26 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_gt_zero_iff
% 5.01/5.26 thf(fact_4411_ln__eq__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ( ln_ln_real @ X2 )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( X2 = one_one_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_eq_zero_iff
% 5.01/5.26 thf(fact_4412_ln__ge__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.26 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_ge_zero_iff
% 5.01/5.26 thf(fact_4413_ln__le__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.01/5.26 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_le_zero_iff
% 5.01/5.26 thf(fact_4414_pochhammer__of__nat,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ ( semiri5074537144036343181t_real @ X2 ) @ N )
% 5.01/5.26 = ( semiri5074537144036343181t_real @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat
% 5.01/5.26 thf(fact_4415_pochhammer__of__nat,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X2 ) @ N )
% 5.01/5.26 = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat
% 5.01/5.26 thf(fact_4416_pochhammer__of__nat,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ ( semiri8010041392384452111omplex @ X2 ) @ N )
% 5.01/5.26 = ( semiri8010041392384452111omplex @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat
% 5.01/5.26 thf(fact_4417_pochhammer__of__nat,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N )
% 5.01/5.26 = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat
% 5.01/5.26 thf(fact_4418_pochhammer__of__nat,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ ( semiri4939895301339042750nteger @ X2 ) @ N )
% 5.01/5.26 = ( semiri4939895301339042750nteger @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat
% 5.01/5.26 thf(fact_4419_ln__less__self,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_less_self
% 5.01/5.26 thf(fact_4420_pochhammer__pos,axiom,
% 5.01/5.26 ! [X2: real,N: nat] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_pos
% 5.01/5.26 thf(fact_4421_pochhammer__pos,axiom,
% 5.01/5.26 ! [X2: rat,N: nat] :
% 5.01/5.26 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.26 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_pos
% 5.01/5.26 thf(fact_4422_pochhammer__pos,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.26 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_pos
% 5.01/5.26 thf(fact_4423_pochhammer__pos,axiom,
% 5.01/5.26 ! [X2: int,N: nat] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.01/5.26 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_pos
% 5.01/5.26 thf(fact_4424_pochhammer__eq__0__mono,axiom,
% 5.01/5.26 ! [A: complex,N: nat,M: nat] :
% 5.01/5.26 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.01/5.26 = zero_zero_complex )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.01/5.26 = zero_zero_complex ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_mono
% 5.01/5.26 thf(fact_4425_pochhammer__eq__0__mono,axiom,
% 5.01/5.26 ! [A: real,N: nat,M: nat] :
% 5.01/5.26 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.01/5.26 = zero_zero_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_mono
% 5.01/5.26 thf(fact_4426_pochhammer__eq__0__mono,axiom,
% 5.01/5.26 ! [A: rat,N: nat,M: nat] :
% 5.01/5.26 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.01/5.26 = zero_zero_rat )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.01/5.26 = zero_zero_rat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_mono
% 5.01/5.26 thf(fact_4427_pochhammer__neq__0__mono,axiom,
% 5.01/5.26 ! [A: complex,M: nat,N: nat] :
% 5.01/5.26 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.01/5.26 != zero_zero_complex )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.01/5.26 != zero_zero_complex ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_neq_0_mono
% 5.01/5.26 thf(fact_4428_pochhammer__neq__0__mono,axiom,
% 5.01/5.26 ! [A: real,M: nat,N: nat] :
% 5.01/5.26 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.01/5.26 != zero_zero_real )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.01/5.26 != zero_zero_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_neq_0_mono
% 5.01/5.26 thf(fact_4429_pochhammer__neq__0__mono,axiom,
% 5.01/5.26 ! [A: rat,M: nat,N: nat] :
% 5.01/5.26 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.01/5.26 != zero_zero_rat )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.01/5.26 != zero_zero_rat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_neq_0_mono
% 5.01/5.26 thf(fact_4430_ln__bound,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_bound
% 5.01/5.26 thf(fact_4431_ln__gt__zero__imp__gt__one,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_gt_zero_imp_gt_one
% 5.01/5.26 thf(fact_4432_ln__less__zero,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.26 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_less_zero
% 5.01/5.26 thf(fact_4433_ln__gt__zero,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.26 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_gt_zero
% 5.01/5.26 thf(fact_4434_ln__ge__zero,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_ge_zero
% 5.01/5.26 thf(fact_4435_pochhammer__nonneg,axiom,
% 5.01/5.26 ! [X2: real,N: nat] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_nonneg
% 5.01/5.26 thf(fact_4436_pochhammer__nonneg,axiom,
% 5.01/5.26 ! [X2: rat,N: nat] :
% 5.01/5.26 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.26 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_nonneg
% 5.01/5.26 thf(fact_4437_pochhammer__nonneg,axiom,
% 5.01/5.26 ! [X2: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.01/5.26 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_nonneg
% 5.01/5.26 thf(fact_4438_pochhammer__nonneg,axiom,
% 5.01/5.26 ! [X2: int,N: nat] :
% 5.01/5.26 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.01/5.26 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_nonneg
% 5.01/5.26 thf(fact_4439_pochhammer__0__left,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ( N = zero_zero_nat )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.01/5.26 = one_one_complex ) )
% 5.01/5.26 & ( ( N != zero_zero_nat )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.01/5.26 = zero_zero_complex ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0_left
% 5.01/5.26 thf(fact_4440_pochhammer__0__left,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ( N = zero_zero_nat )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.01/5.26 = one_one_real ) )
% 5.01/5.26 & ( ( N != zero_zero_nat )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.01/5.26 = zero_zero_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0_left
% 5.01/5.26 thf(fact_4441_pochhammer__0__left,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ( N = zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.01/5.26 = one_one_rat ) )
% 5.01/5.26 & ( ( N != zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.01/5.26 = zero_zero_rat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0_left
% 5.01/5.26 thf(fact_4442_pochhammer__0__left,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ( N = zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.01/5.26 = one_one_nat ) )
% 5.01/5.26 & ( ( N != zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.01/5.26 = zero_zero_nat ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0_left
% 5.01/5.26 thf(fact_4443_pochhammer__0__left,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( ( N = zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.01/5.26 = one_one_int ) )
% 5.01/5.26 & ( ( N != zero_zero_nat )
% 5.01/5.26 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.01/5.26 = zero_zero_int ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_0_left
% 5.01/5.26 thf(fact_4444_ln__ge__zero__imp__ge__one,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_ge_zero_imp_ge_one
% 5.01/5.26 thf(fact_4445_ln__add__one__self__le__self,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_add_one_self_le_self
% 5.01/5.26 thf(fact_4446_ln__mult,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.26 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_mult
% 5.01/5.26 thf(fact_4447_ln__eq__minus__one,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ( ln_ln_real @ X2 )
% 5.01/5.26 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.01/5.26 => ( X2 = one_one_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_eq_minus_one
% 5.01/5.26 thf(fact_4448_ln__div,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.26 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_div
% 5.01/5.26 thf(fact_4449_pochhammer__rec,axiom,
% 5.01/5.26 ! [A: real,N: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec
% 5.01/5.26 thf(fact_4450_pochhammer__rec,axiom,
% 5.01/5.26 ! [A: rat,N: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec
% 5.01/5.26 thf(fact_4451_pochhammer__rec,axiom,
% 5.01/5.26 ! [A: nat,N: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec
% 5.01/5.26 thf(fact_4452_pochhammer__rec,axiom,
% 5.01/5.26 ! [A: int,N: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec
% 5.01/5.26 thf(fact_4453_pochhammer__rec,axiom,
% 5.01/5.26 ! [A: complex,N: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec
% 5.01/5.26 thf(fact_4454_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: rat,N: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4455_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: real,N: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4456_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: int,N: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4457_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: complex,N: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4458_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: nat,N: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4459_pochhammer__rec_H,axiom,
% 5.01/5.26 ! [Z: code_integer,N: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N ) )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z @ N ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_rec'
% 5.01/5.26 thf(fact_4460_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: rat,N: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4461_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: real,N: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4462_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: int,N: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4463_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: complex,N: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4464_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: nat,N: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4465_pochhammer__Suc,axiom,
% 5.01/5.26 ! [A: code_integer,N: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_Suc
% 5.01/5.26 thf(fact_4466_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.01/5.26 = zero_zero_rat ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma
% 5.01/5.26 thf(fact_4467_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.01/5.26 = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma
% 5.01/5.26 thf(fact_4468_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.01/5.26 = zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma
% 5.01/5.26 thf(fact_4469_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.01/5.26 = zero_zero_complex ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma
% 5.01/5.26 thf(fact_4470_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.01/5.26 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma
% 5.01/5.26 thf(fact_4471_pochhammer__of__nat__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.01/5.26 = zero_zero_rat )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_iff
% 5.01/5.26 thf(fact_4472_pochhammer__of__nat__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_iff
% 5.01/5.26 thf(fact_4473_pochhammer__of__nat__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.01/5.26 = zero_zero_int )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_iff
% 5.01/5.26 thf(fact_4474_pochhammer__of__nat__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.01/5.26 = zero_zero_complex )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_iff
% 5.01/5.26 thf(fact_4475_pochhammer__of__nat__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.01/5.26 = zero_z3403309356797280102nteger )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_iff
% 5.01/5.26 thf(fact_4476_pochhammer__eq__0__iff,axiom,
% 5.01/5.26 ! [A: rat,N: nat] :
% 5.01/5.26 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.01/5.26 = zero_zero_rat )
% 5.01/5.26 = ( ? [K2: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K2 @ N )
% 5.01/5.26 & ( A
% 5.01/5.26 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_iff
% 5.01/5.26 thf(fact_4477_pochhammer__eq__0__iff,axiom,
% 5.01/5.26 ! [A: real,N: nat] :
% 5.01/5.26 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( ? [K2: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K2 @ N )
% 5.01/5.26 & ( A
% 5.01/5.26 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_iff
% 5.01/5.26 thf(fact_4478_pochhammer__eq__0__iff,axiom,
% 5.01/5.26 ! [A: complex,N: nat] :
% 5.01/5.26 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.01/5.26 = zero_zero_complex )
% 5.01/5.26 = ( ? [K2: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K2 @ N )
% 5.01/5.26 & ( A
% 5.01/5.26 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_eq_0_iff
% 5.01/5.26 thf(fact_4479_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.01/5.26 != zero_zero_rat ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma'
% 5.01/5.26 thf(fact_4480_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.01/5.26 != zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma'
% 5.01/5.26 thf(fact_4481_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.01/5.26 != zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma'
% 5.01/5.26 thf(fact_4482_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.01/5.26 != zero_zero_complex ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma'
% 5.01/5.26 thf(fact_4483_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.01/5.26 != zero_z3403309356797280102nteger ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_of_nat_eq_0_lemma'
% 5.01/5.26 thf(fact_4484_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: rat,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4485_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: real,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4486_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: int,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4487_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: complex,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4488_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: nat,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4489_pochhammer__product_H,axiom,
% 5.01/5.26 ! [Z: code_integer,N: nat,M: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product'
% 5.01/5.26 thf(fact_4490_binomial__mono,axiom,
% 5.01/5.26 ! [K: nat,K6: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ K6 )
% 5.01/5.26 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.01/5.26 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_mono
% 5.01/5.26 thf(fact_4491_binomial__maximum_H,axiom,
% 5.01/5.26 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_maximum'
% 5.01/5.26 thf(fact_4492_ln__2__less__1,axiom,
% 5.01/5.26 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.01/5.26
% 5.01/5.26 % ln_2_less_1
% 5.01/5.26 thf(fact_4493_binomial__maximum,axiom,
% 5.01/5.26 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_maximum
% 5.01/5.26 thf(fact_4494_binomial__antimono,axiom,
% 5.01/5.26 ! [K: nat,K6: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ K6 )
% 5.01/5.26 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.01/5.26 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.01/5.26 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_antimono
% 5.01/5.26 thf(fact_4495_ln__le__minus__one,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_le_minus_one
% 5.01/5.26 thf(fact_4496_ln__diff__le,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.26 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y ) @ Y ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_diff_le
% 5.01/5.26 thf(fact_4497_ln__add__one__self__le__self2,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.26 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_add_one_self_le_self2
% 5.01/5.26 thf(fact_4498_ln__realpow,axiom,
% 5.01/5.26 ! [X2: real,N: nat] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N ) )
% 5.01/5.26 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_realpow
% 5.01/5.26 thf(fact_4499_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: rat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.01/5.26 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4500_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: real] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.01/5.26 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4501_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: int] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.01/5.26 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4502_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: complex] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.01/5.26 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4503_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.01/5.26 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4504_pochhammer__product,axiom,
% 5.01/5.26 ! [M: nat,N: nat,Z: code_integer] :
% 5.01/5.26 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( comm_s8582702949713902594nteger @ Z @ N )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_product
% 5.01/5.26 thf(fact_4505_binomial__strict__mono,axiom,
% 5.01/5.26 ! [K: nat,K6: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K @ K6 )
% 5.01/5.26 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.01/5.26 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_strict_mono
% 5.01/5.26 thf(fact_4506_binomial__strict__antimono,axiom,
% 5.01/5.26 ! [K: nat,K6: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K @ K6 )
% 5.01/5.26 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.01/5.26 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.01/5.26 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_strict_antimono
% 5.01/5.26 thf(fact_4507_binomial__less__binomial__Suc,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.26 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_less_binomial_Suc
% 5.01/5.26 thf(fact_4508_ln__one__minus__pos__upper__bound,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.26 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_one_minus_pos_upper_bound
% 5.01/5.26 thf(fact_4509_pochhammer__absorb__comp,axiom,
% 5.01/5.26 ! [R: rat,K: nat] :
% 5.01/5.26 ( ( times_times_rat @ ( minus_minus_rat @ R @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R ) @ K ) )
% 5.01/5.26 = ( times_times_rat @ R @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R ) @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_absorb_comp
% 5.01/5.26 thf(fact_4510_pochhammer__absorb__comp,axiom,
% 5.01/5.26 ! [R: real,K: nat] :
% 5.01/5.26 ( ( times_times_real @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R ) @ K ) )
% 5.01/5.26 = ( times_times_real @ R @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R ) @ one_one_real ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_absorb_comp
% 5.01/5.26 thf(fact_4511_pochhammer__absorb__comp,axiom,
% 5.01/5.26 ! [R: int,K: nat] :
% 5.01/5.26 ( ( times_times_int @ ( minus_minus_int @ R @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R ) @ K ) )
% 5.01/5.26 = ( times_times_int @ R @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R ) @ one_one_int ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_absorb_comp
% 5.01/5.26 thf(fact_4512_pochhammer__absorb__comp,axiom,
% 5.01/5.26 ! [R: complex,K: nat] :
% 5.01/5.26 ( ( times_times_complex @ ( minus_minus_complex @ R @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R ) @ K ) )
% 5.01/5.26 = ( times_times_complex @ R @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R ) @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_absorb_comp
% 5.01/5.26 thf(fact_4513_pochhammer__absorb__comp,axiom,
% 5.01/5.26 ! [R: code_integer,K: nat] :
% 5.01/5.26 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R ) @ K ) )
% 5.01/5.26 = ( times_3573771949741848930nteger @ R @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_absorb_comp
% 5.01/5.26 thf(fact_4514_pochhammer__minus_H,axiom,
% 5.01/5.26 ! [B: rat,K: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.01/5.26 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus'
% 5.01/5.26 thf(fact_4515_pochhammer__minus_H,axiom,
% 5.01/5.26 ! [B: real,K: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.01/5.26 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus'
% 5.01/5.26 thf(fact_4516_pochhammer__minus_H,axiom,
% 5.01/5.26 ! [B: int,K: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.01/5.26 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus'
% 5.01/5.26 thf(fact_4517_pochhammer__minus_H,axiom,
% 5.01/5.26 ! [B: complex,K: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.01/5.26 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus'
% 5.01/5.26 thf(fact_4518_pochhammer__minus_H,axiom,
% 5.01/5.26 ! [B: code_integer,K: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus'
% 5.01/5.26 thf(fact_4519_pochhammer__minus,axiom,
% 5.01/5.26 ! [B: rat,K: nat] :
% 5.01/5.26 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.01/5.26 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus
% 5.01/5.26 thf(fact_4520_pochhammer__minus,axiom,
% 5.01/5.26 ! [B: real,K: nat] :
% 5.01/5.26 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.01/5.26 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus
% 5.01/5.26 thf(fact_4521_pochhammer__minus,axiom,
% 5.01/5.26 ! [B: int,K: nat] :
% 5.01/5.26 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.01/5.26 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus
% 5.01/5.26 thf(fact_4522_pochhammer__minus,axiom,
% 5.01/5.26 ! [B: complex,K: nat] :
% 5.01/5.26 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.01/5.26 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus
% 5.01/5.26 thf(fact_4523_pochhammer__minus,axiom,
% 5.01/5.26 ! [B: code_integer,K: nat] :
% 5.01/5.26 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.01/5.26 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % pochhammer_minus
% 5.01/5.26 thf(fact_4524_ln__one__plus__pos__lower__bound,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.26 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % ln_one_plus_pos_lower_bound
% 5.01/5.26 thf(fact_4525_artanh__def,axiom,
% 5.01/5.26 ( artanh_real
% 5.01/5.26 = ( ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % artanh_def
% 5.01/5.26 thf(fact_4526_zero__less__binomial__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.01/5.26 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % zero_less_binomial_iff
% 5.01/5.26 thf(fact_4527_choose__two,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.26 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % choose_two
% 5.01/5.26 thf(fact_4528_binomial__n__0,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ N @ zero_zero_nat )
% 5.01/5.26 = one_one_nat ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_n_0
% 5.01/5.26 thf(fact_4529_binomial__Suc__Suc,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.01/5.26 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_Suc_Suc
% 5.01/5.26 thf(fact_4530_binomial__eq__0__iff,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ( binomial @ N @ K )
% 5.01/5.26 = zero_zero_nat )
% 5.01/5.26 = ( ord_less_nat @ N @ K ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_eq_0_iff
% 5.01/5.26 thf(fact_4531_binomial__0__Suc,axiom,
% 5.01/5.26 ! [K: nat] :
% 5.01/5.26 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.01/5.26 = zero_zero_nat ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_0_Suc
% 5.01/5.26 thf(fact_4532_binomial__1,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.26 = N ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_1
% 5.01/5.26 thf(fact_4533_binomial__Suc__n,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ ( suc @ N ) @ N )
% 5.01/5.26 = ( suc @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_Suc_n
% 5.01/5.26 thf(fact_4534_binomial__n__n,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ N @ N )
% 5.01/5.26 = one_one_nat ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_n_n
% 5.01/5.26 thf(fact_4535_choose__one,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( binomial @ N @ one_one_nat )
% 5.01/5.26 = N ) ).
% 5.01/5.26
% 5.01/5.26 % choose_one
% 5.01/5.26 thf(fact_4536_binomial__eq__0,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ N @ K )
% 5.01/5.26 => ( ( binomial @ N @ K )
% 5.01/5.26 = zero_zero_nat ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_eq_0
% 5.01/5.26 thf(fact_4537_Suc__times__binomial__eq,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.01/5.26 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Suc_times_binomial_eq
% 5.01/5.26 thf(fact_4538_Suc__times__binomial,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.01/5.26 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Suc_times_binomial
% 5.01/5.26 thf(fact_4539_binomial__symmetric,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ( binomial @ N @ K )
% 5.01/5.26 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_symmetric
% 5.01/5.26 thf(fact_4540_choose__mult__lemma,axiom,
% 5.01/5.26 ! [M: nat,R: nat,K: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.01/5.26 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % choose_mult_lemma
% 5.01/5.26 thf(fact_4541_binomial__le__pow,axiom,
% 5.01/5.26 ! [R: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ R @ N )
% 5.01/5.26 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_le_pow
% 5.01/5.26 thf(fact_4542_zero__less__binomial,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % zero_less_binomial
% 5.01/5.26 thf(fact_4543_Suc__times__binomial__add,axiom,
% 5.01/5.26 ! [A: nat,B: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.01/5.26 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % Suc_times_binomial_add
% 5.01/5.26 thf(fact_4544_choose__mult,axiom,
% 5.01/5.26 ! [K: nat,M: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ M )
% 5.01/5.26 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.26 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.01/5.26 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % choose_mult
% 5.01/5.26 thf(fact_4545_binomial__Suc__Suc__eq__times,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.01/5.26 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_Suc_Suc_eq_times
% 5.01/5.26 thf(fact_4546_binomial__absorb__comp,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.01/5.26 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_absorb_comp
% 5.01/5.26 thf(fact_4547_binomial__absorption,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.01/5.26 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_absorption
% 5.01/5.26 thf(fact_4548_binomial__ge__n__over__k__pow__k,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_ge_n_over_k_pow_k
% 5.01/5.26 thf(fact_4549_binomial__ge__n__over__k__pow__k,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.26 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_ge_n_over_k_pow_k
% 5.01/5.26 thf(fact_4550_binomial__le__pow2,axiom,
% 5.01/5.26 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_le_pow2
% 5.01/5.26 thf(fact_4551_choose__reduce__nat,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.26 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.26 => ( ( binomial @ N @ K )
% 5.01/5.26 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % choose_reduce_nat
% 5.01/5.26 thf(fact_4552_times__binomial__minus1__eq,axiom,
% 5.01/5.26 ! [K: nat,N: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.26 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.01/5.26 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % times_binomial_minus1_eq
% 5.01/5.26 thf(fact_4553_binomial__addition__formula,axiom,
% 5.01/5.26 ! [N: nat,K: nat] :
% 5.01/5.26 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.26 => ( ( binomial @ N @ ( suc @ K ) )
% 5.01/5.26 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % binomial_addition_formula
% 5.01/5.26 thf(fact_4554_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.26 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.26 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.01/5.26 thf(fact_4555_tanh__ln__real,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.26 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.26 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_ln_real
% 5.01/5.26 thf(fact_4556_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.26 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_ln_one_plus_x_minus_x_bound
% 5.01/5.26 thf(fact_4557_divmod__BitM__2__eq,axiom,
% 5.01/5.26 ! [M: num] :
% 5.01/5.26 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.01/5.26 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % divmod_BitM_2_eq
% 5.01/5.26 thf(fact_4558_abs__abs,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.01/5.26 = ( abs_abs_real @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_abs
% 5.01/5.26 thf(fact_4559_abs__abs,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.01/5.26 = ( abs_abs_int @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_abs
% 5.01/5.26 thf(fact_4560_abs__abs,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.26 = ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_abs
% 5.01/5.26 thf(fact_4561_abs__abs,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.01/5.26 = ( abs_abs_rat @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_abs
% 5.01/5.26 thf(fact_4562_abs__idempotent,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.01/5.26 = ( abs_abs_real @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_idempotent
% 5.01/5.26 thf(fact_4563_abs__idempotent,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.01/5.26 = ( abs_abs_int @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_idempotent
% 5.01/5.26 thf(fact_4564_abs__idempotent,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.26 = ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_idempotent
% 5.01/5.26 thf(fact_4565_abs__idempotent,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.01/5.26 = ( abs_abs_rat @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_idempotent
% 5.01/5.26 thf(fact_4566_abs__0,axiom,
% 5.01/5.26 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.01/5.26 = zero_z3403309356797280102nteger ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0
% 5.01/5.26 thf(fact_4567_abs__0,axiom,
% 5.01/5.26 ( ( abs_abs_complex @ zero_zero_complex )
% 5.01/5.26 = zero_zero_complex ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0
% 5.01/5.26 thf(fact_4568_abs__0,axiom,
% 5.01/5.26 ( ( abs_abs_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0
% 5.01/5.26 thf(fact_4569_abs__0,axiom,
% 5.01/5.26 ( ( abs_abs_rat @ zero_zero_rat )
% 5.01/5.26 = zero_zero_rat ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0
% 5.01/5.26 thf(fact_4570_abs__0,axiom,
% 5.01/5.26 ( ( abs_abs_int @ zero_zero_int )
% 5.01/5.26 = zero_zero_int ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0
% 5.01/5.26 thf(fact_4571_abs__zero,axiom,
% 5.01/5.26 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.01/5.26 = zero_z3403309356797280102nteger ) ).
% 5.01/5.26
% 5.01/5.26 % abs_zero
% 5.01/5.26 thf(fact_4572_abs__zero,axiom,
% 5.01/5.26 ( ( abs_abs_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % abs_zero
% 5.01/5.26 thf(fact_4573_abs__zero,axiom,
% 5.01/5.26 ( ( abs_abs_rat @ zero_zero_rat )
% 5.01/5.26 = zero_zero_rat ) ).
% 5.01/5.26
% 5.01/5.26 % abs_zero
% 5.01/5.26 thf(fact_4574_abs__zero,axiom,
% 5.01/5.26 ( ( abs_abs_int @ zero_zero_int )
% 5.01/5.26 = zero_zero_int ) ).
% 5.01/5.26
% 5.01/5.26 % abs_zero
% 5.01/5.26 thf(fact_4575_abs__eq__0,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( ( abs_abs_Code_integer @ A )
% 5.01/5.26 = zero_z3403309356797280102nteger )
% 5.01/5.26 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_eq_0
% 5.01/5.26 thf(fact_4576_abs__eq__0,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( ( abs_abs_real @ A )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( A = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_eq_0
% 5.01/5.26 thf(fact_4577_abs__eq__0,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( ( abs_abs_rat @ A )
% 5.01/5.26 = zero_zero_rat )
% 5.01/5.26 = ( A = zero_zero_rat ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_eq_0
% 5.01/5.26 thf(fact_4578_abs__eq__0,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( ( abs_abs_int @ A )
% 5.01/5.26 = zero_zero_int )
% 5.01/5.26 = ( A = zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_eq_0
% 5.01/5.26 thf(fact_4579_abs__0__eq,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( zero_z3403309356797280102nteger
% 5.01/5.26 = ( abs_abs_Code_integer @ A ) )
% 5.01/5.26 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0_eq
% 5.01/5.26 thf(fact_4580_abs__0__eq,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( zero_zero_real
% 5.01/5.26 = ( abs_abs_real @ A ) )
% 5.01/5.26 = ( A = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0_eq
% 5.01/5.26 thf(fact_4581_abs__0__eq,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( zero_zero_rat
% 5.01/5.26 = ( abs_abs_rat @ A ) )
% 5.01/5.26 = ( A = zero_zero_rat ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0_eq
% 5.01/5.26 thf(fact_4582_abs__0__eq,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( zero_zero_int
% 5.01/5.26 = ( abs_abs_int @ A ) )
% 5.01/5.26 = ( A = zero_zero_int ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_0_eq
% 5.01/5.26 thf(fact_4583_abs__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.01/5.26 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_numeral
% 5.01/5.26 thf(fact_4584_abs__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.01/5.26 = ( numeral_numeral_real @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_numeral
% 5.01/5.26 thf(fact_4585_abs__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.01/5.26 = ( numeral_numeral_rat @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_numeral
% 5.01/5.26 thf(fact_4586_abs__numeral,axiom,
% 5.01/5.26 ! [N: num] :
% 5.01/5.26 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.01/5.26 = ( numeral_numeral_int @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_numeral
% 5.01/5.26 thf(fact_4587_abs__mult__self__eq,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.26 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_mult_self_eq
% 5.01/5.26 thf(fact_4588_abs__mult__self__eq,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.01/5.26 = ( times_times_real @ A @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_mult_self_eq
% 5.01/5.26 thf(fact_4589_abs__mult__self__eq,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.01/5.26 = ( times_times_rat @ A @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_mult_self_eq
% 5.01/5.26 thf(fact_4590_abs__mult__self__eq,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.01/5.26 = ( times_times_int @ A @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_mult_self_eq
% 5.01/5.26 thf(fact_4591_abs__add__abs,axiom,
% 5.01/5.26 ! [A: code_integer,B: code_integer] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.01/5.26 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_add_abs
% 5.01/5.26 thf(fact_4592_abs__add__abs,axiom,
% 5.01/5.26 ! [A: real,B: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.01/5.26 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_add_abs
% 5.01/5.26 thf(fact_4593_abs__add__abs,axiom,
% 5.01/5.26 ! [A: rat,B: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.01/5.26 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_add_abs
% 5.01/5.26 thf(fact_4594_abs__add__abs,axiom,
% 5.01/5.26 ! [A: int,B: int] :
% 5.01/5.26 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.01/5.26 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_add_abs
% 5.01/5.26 thf(fact_4595_abs__1,axiom,
% 5.01/5.26 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.01/5.26 = one_one_Code_integer ) ).
% 5.01/5.26
% 5.01/5.26 % abs_1
% 5.01/5.26 thf(fact_4596_abs__1,axiom,
% 5.01/5.26 ( ( abs_abs_complex @ one_one_complex )
% 5.01/5.26 = one_one_complex ) ).
% 5.01/5.26
% 5.01/5.26 % abs_1
% 5.01/5.26 thf(fact_4597_abs__1,axiom,
% 5.01/5.26 ( ( abs_abs_real @ one_one_real )
% 5.01/5.26 = one_one_real ) ).
% 5.01/5.26
% 5.01/5.26 % abs_1
% 5.01/5.26 thf(fact_4598_abs__1,axiom,
% 5.01/5.26 ( ( abs_abs_rat @ one_one_rat )
% 5.01/5.26 = one_one_rat ) ).
% 5.01/5.26
% 5.01/5.26 % abs_1
% 5.01/5.26 thf(fact_4599_abs__1,axiom,
% 5.01/5.26 ( ( abs_abs_int @ one_one_int )
% 5.01/5.26 = one_one_int ) ).
% 5.01/5.26
% 5.01/5.26 % abs_1
% 5.01/5.26 thf(fact_4600_abs__divide,axiom,
% 5.01/5.26 ! [A: complex,B: complex] :
% 5.01/5.26 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.26 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_divide
% 5.01/5.26 thf(fact_4601_abs__divide,axiom,
% 5.01/5.26 ! [A: real,B: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.26 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_divide
% 5.01/5.26 thf(fact_4602_abs__divide,axiom,
% 5.01/5.26 ! [A: rat,B: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.26 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_divide
% 5.01/5.26 thf(fact_4603_abs__minus__cancel,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.01/5.26 = ( abs_abs_real @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus_cancel
% 5.01/5.26 thf(fact_4604_abs__minus__cancel,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.01/5.26 = ( abs_abs_int @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus_cancel
% 5.01/5.26 thf(fact_4605_abs__minus__cancel,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.01/5.26 = ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus_cancel
% 5.01/5.26 thf(fact_4606_abs__minus__cancel,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.01/5.26 = ( abs_abs_rat @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus_cancel
% 5.01/5.26 thf(fact_4607_abs__minus,axiom,
% 5.01/5.26 ! [A: real] :
% 5.01/5.26 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.01/5.26 = ( abs_abs_real @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus
% 5.01/5.26 thf(fact_4608_abs__minus,axiom,
% 5.01/5.26 ! [A: int] :
% 5.01/5.26 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.01/5.26 = ( abs_abs_int @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus
% 5.01/5.26 thf(fact_4609_abs__minus,axiom,
% 5.01/5.26 ! [A: complex] :
% 5.01/5.26 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.01/5.26 = ( abs_abs_complex @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus
% 5.01/5.26 thf(fact_4610_abs__minus,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.01/5.26 = ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus
% 5.01/5.26 thf(fact_4611_abs__minus,axiom,
% 5.01/5.26 ! [A: rat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.01/5.26 = ( abs_abs_rat @ A ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_minus
% 5.01/5.26 thf(fact_4612_abs__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.01/5.26 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_of_nat
% 5.01/5.26 thf(fact_4613_abs__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.26 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_of_nat
% 5.01/5.26 thf(fact_4614_abs__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.26 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_of_nat
% 5.01/5.26 thf(fact_4615_abs__of__nat,axiom,
% 5.01/5.26 ! [N: nat] :
% 5.01/5.26 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.26 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.01/5.26
% 5.01/5.26 % abs_of_nat
% 5.01/5.26 thf(fact_4616_tanh__0,axiom,
% 5.01/5.26 ( ( tanh_complex @ zero_zero_complex )
% 5.01/5.26 = zero_zero_complex ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_0
% 5.01/5.26 thf(fact_4617_tanh__0,axiom,
% 5.01/5.26 ( ( tanh_real @ zero_zero_real )
% 5.01/5.26 = zero_zero_real ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_0
% 5.01/5.26 thf(fact_4618_tanh__minus,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( tanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.26 = ( uminus_uminus_real @ ( tanh_real @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_minus
% 5.01/5.26 thf(fact_4619_tanh__minus,axiom,
% 5.01/5.26 ! [X2: complex] :
% 5.01/5.26 ( ( tanh_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.26 = ( uminus1482373934393186551omplex @ ( tanh_complex @ X2 ) ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_minus
% 5.01/5.26 thf(fact_4620_tanh__real__zero__iff,axiom,
% 5.01/5.26 ! [X2: real] :
% 5.01/5.26 ( ( ( tanh_real @ X2 )
% 5.01/5.26 = zero_zero_real )
% 5.01/5.26 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_real_zero_iff
% 5.01/5.26 thf(fact_4621_tanh__real__less__iff,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y ) )
% 5.01/5.26 = ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_real_less_iff
% 5.01/5.26 thf(fact_4622_tanh__real__le__iff,axiom,
% 5.01/5.26 ! [X2: real,Y: real] :
% 5.01/5.26 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y ) )
% 5.01/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.26
% 5.01/5.26 % tanh_real_le_iff
% 5.01/5.26 thf(fact_4623_abs__le__zero__iff,axiom,
% 5.01/5.26 ! [A: code_integer] :
% 5.01/5.26 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.01/5.27 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_zero_iff
% 5.01/5.27 thf(fact_4624_abs__le__zero__iff,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.01/5.27 = ( A = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_zero_iff
% 5.01/5.27 thf(fact_4625_abs__le__zero__iff,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.01/5.27 = ( A = zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_zero_iff
% 5.01/5.27 thf(fact_4626_abs__le__zero__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.01/5.27 = ( A = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_zero_iff
% 5.01/5.27 thf(fact_4627_abs__le__self__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.01/5.27 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_self_iff
% 5.01/5.27 thf(fact_4628_abs__le__self__iff,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.01/5.27 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_self_iff
% 5.01/5.27 thf(fact_4629_abs__le__self__iff,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.01/5.27 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_self_iff
% 5.01/5.27 thf(fact_4630_abs__le__self__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.01/5.27 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_self_iff
% 5.01/5.27 thf(fact_4631_abs__of__nonneg,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 => ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonneg
% 5.01/5.27 thf(fact_4632_abs__of__nonneg,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.27 => ( ( abs_abs_real @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonneg
% 5.01/5.27 thf(fact_4633_abs__of__nonneg,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.27 => ( ( abs_abs_rat @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonneg
% 5.01/5.27 thf(fact_4634_abs__of__nonneg,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.27 => ( ( abs_abs_int @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonneg
% 5.01/5.27 thf(fact_4635_zero__less__abs__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.27 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_abs_iff
% 5.01/5.27 thf(fact_4636_zero__less__abs__iff,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.01/5.27 = ( A != zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_abs_iff
% 5.01/5.27 thf(fact_4637_zero__less__abs__iff,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.01/5.27 = ( A != zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_abs_iff
% 5.01/5.27 thf(fact_4638_zero__less__abs__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.01/5.27 = ( A != zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_abs_iff
% 5.01/5.27 thf(fact_4639_abs__neg__numeral,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.01/5.27 = ( numeral_numeral_real @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_numeral
% 5.01/5.27 thf(fact_4640_abs__neg__numeral,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.27 = ( numeral_numeral_int @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_numeral
% 5.01/5.27 thf(fact_4641_abs__neg__numeral,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.01/5.27 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_numeral
% 5.01/5.27 thf(fact_4642_abs__neg__numeral,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.01/5.27 = ( numeral_numeral_rat @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_numeral
% 5.01/5.27 thf(fact_4643_abs__neg__one,axiom,
% 5.01/5.27 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.27 = one_one_real ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_one
% 5.01/5.27 thf(fact_4644_abs__neg__one,axiom,
% 5.01/5.27 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.27 = one_one_int ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_one
% 5.01/5.27 thf(fact_4645_abs__neg__one,axiom,
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.27 = one_one_Code_integer ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_one
% 5.01/5.27 thf(fact_4646_abs__neg__one,axiom,
% 5.01/5.27 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.27 = one_one_rat ) ).
% 5.01/5.27
% 5.01/5.27 % abs_neg_one
% 5.01/5.27 thf(fact_4647_abs__power__minus,axiom,
% 5.01/5.27 ! [A: real,N: nat] :
% 5.01/5.27 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.01/5.27 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power_minus
% 5.01/5.27 thf(fact_4648_abs__power__minus,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.01/5.27 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power_minus
% 5.01/5.27 thf(fact_4649_abs__power__minus,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.01/5.27 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power_minus
% 5.01/5.27 thf(fact_4650_abs__power__minus,axiom,
% 5.01/5.27 ! [A: rat,N: nat] :
% 5.01/5.27 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.01/5.27 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power_minus
% 5.01/5.27 thf(fact_4651_tanh__real__neg__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.01/5.27 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_neg_iff
% 5.01/5.27 thf(fact_4652_tanh__real__pos__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.01/5.27 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_pos_iff
% 5.01/5.27 thf(fact_4653_tanh__real__nonpos__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.01/5.27 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_nonpos_iff
% 5.01/5.27 thf(fact_4654_tanh__real__nonneg__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.01/5.27 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_nonneg_iff
% 5.01/5.27 thf(fact_4655_dbl__dec__simps_I5_J,axiom,
% 5.01/5.27 ! [K: num] :
% 5.01/5.27 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.01/5.27 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dbl_dec_simps(5)
% 5.01/5.27 thf(fact_4656_dbl__dec__simps_I5_J,axiom,
% 5.01/5.27 ! [K: num] :
% 5.01/5.27 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.01/5.27 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dbl_dec_simps(5)
% 5.01/5.27 thf(fact_4657_dbl__dec__simps_I5_J,axiom,
% 5.01/5.27 ! [K: num] :
% 5.01/5.27 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.01/5.27 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dbl_dec_simps(5)
% 5.01/5.27 thf(fact_4658_dbl__dec__simps_I5_J,axiom,
% 5.01/5.27 ! [K: num] :
% 5.01/5.27 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.01/5.27 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dbl_dec_simps(5)
% 5.01/5.27 thf(fact_4659_divide__le__0__abs__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.01/5.27 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.27 | ( B = zero_zero_real ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % divide_le_0_abs_iff
% 5.01/5.27 thf(fact_4660_divide__le__0__abs__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.01/5.27 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.27 | ( B = zero_zero_rat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % divide_le_0_abs_iff
% 5.01/5.27 thf(fact_4661_zero__le__divide__abs__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.01/5.27 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.27 | ( B = zero_zero_real ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_divide_abs_iff
% 5.01/5.27 thf(fact_4662_zero__le__divide__abs__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.01/5.27 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.27 | ( B = zero_zero_rat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_divide_abs_iff
% 5.01/5.27 thf(fact_4663_abs__of__nonpos,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.27 => ( ( abs_abs_real @ A )
% 5.01/5.27 = ( uminus_uminus_real @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonpos
% 5.01/5.27 thf(fact_4664_abs__of__nonpos,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.01/5.27 => ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonpos
% 5.01/5.27 thf(fact_4665_abs__of__nonpos,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.01/5.27 => ( ( abs_abs_rat @ A )
% 5.01/5.27 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonpos
% 5.01/5.27 thf(fact_4666_abs__of__nonpos,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.01/5.27 => ( ( abs_abs_int @ A )
% 5.01/5.27 = ( uminus_uminus_int @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_nonpos
% 5.01/5.27 thf(fact_4667_artanh__minus__real,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.27 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.27 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % artanh_minus_real
% 5.01/5.27 thf(fact_4668_pred__numeral__simps_I2_J,axiom,
% 5.01/5.27 ! [K: num] :
% 5.01/5.27 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.01/5.27 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % pred_numeral_simps(2)
% 5.01/5.27 thf(fact_4669_zero__less__power__abs__iff,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.01/5.27 = ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.27 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_abs_iff
% 5.01/5.27 thf(fact_4670_zero__less__power__abs__iff,axiom,
% 5.01/5.27 ! [A: real,N: nat] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.01/5.27 = ( ( A != zero_zero_real )
% 5.01/5.27 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_abs_iff
% 5.01/5.27 thf(fact_4671_zero__less__power__abs__iff,axiom,
% 5.01/5.27 ! [A: rat,N: nat] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.01/5.27 = ( ( A != zero_zero_rat )
% 5.01/5.27 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_abs_iff
% 5.01/5.27 thf(fact_4672_zero__less__power__abs__iff,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.01/5.27 = ( ( A != zero_zero_int )
% 5.01/5.27 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_abs_iff
% 5.01/5.27 thf(fact_4673_power2__abs,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_abs
% 5.01/5.27 thf(fact_4674_power2__abs,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_abs
% 5.01/5.27 thf(fact_4675_power2__abs,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_abs
% 5.01/5.27 thf(fact_4676_power2__abs,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_abs
% 5.01/5.27 thf(fact_4677_abs__power2,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power2
% 5.01/5.27 thf(fact_4678_abs__power2,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power2
% 5.01/5.27 thf(fact_4679_abs__power2,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power2
% 5.01/5.27 thf(fact_4680_abs__power2,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_power2
% 5.01/5.27 thf(fact_4681_abs__ge__self,axiom,
% 5.01/5.27 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_self
% 5.01/5.27 thf(fact_4682_abs__ge__self,axiom,
% 5.01/5.27 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_self
% 5.01/5.27 thf(fact_4683_abs__ge__self,axiom,
% 5.01/5.27 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_self
% 5.01/5.27 thf(fact_4684_abs__ge__self,axiom,
% 5.01/5.27 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_self
% 5.01/5.27 thf(fact_4685_abs__le__D1,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D1
% 5.01/5.27 thf(fact_4686_abs__le__D1,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.01/5.27 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D1
% 5.01/5.27 thf(fact_4687_abs__le__D1,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D1
% 5.01/5.27 thf(fact_4688_abs__le__D1,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D1
% 5.01/5.27 thf(fact_4689_abs__eq__0__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = zero_z3403309356797280102nteger )
% 5.01/5.27 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_0_iff
% 5.01/5.27 thf(fact_4690_abs__eq__0__iff,axiom,
% 5.01/5.27 ! [A: complex] :
% 5.01/5.27 ( ( ( abs_abs_complex @ A )
% 5.01/5.27 = zero_zero_complex )
% 5.01/5.27 = ( A = zero_zero_complex ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_0_iff
% 5.01/5.27 thf(fact_4691_abs__eq__0__iff,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ( abs_abs_real @ A )
% 5.01/5.27 = zero_zero_real )
% 5.01/5.27 = ( A = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_0_iff
% 5.01/5.27 thf(fact_4692_abs__eq__0__iff,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ( abs_abs_rat @ A )
% 5.01/5.27 = zero_zero_rat )
% 5.01/5.27 = ( A = zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_0_iff
% 5.01/5.27 thf(fact_4693_abs__eq__0__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ( abs_abs_int @ A )
% 5.01/5.27 = zero_zero_int )
% 5.01/5.27 = ( A = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_0_iff
% 5.01/5.27 thf(fact_4694_abs__mult,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.01/5.27 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult
% 5.01/5.27 thf(fact_4695_abs__mult,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.01/5.27 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult
% 5.01/5.27 thf(fact_4696_abs__mult,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.27 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult
% 5.01/5.27 thf(fact_4697_abs__mult,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.01/5.27 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult
% 5.01/5.27 thf(fact_4698_abs__mult,axiom,
% 5.01/5.27 ! [A: complex,B: complex] :
% 5.01/5.27 ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 5.01/5.27 = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult
% 5.01/5.27 thf(fact_4699_abs__one,axiom,
% 5.01/5.27 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.01/5.27 = one_one_Code_integer ) ).
% 5.01/5.27
% 5.01/5.27 % abs_one
% 5.01/5.27 thf(fact_4700_abs__one,axiom,
% 5.01/5.27 ( ( abs_abs_real @ one_one_real )
% 5.01/5.27 = one_one_real ) ).
% 5.01/5.27
% 5.01/5.27 % abs_one
% 5.01/5.27 thf(fact_4701_abs__one,axiom,
% 5.01/5.27 ( ( abs_abs_rat @ one_one_rat )
% 5.01/5.27 = one_one_rat ) ).
% 5.01/5.27
% 5.01/5.27 % abs_one
% 5.01/5.27 thf(fact_4702_abs__one,axiom,
% 5.01/5.27 ( ( abs_abs_int @ one_one_int )
% 5.01/5.27 = one_one_int ) ).
% 5.01/5.27
% 5.01/5.27 % abs_one
% 5.01/5.27 thf(fact_4703_abs__minus__commute,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.01/5.27 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_commute
% 5.01/5.27 thf(fact_4704_abs__minus__commute,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.01/5.27 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_commute
% 5.01/5.27 thf(fact_4705_abs__minus__commute,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.01/5.27 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_commute
% 5.01/5.27 thf(fact_4706_abs__minus__commute,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.01/5.27 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_commute
% 5.01/5.27 thf(fact_4707_abs__eq__iff,axiom,
% 5.01/5.27 ! [X2: real,Y: real] :
% 5.01/5.27 ( ( ( abs_abs_real @ X2 )
% 5.01/5.27 = ( abs_abs_real @ Y ) )
% 5.01/5.27 = ( ( X2 = Y )
% 5.01/5.27 | ( X2
% 5.01/5.27 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff
% 5.01/5.27 thf(fact_4708_abs__eq__iff,axiom,
% 5.01/5.27 ! [X2: int,Y: int] :
% 5.01/5.27 ( ( ( abs_abs_int @ X2 )
% 5.01/5.27 = ( abs_abs_int @ Y ) )
% 5.01/5.27 = ( ( X2 = Y )
% 5.01/5.27 | ( X2
% 5.01/5.27 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff
% 5.01/5.27 thf(fact_4709_abs__eq__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.27 ( ( ( abs_abs_Code_integer @ X2 )
% 5.01/5.27 = ( abs_abs_Code_integer @ Y ) )
% 5.01/5.27 = ( ( X2 = Y )
% 5.01/5.27 | ( X2
% 5.01/5.27 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff
% 5.01/5.27 thf(fact_4710_abs__eq__iff,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat] :
% 5.01/5.27 ( ( ( abs_abs_rat @ X2 )
% 5.01/5.27 = ( abs_abs_rat @ Y ) )
% 5.01/5.27 = ( ( X2 = Y )
% 5.01/5.27 | ( X2
% 5.01/5.27 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff
% 5.01/5.27 thf(fact_4711_power__abs,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.01/5.27 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_abs
% 5.01/5.27 thf(fact_4712_power__abs,axiom,
% 5.01/5.27 ! [A: rat,N: nat] :
% 5.01/5.27 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.01/5.27 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_abs
% 5.01/5.27 thf(fact_4713_power__abs,axiom,
% 5.01/5.27 ! [A: real,N: nat] :
% 5.01/5.27 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.01/5.27 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_abs
% 5.01/5.27 thf(fact_4714_power__abs,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.01/5.27 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_abs
% 5.01/5.27 thf(fact_4715_semiring__norm_I26_J,axiom,
% 5.01/5.27 ( ( bitM @ one )
% 5.01/5.27 = one ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_norm(26)
% 5.01/5.27 thf(fact_4716_abs__ge__zero,axiom,
% 5.01/5.27 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_zero
% 5.01/5.27 thf(fact_4717_abs__ge__zero,axiom,
% 5.01/5.27 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_zero
% 5.01/5.27 thf(fact_4718_abs__ge__zero,axiom,
% 5.01/5.27 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_zero
% 5.01/5.27 thf(fact_4719_abs__ge__zero,axiom,
% 5.01/5.27 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_zero
% 5.01/5.27 thf(fact_4720_abs__of__pos,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 => ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_pos
% 5.01/5.27 thf(fact_4721_abs__of__pos,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.27 => ( ( abs_abs_real @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_pos
% 5.01/5.27 thf(fact_4722_abs__of__pos,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.27 => ( ( abs_abs_rat @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_pos
% 5.01/5.27 thf(fact_4723_abs__of__pos,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.27 => ( ( abs_abs_int @ A )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_pos
% 5.01/5.27 thf(fact_4724_abs__not__less__zero,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.01/5.27
% 5.01/5.27 % abs_not_less_zero
% 5.01/5.27 thf(fact_4725_abs__not__less__zero,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.01/5.27
% 5.01/5.27 % abs_not_less_zero
% 5.01/5.27 thf(fact_4726_abs__not__less__zero,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.01/5.27
% 5.01/5.27 % abs_not_less_zero
% 5.01/5.27 thf(fact_4727_abs__not__less__zero,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.01/5.27
% 5.01/5.27 % abs_not_less_zero
% 5.01/5.27 thf(fact_4728_abs__triangle__ineq,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq
% 5.01/5.27 thf(fact_4729_abs__triangle__ineq,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq
% 5.01/5.27 thf(fact_4730_abs__triangle__ineq,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq
% 5.01/5.27 thf(fact_4731_abs__triangle__ineq,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq
% 5.01/5.27 thf(fact_4732_abs__mult__less,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.01/5.27 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.01/5.27 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_less
% 5.01/5.27 thf(fact_4733_abs__mult__less,axiom,
% 5.01/5.27 ! [A: real,C: real,B: real,D: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.01/5.27 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.01/5.27 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_less
% 5.01/5.27 thf(fact_4734_abs__mult__less,axiom,
% 5.01/5.27 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.01/5.27 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.01/5.27 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.01/5.27 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_less
% 5.01/5.27 thf(fact_4735_abs__mult__less,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int,D: int] :
% 5.01/5.27 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.01/5.27 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.01/5.27 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_less
% 5.01/5.27 thf(fact_4736_abs__triangle__ineq2__sym,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2_sym
% 5.01/5.27 thf(fact_4737_abs__triangle__ineq2__sym,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2_sym
% 5.01/5.27 thf(fact_4738_abs__triangle__ineq2__sym,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2_sym
% 5.01/5.27 thf(fact_4739_abs__triangle__ineq2__sym,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2_sym
% 5.01/5.27 thf(fact_4740_abs__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq3
% 5.01/5.27 thf(fact_4741_abs__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq3
% 5.01/5.27 thf(fact_4742_abs__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq3
% 5.01/5.27 thf(fact_4743_abs__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq3
% 5.01/5.27 thf(fact_4744_abs__triangle__ineq2,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2
% 5.01/5.27 thf(fact_4745_abs__triangle__ineq2,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2
% 5.01/5.27 thf(fact_4746_abs__triangle__ineq2,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2
% 5.01/5.27 thf(fact_4747_abs__triangle__ineq2,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq2
% 5.01/5.27 thf(fact_4748_abs__ge__minus__self,axiom,
% 5.01/5.27 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_minus_self
% 5.01/5.27 thf(fact_4749_abs__ge__minus__self,axiom,
% 5.01/5.27 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_minus_self
% 5.01/5.27 thf(fact_4750_abs__ge__minus__self,axiom,
% 5.01/5.27 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_minus_self
% 5.01/5.27 thf(fact_4751_abs__ge__minus__self,axiom,
% 5.01/5.27 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ge_minus_self
% 5.01/5.27 thf(fact_4752_abs__le__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_eq_real @ A @ B )
% 5.01/5.27 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_iff
% 5.01/5.27 thf(fact_4753_abs__le__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.01/5.27 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.01/5.27 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_iff
% 5.01/5.27 thf(fact_4754_abs__le__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.27 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_iff
% 5.01/5.27 thf(fact_4755_abs__le__iff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_eq_int @ A @ B )
% 5.01/5.27 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_iff
% 5.01/5.27 thf(fact_4756_abs__le__D2,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D2
% 5.01/5.27 thf(fact_4757_abs__le__D2,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.01/5.27 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D2
% 5.01/5.27 thf(fact_4758_abs__le__D2,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D2
% 5.01/5.27 thf(fact_4759_abs__le__D2,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_D2
% 5.01/5.27 thf(fact_4760_abs__leI,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.27 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_leI
% 5.01/5.27 thf(fact_4761_abs__leI,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.01/5.27 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.01/5.27 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_leI
% 5.01/5.27 thf(fact_4762_abs__leI,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.27 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_leI
% 5.01/5.27 thf(fact_4763_abs__leI,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.27 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.27 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_leI
% 5.01/5.27 thf(fact_4764_nonzero__abs__divide,axiom,
% 5.01/5.27 ! [B: real,A: real] :
% 5.01/5.27 ( ( B != zero_zero_real )
% 5.01/5.27 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.27 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % nonzero_abs_divide
% 5.01/5.27 thf(fact_4765_nonzero__abs__divide,axiom,
% 5.01/5.27 ! [B: rat,A: rat] :
% 5.01/5.27 ( ( B != zero_zero_rat )
% 5.01/5.27 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.27 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % nonzero_abs_divide
% 5.01/5.27 thf(fact_4766_abs__less__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_real @ A @ B )
% 5.01/5.27 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_less_iff
% 5.01/5.27 thf(fact_4767_abs__less__iff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_int @ A @ B )
% 5.01/5.27 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_less_iff
% 5.01/5.27 thf(fact_4768_abs__less__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.01/5.27 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.01/5.27 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_less_iff
% 5.01/5.27 thf(fact_4769_abs__less__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.01/5.27 = ( ( ord_less_rat @ A @ B )
% 5.01/5.27 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_less_iff
% 5.01/5.27 thf(fact_4770_tanh__real__lt__1,axiom,
% 5.01/5.27 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_lt_1
% 5.01/5.27 thf(fact_4771_semiring__norm_I27_J,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( bitM @ ( bit0 @ N ) )
% 5.01/5.27 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_norm(27)
% 5.01/5.27 thf(fact_4772_semiring__norm_I28_J,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( bitM @ ( bit1 @ N ) )
% 5.01/5.27 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_norm(28)
% 5.01/5.27 thf(fact_4773_dense__eq0__I,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ! [E2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.27 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E2 ) )
% 5.01/5.27 => ( X2 = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % dense_eq0_I
% 5.01/5.27 thf(fact_4774_dense__eq0__I,axiom,
% 5.01/5.27 ! [X2: rat] :
% 5.01/5.27 ( ! [E2: rat] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.01/5.27 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E2 ) )
% 5.01/5.27 => ( X2 = zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dense_eq0_I
% 5.01/5.27 thf(fact_4775_abs__eq__mult,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.01/5.27 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.27 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.01/5.27 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.01/5.27 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_mult
% 5.01/5.27 thf(fact_4776_abs__eq__mult,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.27 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.01/5.27 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.27 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.01/5.27 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.01/5.27 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_mult
% 5.01/5.27 thf(fact_4777_abs__eq__mult,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.27 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.01/5.27 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.27 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.01/5.27 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.27 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_mult
% 5.01/5.27 thf(fact_4778_abs__eq__mult,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.27 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.01/5.27 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.27 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.01/5.27 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.01/5.27 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_mult
% 5.01/5.27 thf(fact_4779_abs__mult__pos,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.01/5.27 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X2 )
% 5.01/5.27 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_pos
% 5.01/5.27 thf(fact_4780_abs__mult__pos,axiom,
% 5.01/5.27 ! [X2: real,Y: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.27 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X2 )
% 5.01/5.27 = ( abs_abs_real @ ( times_times_real @ Y @ X2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_pos
% 5.01/5.27 thf(fact_4781_abs__mult__pos,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.27 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X2 )
% 5.01/5.27 = ( abs_abs_rat @ ( times_times_rat @ Y @ X2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_pos
% 5.01/5.27 thf(fact_4782_abs__mult__pos,axiom,
% 5.01/5.27 ! [X2: int,Y: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.27 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X2 )
% 5.01/5.27 = ( abs_abs_int @ ( times_times_int @ Y @ X2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_mult_pos
% 5.01/5.27 thf(fact_4783_abs__minus__le__zero,axiom,
% 5.01/5.27 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_le_zero
% 5.01/5.27 thf(fact_4784_abs__minus__le__zero,axiom,
% 5.01/5.27 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_le_zero
% 5.01/5.27 thf(fact_4785_abs__minus__le__zero,axiom,
% 5.01/5.27 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_le_zero
% 5.01/5.27 thf(fact_4786_abs__minus__le__zero,axiom,
% 5.01/5.27 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.01/5.27
% 5.01/5.27 % abs_minus_le_zero
% 5.01/5.27 thf(fact_4787_eq__abs__iff_H,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( abs_abs_real @ B ) )
% 5.01/5.27 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.27 & ( ( B = A )
% 5.01/5.27 | ( B
% 5.01/5.27 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % eq_abs_iff'
% 5.01/5.27 thf(fact_4788_eq__abs__iff_H,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( abs_abs_Code_integer @ B ) )
% 5.01/5.27 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 & ( ( B = A )
% 5.01/5.27 | ( B
% 5.01/5.27 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % eq_abs_iff'
% 5.01/5.27 thf(fact_4789_eq__abs__iff_H,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( abs_abs_rat @ B ) )
% 5.01/5.27 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.27 & ( ( B = A )
% 5.01/5.27 | ( B
% 5.01/5.27 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % eq_abs_iff'
% 5.01/5.27 thf(fact_4790_eq__abs__iff_H,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( abs_abs_int @ B ) )
% 5.01/5.27 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.01/5.27 & ( ( B = A )
% 5.01/5.27 | ( B
% 5.01/5.27 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % eq_abs_iff'
% 5.01/5.27 thf(fact_4791_abs__eq__iff_H,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( ( abs_abs_real @ A )
% 5.01/5.27 = B )
% 5.01/5.27 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.27 & ( ( A = B )
% 5.01/5.27 | ( A
% 5.01/5.27 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff'
% 5.01/5.27 thf(fact_4792_abs__eq__iff_H,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = B )
% 5.01/5.27 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.01/5.27 & ( ( A = B )
% 5.01/5.27 | ( A
% 5.01/5.27 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff'
% 5.01/5.27 thf(fact_4793_abs__eq__iff_H,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( ( abs_abs_rat @ A )
% 5.01/5.27 = B )
% 5.01/5.27 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.27 & ( ( A = B )
% 5.01/5.27 | ( A
% 5.01/5.27 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff'
% 5.01/5.27 thf(fact_4794_abs__eq__iff_H,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ( abs_abs_int @ A )
% 5.01/5.27 = B )
% 5.01/5.27 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.27 & ( ( A = B )
% 5.01/5.27 | ( A
% 5.01/5.27 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_eq_iff'
% 5.01/5.27 thf(fact_4795_zero__le__power__abs,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_abs
% 5.01/5.27 thf(fact_4796_zero__le__power__abs,axiom,
% 5.01/5.27 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_abs
% 5.01/5.27 thf(fact_4797_zero__le__power__abs,axiom,
% 5.01/5.27 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_abs
% 5.01/5.27 thf(fact_4798_zero__le__power__abs,axiom,
% 5.01/5.27 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_abs
% 5.01/5.27 thf(fact_4799_abs__div__pos,axiom,
% 5.01/5.27 ! [Y: real,X2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.27 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y )
% 5.01/5.27 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_div_pos
% 5.01/5.27 thf(fact_4800_abs__div__pos,axiom,
% 5.01/5.27 ! [Y: rat,X2: rat] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.01/5.27 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y )
% 5.01/5.27 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_div_pos
% 5.01/5.27 thf(fact_4801_abs__of__neg,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.27 => ( ( abs_abs_real @ A )
% 5.01/5.27 = ( uminus_uminus_real @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_neg
% 5.01/5.27 thf(fact_4802_abs__of__neg,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.27 => ( ( abs_abs_int @ A )
% 5.01/5.27 = ( uminus_uminus_int @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_neg
% 5.01/5.27 thf(fact_4803_abs__of__neg,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.01/5.27 => ( ( abs_abs_Code_integer @ A )
% 5.01/5.27 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_neg
% 5.01/5.27 thf(fact_4804_abs__of__neg,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.27 => ( ( abs_abs_rat @ A )
% 5.01/5.27 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_of_neg
% 5.01/5.27 thf(fact_4805_abs__if,axiom,
% 5.01/5.27 ( abs_abs_real
% 5.01/5.27 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if
% 5.01/5.27 thf(fact_4806_abs__if,axiom,
% 5.01/5.27 ( abs_abs_int
% 5.01/5.27 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if
% 5.01/5.27 thf(fact_4807_abs__if,axiom,
% 5.01/5.27 ( abs_abs_Code_integer
% 5.01/5.27 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if
% 5.01/5.27 thf(fact_4808_abs__if,axiom,
% 5.01/5.27 ( abs_abs_rat
% 5.01/5.27 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if
% 5.01/5.27 thf(fact_4809_abs__if__raw,axiom,
% 5.01/5.27 ( abs_abs_real
% 5.01/5.27 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if_raw
% 5.01/5.27 thf(fact_4810_abs__if__raw,axiom,
% 5.01/5.27 ( abs_abs_int
% 5.01/5.27 = ( ^ [A4: int] : ( if_int @ ( ord_less_int @ A4 @ zero_zero_int ) @ ( uminus_uminus_int @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if_raw
% 5.01/5.27 thf(fact_4811_abs__if__raw,axiom,
% 5.01/5.27 ( abs_abs_Code_integer
% 5.01/5.27 = ( ^ [A4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if_raw
% 5.01/5.27 thf(fact_4812_abs__if__raw,axiom,
% 5.01/5.27 ( abs_abs_rat
% 5.01/5.27 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_if_raw
% 5.01/5.27 thf(fact_4813_abs__diff__triangle__ineq,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_triangle_ineq
% 5.01/5.27 thf(fact_4814_abs__diff__triangle__ineq,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_triangle_ineq
% 5.01/5.27 thf(fact_4815_abs__diff__triangle__ineq,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_triangle_ineq
% 5.01/5.27 thf(fact_4816_abs__diff__triangle__ineq,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_triangle_ineq
% 5.01/5.27 thf(fact_4817_abs__triangle__ineq4,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq4
% 5.01/5.27 thf(fact_4818_abs__triangle__ineq4,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq4
% 5.01/5.27 thf(fact_4819_abs__triangle__ineq4,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq4
% 5.01/5.27 thf(fact_4820_abs__triangle__ineq4,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_triangle_ineq4
% 5.01/5.27 thf(fact_4821_abs__diff__le__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_le_iff
% 5.01/5.27 thf(fact_4822_abs__diff__le__iff,axiom,
% 5.01/5.27 ! [X2: real,A: real,R: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_le_iff
% 5.01/5.27 thf(fact_4823_abs__diff__le__iff,axiom,
% 5.01/5.27 ! [X2: rat,A: rat,R: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_le_iff
% 5.01/5.27 thf(fact_4824_abs__diff__le__iff,axiom,
% 5.01/5.27 ! [X2: int,A: int,R: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_le_iff
% 5.01/5.27 thf(fact_4825_abs__diff__less__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,A: code_integer,R: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_less_iff
% 5.01/5.27 thf(fact_4826_abs__diff__less__iff,axiom,
% 5.01/5.27 ! [X2: real,A: real,R: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_less_iff
% 5.01/5.27 thf(fact_4827_abs__diff__less__iff,axiom,
% 5.01/5.27 ! [X2: rat,A: rat,R: rat] :
% 5.01/5.27 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_less_iff
% 5.01/5.27 thf(fact_4828_abs__diff__less__iff,axiom,
% 5.01/5.27 ! [X2: int,A: int,R: int] :
% 5.01/5.27 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R )
% 5.01/5.27 = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X2 )
% 5.01/5.27 & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_diff_less_iff
% 5.01/5.27 thf(fact_4829_abs__real__def,axiom,
% 5.01/5.27 ( abs_abs_real
% 5.01/5.27 = ( ^ [A4: real] : ( if_real @ ( ord_less_real @ A4 @ zero_zero_real ) @ ( uminus_uminus_real @ A4 ) @ A4 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_real_def
% 5.01/5.27 thf(fact_4830_lemma__interval__lt,axiom,
% 5.01/5.27 ! [A: real,X2: real,B: real] :
% 5.01/5.27 ( ( ord_less_real @ A @ X2 )
% 5.01/5.27 => ( ( ord_less_real @ X2 @ B )
% 5.01/5.27 => ? [D2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.27 & ! [Y4: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D2 )
% 5.01/5.27 => ( ( ord_less_real @ A @ Y4 )
% 5.01/5.27 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % lemma_interval_lt
% 5.01/5.27 thf(fact_4831_sin__bound__lemma,axiom,
% 5.01/5.27 ! [X2: real,Y: real,U: real,V: real] :
% 5.01/5.27 ( ( X2 = Y )
% 5.01/5.27 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.01/5.27 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y ) ) @ V ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % sin_bound_lemma
% 5.01/5.27 thf(fact_4832_eval__nat__numeral_I2_J,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.01/5.27 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % eval_nat_numeral(2)
% 5.01/5.27 thf(fact_4833_tanh__real__gt__neg1,axiom,
% 5.01/5.27 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.01/5.27
% 5.01/5.27 % tanh_real_gt_neg1
% 5.01/5.27 thf(fact_4834_full__exhaustive__int_H_Ocases,axiom,
% 5.01/5.27 ! [X2: produc2285326912895808259nt_int] :
% 5.01/5.27 ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D2: int,I3: int] :
% 5.01/5.27 ( X2
% 5.01/5.27 != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D2 @ I3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % full_exhaustive_int'.cases
% 5.01/5.27 thf(fact_4835_exhaustive__int_H_Ocases,axiom,
% 5.01/5.27 ! [X2: produc7773217078559923341nt_int] :
% 5.01/5.27 ~ ! [F2: int > option6357759511663192854e_term,D2: int,I3: int] :
% 5.01/5.27 ( X2
% 5.01/5.27 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D2 @ I3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % exhaustive_int'.cases
% 5.01/5.27 thf(fact_4836_small__lazy_H_Ocases,axiom,
% 5.01/5.27 ! [X2: product_prod_int_int] :
% 5.01/5.27 ~ ! [D2: int,I3: int] :
% 5.01/5.27 ( X2
% 5.01/5.27 != ( product_Pair_int_int @ D2 @ I3 ) ) ).
% 5.01/5.27
% 5.01/5.27 % small_lazy'.cases
% 5.01/5.27 thf(fact_4837_abs__add__one__gt__zero,axiom,
% 5.01/5.27 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_add_one_gt_zero
% 5.01/5.27 thf(fact_4838_abs__add__one__gt__zero,axiom,
% 5.01/5.27 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_add_one_gt_zero
% 5.01/5.27 thf(fact_4839_abs__add__one__gt__zero,axiom,
% 5.01/5.27 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_add_one_gt_zero
% 5.01/5.27 thf(fact_4840_abs__add__one__gt__zero,axiom,
% 5.01/5.27 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_add_one_gt_zero
% 5.01/5.27 thf(fact_4841_one__plus__BitM,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.01/5.27 = ( bit0 @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % one_plus_BitM
% 5.01/5.27 thf(fact_4842_BitM__plus__one,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.01/5.27 = ( bit0 @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % BitM_plus_one
% 5.01/5.27 thf(fact_4843_lemma__interval,axiom,
% 5.01/5.27 ! [A: real,X2: real,B: real] :
% 5.01/5.27 ( ( ord_less_real @ A @ X2 )
% 5.01/5.27 => ( ( ord_less_real @ X2 @ B )
% 5.01/5.27 => ? [D2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.27 & ! [Y4: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ D2 )
% 5.01/5.27 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.01/5.27 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % lemma_interval
% 5.01/5.27 thf(fact_4844_norm__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % norm_triangle_ineq3
% 5.01/5.27 thf(fact_4845_norm__triangle__ineq3,axiom,
% 5.01/5.27 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % norm_triangle_ineq3
% 5.01/5.27 thf(fact_4846_numeral__BitM,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.01/5.27 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.01/5.27
% 5.01/5.27 % numeral_BitM
% 5.01/5.27 thf(fact_4847_numeral__BitM,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.01/5.27 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % numeral_BitM
% 5.01/5.27 thf(fact_4848_numeral__BitM,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.01/5.27 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % numeral_BitM
% 5.01/5.27 thf(fact_4849_numeral__BitM,axiom,
% 5.01/5.27 ! [N: num] :
% 5.01/5.27 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.01/5.27 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % numeral_BitM
% 5.01/5.27 thf(fact_4850_abs__le__square__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y ) )
% 5.01/5.27 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_square_iff
% 5.01/5.27 thf(fact_4851_abs__le__square__iff,axiom,
% 5.01/5.27 ! [X2: real,Y: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y ) )
% 5.01/5.27 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_square_iff
% 5.01/5.27 thf(fact_4852_abs__le__square__iff,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y ) )
% 5.01/5.27 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_square_iff
% 5.01/5.27 thf(fact_4853_abs__le__square__iff,axiom,
% 5.01/5.27 ! [X2: int,Y: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y ) )
% 5.01/5.27 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_le_square_iff
% 5.01/5.27 thf(fact_4854_abs__square__eq__1,axiom,
% 5.01/5.27 ! [X2: code_integer] :
% 5.01/5.27 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = one_one_Code_integer )
% 5.01/5.27 = ( ( abs_abs_Code_integer @ X2 )
% 5.01/5.27 = one_one_Code_integer ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_eq_1
% 5.01/5.27 thf(fact_4855_abs__square__eq__1,axiom,
% 5.01/5.27 ! [X2: rat] :
% 5.01/5.27 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = one_one_rat )
% 5.01/5.27 = ( ( abs_abs_rat @ X2 )
% 5.01/5.27 = one_one_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_eq_1
% 5.01/5.27 thf(fact_4856_abs__square__eq__1,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = one_one_real )
% 5.01/5.27 = ( ( abs_abs_real @ X2 )
% 5.01/5.27 = one_one_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_eq_1
% 5.01/5.27 thf(fact_4857_abs__square__eq__1,axiom,
% 5.01/5.27 ! [X2: int] :
% 5.01/5.27 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = one_one_int )
% 5.01/5.27 = ( ( abs_abs_int @ X2 )
% 5.01/5.27 = one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_eq_1
% 5.01/5.27 thf(fact_4858_power2__le__iff__abs__le,axiom,
% 5.01/5.27 ! [Y: code_integer,X2: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.01/5.27 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_le_iff_abs_le
% 5.01/5.27 thf(fact_4859_power2__le__iff__abs__le,axiom,
% 5.01/5.27 ! [Y: real,X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.27 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_le_iff_abs_le
% 5.01/5.27 thf(fact_4860_power2__le__iff__abs__le,axiom,
% 5.01/5.27 ! [Y: rat,X2: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.01/5.27 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_le_iff_abs_le
% 5.01/5.27 thf(fact_4861_power2__le__iff__abs__le,axiom,
% 5.01/5.27 ! [Y: int,X2: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.27 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power2_le_iff_abs_le
% 5.01/5.27 thf(fact_4862_abs__square__le__1,axiom,
% 5.01/5.27 ! [X2: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.01/5.27 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_le_1
% 5.01/5.27 thf(fact_4863_abs__square__le__1,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.01/5.27 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_le_1
% 5.01/5.27 thf(fact_4864_abs__square__le__1,axiom,
% 5.01/5.27 ! [X2: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.01/5.27 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_le_1
% 5.01/5.27 thf(fact_4865_abs__square__le__1,axiom,
% 5.01/5.27 ! [X2: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.01/5.27 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_le_1
% 5.01/5.27 thf(fact_4866_abs__square__less__1,axiom,
% 5.01/5.27 ! [X2: code_integer] :
% 5.01/5.27 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.01/5.27 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_less_1
% 5.01/5.27 thf(fact_4867_abs__square__less__1,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.01/5.27 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_less_1
% 5.01/5.27 thf(fact_4868_abs__square__less__1,axiom,
% 5.01/5.27 ! [X2: rat] :
% 5.01/5.27 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.01/5.27 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_less_1
% 5.01/5.27 thf(fact_4869_abs__square__less__1,axiom,
% 5.01/5.27 ! [X2: int] :
% 5.01/5.27 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.01/5.27 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_square_less_1
% 5.01/5.27 thf(fact_4870_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.27 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.27 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.01/5.27 thf(fact_4871_abs__sqrt__wlog,axiom,
% 5.01/5.27 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.01/5.27 ( ! [X4: code_integer] :
% 5.01/5.27 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.01/5.27 => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.27 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_sqrt_wlog
% 5.01/5.27 thf(fact_4872_abs__sqrt__wlog,axiom,
% 5.01/5.27 ! [P: real > real > $o,X2: real] :
% 5.01/5.27 ( ! [X4: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.01/5.27 => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.27 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_sqrt_wlog
% 5.01/5.27 thf(fact_4873_abs__sqrt__wlog,axiom,
% 5.01/5.27 ! [P: rat > rat > $o,X2: rat] :
% 5.01/5.27 ( ! [X4: rat] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.01/5.27 => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.27 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_sqrt_wlog
% 5.01/5.27 thf(fact_4874_abs__sqrt__wlog,axiom,
% 5.01/5.27 ! [P: int > int > $o,X2: int] :
% 5.01/5.27 ( ! [X4: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.01/5.27 => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.27 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_sqrt_wlog
% 5.01/5.27 thf(fact_4875_arctan__double,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.27 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.01/5.27 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % arctan_double
% 5.01/5.27 thf(fact_4876_gcd__nat__induct,axiom,
% 5.01/5.27 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.01/5.27 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.01/5.27 => ( ! [M4: nat,N3: nat] :
% 5.01/5.27 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.27 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.01/5.27 => ( P @ M4 @ N3 ) ) )
% 5.01/5.27 => ( P @ M @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat_induct
% 5.01/5.27 thf(fact_4877_concat__bit__Suc,axiom,
% 5.01/5.27 ! [N: nat,K: int,L: int] :
% 5.01/5.27 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.01/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % concat_bit_Suc
% 5.01/5.27 thf(fact_4878_option_Osize__gen_I2_J,axiom,
% 5.01/5.27 ! [X2: product_prod_nat_nat > nat,X23: product_prod_nat_nat] :
% 5.01/5.27 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X23 ) )
% 5.01/5.27 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % option.size_gen(2)
% 5.01/5.27 thf(fact_4879_option_Osize__gen_I2_J,axiom,
% 5.01/5.27 ! [X2: num > nat,X23: num] :
% 5.01/5.27 ( ( size_option_num @ X2 @ ( some_num @ X23 ) )
% 5.01/5.27 = ( plus_plus_nat @ ( X2 @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % option.size_gen(2)
% 5.01/5.27 thf(fact_4880_even__succ__mod__exp,axiom,
% 5.01/5.27 ! [A: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_mod_exp
% 5.01/5.27 thf(fact_4881_even__succ__mod__exp,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_mod_exp
% 5.01/5.27 thf(fact_4882_even__succ__mod__exp,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_mod_exp
% 5.01/5.27 thf(fact_4883_even__succ__div__exp,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_exp
% 5.01/5.27 thf(fact_4884_even__succ__div__exp,axiom,
% 5.01/5.27 ! [A: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_exp
% 5.01/5.27 thf(fact_4885_even__succ__div__exp,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.27 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_exp
% 5.01/5.27 thf(fact_4886_zdvd1__eq,axiom,
% 5.01/5.27 ! [X2: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.01/5.27 = ( ( abs_abs_int @ X2 )
% 5.01/5.27 = one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % zdvd1_eq
% 5.01/5.27 thf(fact_4887_nat__dvd__1__iff__1,axiom,
% 5.01/5.27 ! [M: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.01/5.27 = ( M = one_one_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % nat_dvd_1_iff_1
% 5.01/5.27 thf(fact_4888_int__dvd__int__iff,axiom,
% 5.01/5.27 ! [M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % int_dvd_int_iff
% 5.01/5.27 thf(fact_4889_dvd__0__right,axiom,
% 5.01/5.27 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4890_dvd__0__right,axiom,
% 5.01/5.27 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4891_dvd__0__right,axiom,
% 5.01/5.27 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4892_dvd__0__right,axiom,
% 5.01/5.27 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4893_dvd__0__right,axiom,
% 5.01/5.27 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4894_dvd__0__right,axiom,
% 5.01/5.27 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_right
% 5.01/5.27 thf(fact_4895_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4896_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.01/5.27 = ( A = zero_zero_complex ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4897_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.01/5.27 = ( A = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4898_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.01/5.27 = ( A = zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4899_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.01/5.27 = ( A = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4900_dvd__0__left__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.01/5.27 = ( A = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left_iff
% 5.01/5.27 thf(fact_4901_dvd__add__triv__right__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_right_iff
% 5.01/5.27 thf(fact_4902_dvd__add__triv__right__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_right_iff
% 5.01/5.27 thf(fact_4903_dvd__add__triv__right__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_right_iff
% 5.01/5.27 thf(fact_4904_dvd__add__triv__right__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_right_iff
% 5.01/5.27 thf(fact_4905_dvd__add__triv__right__iff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_right_iff
% 5.01/5.27 thf(fact_4906_dvd__add__triv__left__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_left_iff
% 5.01/5.27 thf(fact_4907_dvd__add__triv__left__iff,axiom,
% 5.01/5.27 ! [A: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_left_iff
% 5.01/5.27 thf(fact_4908_dvd__add__triv__left__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_left_iff
% 5.01/5.27 thf(fact_4909_dvd__add__triv__left__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_left_iff
% 5.01/5.27 thf(fact_4910_dvd__add__triv__left__iff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_triv_left_iff
% 5.01/5.27 thf(fact_4911_dvd__1__left,axiom,
% 5.01/5.27 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_1_left
% 5.01/5.27 thf(fact_4912_dvd__1__iff__1,axiom,
% 5.01/5.27 ! [M: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.01/5.27 = ( M
% 5.01/5.27 = ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_1_iff_1
% 5.01/5.27 thf(fact_4913_div__dvd__div,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_dvd_div
% 5.01/5.27 thf(fact_4914_div__dvd__div,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_dvd_div
% 5.01/5.27 thf(fact_4915_div__dvd__div,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_dvd_div
% 5.01/5.27 thf(fact_4916_minus__dvd__iff,axiom,
% 5.01/5.27 ! [X2: real,Y: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X2 ) @ Y )
% 5.01/5.27 = ( dvd_dvd_real @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % minus_dvd_iff
% 5.01/5.27 thf(fact_4917_minus__dvd__iff,axiom,
% 5.01/5.27 ! [X2: int,Y: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X2 ) @ Y )
% 5.01/5.27 = ( dvd_dvd_int @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % minus_dvd_iff
% 5.01/5.27 thf(fact_4918_minus__dvd__iff,axiom,
% 5.01/5.27 ! [X2: complex,Y: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y )
% 5.01/5.27 = ( dvd_dvd_complex @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % minus_dvd_iff
% 5.01/5.27 thf(fact_4919_minus__dvd__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ Y )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % minus_dvd_iff
% 5.01/5.27 thf(fact_4920_minus__dvd__iff,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X2 ) @ Y )
% 5.01/5.27 = ( dvd_dvd_rat @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % minus_dvd_iff
% 5.01/5.27 thf(fact_4921_dvd__minus__iff,axiom,
% 5.01/5.27 ! [X2: real,Y: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ X2 @ ( uminus_uminus_real @ Y ) )
% 5.01/5.27 = ( dvd_dvd_real @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_minus_iff
% 5.01/5.27 thf(fact_4922_dvd__minus__iff,axiom,
% 5.01/5.27 ! [X2: int,Y: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ X2 @ ( uminus_uminus_int @ Y ) )
% 5.01/5.27 = ( dvd_dvd_int @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_minus_iff
% 5.01/5.27 thf(fact_4923_dvd__minus__iff,axiom,
% 5.01/5.27 ! [X2: complex,Y: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ X2 @ ( uminus1482373934393186551omplex @ Y ) )
% 5.01/5.27 = ( dvd_dvd_complex @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_minus_iff
% 5.01/5.27 thf(fact_4924_dvd__minus__iff,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ X2 @ ( uminus1351360451143612070nteger @ Y ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_minus_iff
% 5.01/5.27 thf(fact_4925_dvd__minus__iff,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ X2 @ ( uminus_uminus_rat @ Y ) )
% 5.01/5.27 = ( dvd_dvd_rat @ X2 @ Y ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_minus_iff
% 5.01/5.27 thf(fact_4926_abs__dvd__iff,axiom,
% 5.01/5.27 ! [M: real,K: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.01/5.27 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_dvd_iff
% 5.01/5.27 thf(fact_4927_abs__dvd__iff,axiom,
% 5.01/5.27 ! [M: int,K: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.01/5.27 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_dvd_iff
% 5.01/5.27 thf(fact_4928_abs__dvd__iff,axiom,
% 5.01/5.27 ! [M: code_integer,K: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_dvd_iff
% 5.01/5.27 thf(fact_4929_abs__dvd__iff,axiom,
% 5.01/5.27 ! [M: rat,K: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.01/5.27 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_dvd_iff
% 5.01/5.27 thf(fact_4930_dvd__abs__iff,axiom,
% 5.01/5.27 ! [M: real,K: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.01/5.27 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_abs_iff
% 5.01/5.27 thf(fact_4931_dvd__abs__iff,axiom,
% 5.01/5.27 ! [M: int,K: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.01/5.27 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_abs_iff
% 5.01/5.27 thf(fact_4932_dvd__abs__iff,axiom,
% 5.01/5.27 ! [M: code_integer,K: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_abs_iff
% 5.01/5.27 thf(fact_4933_dvd__abs__iff,axiom,
% 5.01/5.27 ! [M: rat,K: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.01/5.27 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_abs_iff
% 5.01/5.27 thf(fact_4934_nat__mult__dvd__cancel__disj,axiom,
% 5.01/5.27 ! [K: nat,M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.27 = ( ( K = zero_zero_nat )
% 5.01/5.27 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % nat_mult_dvd_cancel_disj
% 5.01/5.27 thf(fact_4935_arctan__zero__zero,axiom,
% 5.01/5.27 ( ( arctan @ zero_zero_real )
% 5.01/5.27 = zero_zero_real ) ).
% 5.01/5.27
% 5.01/5.27 % arctan_zero_zero
% 5.01/5.27 thf(fact_4936_arctan__eq__zero__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ( arctan @ X2 )
% 5.01/5.27 = zero_zero_real )
% 5.01/5.27 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % arctan_eq_zero_iff
% 5.01/5.27 thf(fact_4937_concat__bit__0,axiom,
% 5.01/5.27 ! [K: int,L: int] :
% 5.01/5.27 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.01/5.27 = L ) ).
% 5.01/5.27
% 5.01/5.27 % concat_bit_0
% 5.01/5.27 thf(fact_4938_dvd__mult__cancel__left,axiom,
% 5.01/5.27 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.01/5.27 = ( ( C = zero_z3403309356797280102nteger )
% 5.01/5.27 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_left
% 5.01/5.27 thf(fact_4939_dvd__mult__cancel__left,axiom,
% 5.01/5.27 ! [C: real,A: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.01/5.27 = ( ( C = zero_zero_real )
% 5.01/5.27 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_left
% 5.01/5.27 thf(fact_4940_dvd__mult__cancel__left,axiom,
% 5.01/5.27 ! [C: rat,A: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.01/5.27 = ( ( C = zero_zero_rat )
% 5.01/5.27 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_left
% 5.01/5.27 thf(fact_4941_dvd__mult__cancel__left,axiom,
% 5.01/5.27 ! [C: int,A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.01/5.27 = ( ( C = zero_zero_int )
% 5.01/5.27 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_left
% 5.01/5.27 thf(fact_4942_dvd__mult__cancel__left,axiom,
% 5.01/5.27 ! [C: complex,A: complex,B: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.01/5.27 = ( ( C = zero_zero_complex )
% 5.01/5.27 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_left
% 5.01/5.27 thf(fact_4943_dvd__mult__cancel__right,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.27 = ( ( C = zero_z3403309356797280102nteger )
% 5.01/5.27 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_right
% 5.01/5.27 thf(fact_4944_dvd__mult__cancel__right,axiom,
% 5.01/5.27 ! [A: real,C: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.01/5.27 = ( ( C = zero_zero_real )
% 5.01/5.27 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_right
% 5.01/5.27 thf(fact_4945_dvd__mult__cancel__right,axiom,
% 5.01/5.27 ! [A: rat,C: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.01/5.27 = ( ( C = zero_zero_rat )
% 5.01/5.27 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_right
% 5.01/5.27 thf(fact_4946_dvd__mult__cancel__right,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.01/5.27 = ( ( C = zero_zero_int )
% 5.01/5.27 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_right
% 5.01/5.27 thf(fact_4947_dvd__mult__cancel__right,axiom,
% 5.01/5.27 ! [A: complex,C: complex,B: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.01/5.27 = ( ( C = zero_zero_complex )
% 5.01/5.27 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_cancel_right
% 5.01/5.27 thf(fact_4948_dvd__times__left__cancel__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_left_cancel_iff
% 5.01/5.27 thf(fact_4949_dvd__times__left__cancel__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( A != zero_zero_nat )
% 5.01/5.27 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.01/5.27 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_left_cancel_iff
% 5.01/5.27 thf(fact_4950_dvd__times__left__cancel__iff,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( A != zero_zero_int )
% 5.01/5.27 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.01/5.27 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_left_cancel_iff
% 5.01/5.27 thf(fact_4951_dvd__times__right__cancel__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_right_cancel_iff
% 5.01/5.27 thf(fact_4952_dvd__times__right__cancel__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( A != zero_zero_nat )
% 5.01/5.27 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_right_cancel_iff
% 5.01/5.27 thf(fact_4953_dvd__times__right__cancel__iff,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( A != zero_zero_int )
% 5.01/5.27 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.01/5.27 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_times_right_cancel_iff
% 5.01/5.27 thf(fact_4954_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4955_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: real,C: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4956_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: rat,C: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4957_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: nat,C: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4958_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4959_dvd__add__times__triv__left__iff,axiom,
% 5.01/5.27 ! [A: complex,C: complex,B: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 5.01/5.27 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_left_iff
% 5.01/5.27 thf(fact_4960_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4961_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4962_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4963_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4964_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4965_dvd__add__times__triv__right__iff,axiom,
% 5.01/5.27 ! [A: complex,B: complex,C: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 5.01/5.27 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_times_triv_right_iff
% 5.01/5.27 thf(fact_4966_unit__prod,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_prod
% 5.01/5.27 thf(fact_4967_unit__prod,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.27 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_prod
% 5.01/5.27 thf(fact_4968_unit__prod,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.27 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_prod
% 5.01/5.27 thf(fact_4969_dvd__div__mult__self,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_div_mult_self
% 5.01/5.27 thf(fact_4970_dvd__div__mult__self,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_div_mult_self
% 5.01/5.27 thf(fact_4971_dvd__div__mult__self,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_div_mult_self
% 5.01/5.27 thf(fact_4972_dvd__mult__div__cancel,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_div_cancel
% 5.01/5.27 thf(fact_4973_dvd__mult__div__cancel,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_div_cancel
% 5.01/5.27 thf(fact_4974_dvd__mult__div__cancel,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_div_cancel
% 5.01/5.27 thf(fact_4975_div__add,axiom,
% 5.01/5.27 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.01/5.27 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_add
% 5.01/5.27 thf(fact_4976_div__add,axiom,
% 5.01/5.27 ! [C: nat,A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ C @ A )
% 5.01/5.27 => ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.01/5.27 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_add
% 5.01/5.27 thf(fact_4977_div__add,axiom,
% 5.01/5.27 ! [C: int,A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ C @ A )
% 5.01/5.27 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.01/5.27 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_add
% 5.01/5.27 thf(fact_4978_unit__div__1__div__1,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_div_1
% 5.01/5.27 thf(fact_4979_unit__div__1__div__1,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_div_1
% 5.01/5.27 thf(fact_4980_unit__div__1__div__1,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_div_1
% 5.01/5.27 thf(fact_4981_unit__div__1__unit,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_unit
% 5.01/5.27 thf(fact_4982_unit__div__1__unit,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_unit
% 5.01/5.27 thf(fact_4983_unit__div__1__unit,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_1_unit
% 5.01/5.27 thf(fact_4984_unit__div,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div
% 5.01/5.27 thf(fact_4985_unit__div,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.27 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div
% 5.01/5.27 thf(fact_4986_unit__div,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.27 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div
% 5.01/5.27 thf(fact_4987_div__diff,axiom,
% 5.01/5.27 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.01/5.27 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_diff
% 5.01/5.27 thf(fact_4988_div__diff,axiom,
% 5.01/5.27 ! [C: int,A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ C @ A )
% 5.01/5.27 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.27 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.01/5.27 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_diff
% 5.01/5.27 thf(fact_4989_dvd__imp__mod__0,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( modulo_modulo_nat @ B @ A )
% 5.01/5.27 = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_imp_mod_0
% 5.01/5.27 thf(fact_4990_dvd__imp__mod__0,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( modulo_modulo_int @ B @ A )
% 5.01/5.27 = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_imp_mod_0
% 5.01/5.27 thf(fact_4991_dvd__imp__mod__0,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.01/5.27 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_imp_mod_0
% 5.01/5.27 thf(fact_4992_zabs__less__one__iff,axiom,
% 5.01/5.27 ! [Z: int] :
% 5.01/5.27 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.01/5.27 = ( Z = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % zabs_less_one_iff
% 5.01/5.27 thf(fact_4993_zero__less__arctan__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.01/5.27 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_arctan_iff
% 5.01/5.27 thf(fact_4994_arctan__less__zero__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.01/5.27 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % arctan_less_zero_iff
% 5.01/5.27 thf(fact_4995_arctan__le__zero__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.01/5.27 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % arctan_le_zero_iff
% 5.01/5.27 thf(fact_4996_zero__le__arctan__iff,axiom,
% 5.01/5.27 ! [X2: real] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.01/5.27 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_arctan_iff
% 5.01/5.27 thf(fact_4997_concat__bit__nonnegative__iff,axiom,
% 5.01/5.27 ! [N: nat,K: int,L: int] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.01/5.27 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.01/5.27
% 5.01/5.27 % concat_bit_nonnegative_iff
% 5.01/5.27 thf(fact_4998_concat__bit__negative__iff,axiom,
% 5.01/5.27 ! [N: nat,K: int,L: int] :
% 5.01/5.27 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.01/5.27 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % concat_bit_negative_iff
% 5.01/5.27 thf(fact_4999_unit__div__mult__self,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_mult_self
% 5.01/5.27 thf(fact_5000_unit__div__mult__self,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_mult_self
% 5.01/5.27 thf(fact_5001_unit__div__mult__self,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.01/5.27 = B ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_div_mult_self
% 5.01/5.27 thf(fact_5002_unit__mult__div__div,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.27 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.01/5.27 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_mult_div_div
% 5.01/5.27 thf(fact_5003_unit__mult__div__div,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.27 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.01/5.27 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_mult_div_div
% 5.01/5.27 thf(fact_5004_unit__mult__div__div,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.27 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.01/5.27 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_mult_div_div
% 5.01/5.27 thf(fact_5005_even__Suc,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_Suc
% 5.01/5.27 thf(fact_5006_even__Suc__Suc__iff,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_Suc_Suc_iff
% 5.01/5.27 thf(fact_5007_pow__divides__pow__iff,axiom,
% 5.01/5.27 ! [N: nat,A: nat,B: nat] :
% 5.01/5.27 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % pow_divides_pow_iff
% 5.01/5.27 thf(fact_5008_pow__divides__pow__iff,axiom,
% 5.01/5.27 ! [N: nat,A: int,B: int] :
% 5.01/5.27 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.27 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % pow_divides_pow_iff
% 5.01/5.27 thf(fact_5009_even__mult__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mult_iff
% 5.01/5.27 thf(fact_5010_even__mult__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mult_iff
% 5.01/5.27 thf(fact_5011_even__mult__iff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mult_iff
% 5.01/5.27 thf(fact_5012_odd__add,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.01/5.27 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.27 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_add
% 5.01/5.27 thf(fact_5013_odd__add,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.01/5.27 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.27 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_add
% 5.01/5.27 thf(fact_5014_odd__add,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.01/5.27 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.27 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_add
% 5.01/5.27 thf(fact_5015_even__add,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_add
% 5.01/5.27 thf(fact_5016_even__add,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_add
% 5.01/5.27 thf(fact_5017_even__add,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.01/5.27 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_add
% 5.01/5.27 thf(fact_5018_power__minus__odd,axiom,
% 5.01/5.27 ! [N: nat,A: real] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.01/5.27 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_minus_odd
% 5.01/5.27 thf(fact_5019_power__minus__odd,axiom,
% 5.01/5.27 ! [N: nat,A: int] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.01/5.27 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_minus_odd
% 5.01/5.27 thf(fact_5020_power__minus__odd,axiom,
% 5.01/5.27 ! [N: nat,A: complex] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.01/5.27 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_minus_odd
% 5.01/5.27 thf(fact_5021_power__minus__odd,axiom,
% 5.01/5.27 ! [N: nat,A: code_integer] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.01/5.27 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_minus_odd
% 5.01/5.27 thf(fact_5022_power__minus__odd,axiom,
% 5.01/5.27 ! [N: nat,A: rat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.01/5.27 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_minus_odd
% 5.01/5.27 thf(fact_5023_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.01/5.27 ! [N: nat,A: real] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.01/5.27 = ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % Parity.ring_1_class.power_minus_even
% 5.01/5.27 thf(fact_5024_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.01/5.27 ! [N: nat,A: int] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.01/5.27 = ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % Parity.ring_1_class.power_minus_even
% 5.01/5.27 thf(fact_5025_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.01/5.27 ! [N: nat,A: complex] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.01/5.27 = ( power_power_complex @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % Parity.ring_1_class.power_minus_even
% 5.01/5.27 thf(fact_5026_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.01/5.27 ! [N: nat,A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.01/5.27 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % Parity.ring_1_class.power_minus_even
% 5.01/5.27 thf(fact_5027_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.01/5.27 ! [N: nat,A: rat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.01/5.27 = ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % Parity.ring_1_class.power_minus_even
% 5.01/5.27 thf(fact_5028_even__mod__2__iff,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mod_2_iff
% 5.01/5.27 thf(fact_5029_even__mod__2__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mod_2_iff
% 5.01/5.27 thf(fact_5030_even__mod__2__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_mod_2_iff
% 5.01/5.27 thf(fact_5031_power__even__abs__numeral,axiom,
% 5.01/5.27 ! [W: num,A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_even_abs_numeral
% 5.01/5.27 thf(fact_5032_power__even__abs__numeral,axiom,
% 5.01/5.27 ! [W: num,A: rat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_even_abs_numeral
% 5.01/5.27 thf(fact_5033_power__even__abs__numeral,axiom,
% 5.01/5.27 ! [W: num,A: real] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_even_abs_numeral
% 5.01/5.27 thf(fact_5034_power__even__abs__numeral,axiom,
% 5.01/5.27 ! [W: num,A: int] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_even_abs_numeral
% 5.01/5.27 thf(fact_5035_even__Suc__div__two,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_Suc_div_two
% 5.01/5.27 thf(fact_5036_odd__Suc__div__two,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_Suc_div_two
% 5.01/5.27 thf(fact_5037_dvd__numeral__simp,axiom,
% 5.01/5.27 ! [M: num,N: num] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.27 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_numeral_simp
% 5.01/5.27 thf(fact_5038_dvd__numeral__simp,axiom,
% 5.01/5.27 ! [M: num,N: num] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.27 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_numeral_simp
% 5.01/5.27 thf(fact_5039_dvd__numeral__simp,axiom,
% 5.01/5.27 ! [M: num,N: num] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.01/5.27 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_numeral_simp
% 5.01/5.27 thf(fact_5040_zero__le__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: real,W: num] :
% 5.01/5.27 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_eq_numeral
% 5.01/5.27 thf(fact_5041_zero__le__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: rat,W: num] :
% 5.01/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_eq_numeral
% 5.01/5.27 thf(fact_5042_zero__le__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: int,W: num] :
% 5.01/5.27 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_le_power_eq_numeral
% 5.01/5.27 thf(fact_5043_power__less__zero__eq,axiom,
% 5.01/5.27 ! [A: real,N: nat] :
% 5.01/5.27 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq
% 5.01/5.27 thf(fact_5044_power__less__zero__eq,axiom,
% 5.01/5.27 ! [A: rat,N: nat] :
% 5.01/5.27 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq
% 5.01/5.27 thf(fact_5045_power__less__zero__eq,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq
% 5.01/5.27 thf(fact_5046_power__less__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: real,W: num] :
% 5.01/5.27 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq_numeral
% 5.01/5.27 thf(fact_5047_power__less__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: rat,W: num] :
% 5.01/5.27 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq_numeral
% 5.01/5.27 thf(fact_5048_power__less__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: int,W: num] :
% 5.01/5.27 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_less_zero_eq_numeral
% 5.01/5.27 thf(fact_5049_even__plus__one__iff,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.01/5.27 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_plus_one_iff
% 5.01/5.27 thf(fact_5050_even__plus__one__iff,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.01/5.27 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_plus_one_iff
% 5.01/5.27 thf(fact_5051_even__plus__one__iff,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.01/5.27 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_plus_one_iff
% 5.01/5.27 thf(fact_5052_even__diff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_diff
% 5.01/5.27 thf(fact_5053_even__diff,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.01/5.27 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_diff
% 5.01/5.27 thf(fact_5054_neg__one__odd__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.01/5.27 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_odd_power
% 5.01/5.27 thf(fact_5055_neg__one__odd__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.01/5.27 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_odd_power
% 5.01/5.27 thf(fact_5056_neg__one__odd__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.01/5.27 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_odd_power
% 5.01/5.27 thf(fact_5057_neg__one__odd__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.01/5.27 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_odd_power
% 5.01/5.27 thf(fact_5058_neg__one__odd__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.01/5.27 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_odd_power
% 5.01/5.27 thf(fact_5059_neg__one__even__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.01/5.27 = one_one_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_even_power
% 5.01/5.27 thf(fact_5060_neg__one__even__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.01/5.27 = one_one_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_even_power
% 5.01/5.27 thf(fact_5061_neg__one__even__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.01/5.27 = one_one_complex ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_even_power
% 5.01/5.27 thf(fact_5062_neg__one__even__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.01/5.27 = one_one_Code_integer ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_even_power
% 5.01/5.27 thf(fact_5063_neg__one__even__power,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.01/5.27 = one_one_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % neg_one_even_power
% 5.01/5.27 thf(fact_5064_even__of__nat,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_of_nat
% 5.01/5.27 thf(fact_5065_even__of__nat,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_of_nat
% 5.01/5.27 thf(fact_5066_even__of__nat,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_of_nat
% 5.01/5.27 thf(fact_5067_odd__Suc__minus__one,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.01/5.27 = N ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_Suc_minus_one
% 5.01/5.27 thf(fact_5068_even__diff__nat,axiom,
% 5.01/5.27 ! [M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.27 = ( ( ord_less_nat @ M @ N )
% 5.01/5.27 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_diff_nat
% 5.01/5.27 thf(fact_5069_zero__less__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: real,W: num] :
% 5.01/5.27 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( ( numeral_numeral_nat @ W )
% 5.01/5.27 = zero_zero_nat )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A != zero_zero_real ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_eq_numeral
% 5.01/5.27 thf(fact_5070_zero__less__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: rat,W: num] :
% 5.01/5.27 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( ( numeral_numeral_nat @ W )
% 5.01/5.27 = zero_zero_nat )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A != zero_zero_rat ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_eq_numeral
% 5.01/5.27 thf(fact_5071_zero__less__power__eq__numeral,axiom,
% 5.01/5.27 ! [A: int,W: num] :
% 5.01/5.27 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.01/5.27 = ( ( ( numeral_numeral_nat @ W )
% 5.01/5.27 = zero_zero_nat )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A != zero_zero_int ) )
% 5.01/5.27 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % zero_less_power_eq_numeral
% 5.01/5.27 thf(fact_5072_even__succ__div__2,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_2
% 5.01/5.27 thf(fact_5073_even__succ__div__2,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_2
% 5.01/5.27 thf(fact_5074_even__succ__div__2,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_2
% 5.01/5.27 thf(fact_5075_odd__succ__div__two,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_succ_div_two
% 5.01/5.27 thf(fact_5076_odd__succ__div__two,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_succ_div_two
% 5.01/5.27 thf(fact_5077_odd__succ__div__two,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_succ_div_two
% 5.01/5.27 thf(fact_5078_even__succ__div__two,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_two
% 5.01/5.27 thf(fact_5079_even__succ__div__two,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_two
% 5.01/5.27 thf(fact_5080_even__succ__div__two,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.27 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_succ_div_two
% 5.01/5.27 thf(fact_5081_even__power,axiom,
% 5.01/5.27 ! [A: code_integer,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.01/5.27 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_power
% 5.01/5.27 thf(fact_5082_even__power,axiom,
% 5.01/5.27 ! [A: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.01/5.27 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_power
% 5.01/5.27 thf(fact_5083_even__power,axiom,
% 5.01/5.27 ! [A: int,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.01/5.27 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % even_power
% 5.01/5.27 thf(fact_5084_odd__two__times__div__two__nat,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.27 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.27 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_two_times_div_two_nat
% 5.01/5.27 thf(fact_5085_odd__two__times__div__two__succ,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_two_times_div_two_succ
% 5.01/5.27 thf(fact_5086_odd__two__times__div__two__succ,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_two_times_div_two_succ
% 5.01/5.27 thf(fact_5087_odd__two__times__div__two__succ,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.27 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.01/5.27 = A ) ) ).
% 5.01/5.27
% 5.01/5.27 % odd_two_times_div_two_succ
% 5.01/5.27 thf(fact_5088_power__le__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: real,W: num] :
% 5.01/5.27 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.01/5.27 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_le_zero_eq_numeral
% 5.01/5.27 thf(fact_5089_power__le__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: rat,W: num] :
% 5.01/5.27 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.01/5.27 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_le_zero_eq_numeral
% 5.01/5.27 thf(fact_5090_power__le__zero__eq__numeral,axiom,
% 5.01/5.27 ! [A: int,W: num] :
% 5.01/5.27 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.01/5.27 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.01/5.27 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.01/5.27 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % power_le_zero_eq_numeral
% 5.01/5.27 thf(fact_5091_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.01/5.27 = ( N = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_parity_class.even_mask_iff
% 5.01/5.27 thf(fact_5092_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.01/5.27 = ( N = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_parity_class.even_mask_iff
% 5.01/5.27 thf(fact_5093_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.01/5.27 ! [N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.01/5.27 = ( N = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % semiring_parity_class.even_mask_iff
% 5.01/5.27 thf(fact_5094_abs__div,axiom,
% 5.01/5.27 ! [Y: int,X2: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ Y @ X2 )
% 5.01/5.27 => ( ( abs_abs_int @ ( divide_divide_int @ X2 @ Y ) )
% 5.01/5.27 = ( divide_divide_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % abs_div
% 5.01/5.27 thf(fact_5095_dvd__productE,axiom,
% 5.01/5.27 ! [P4: nat,A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 5.01/5.27 => ~ ! [X4: nat,Y3: nat] :
% 5.01/5.27 ( ( P4
% 5.01/5.27 = ( times_times_nat @ X4 @ Y3 ) )
% 5.01/5.27 => ( ( dvd_dvd_nat @ X4 @ A )
% 5.01/5.27 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_productE
% 5.01/5.27 thf(fact_5096_dvd__productE,axiom,
% 5.01/5.27 ! [P4: int,A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 5.01/5.27 => ~ ! [X4: int,Y3: int] :
% 5.01/5.27 ( ( P4
% 5.01/5.27 = ( times_times_int @ X4 @ Y3 ) )
% 5.01/5.27 => ( ( dvd_dvd_int @ X4 @ A )
% 5.01/5.27 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_productE
% 5.01/5.27 thf(fact_5097_division__decomp,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.27 => ? [B6: nat,C4: nat] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_nat @ B6 @ C4 ) )
% 5.01/5.27 & ( dvd_dvd_nat @ B6 @ B )
% 5.01/5.27 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % division_decomp
% 5.01/5.27 thf(fact_5098_division__decomp,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.27 => ? [B6: int,C4: int] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_int @ B6 @ C4 ) )
% 5.01/5.27 & ( dvd_dvd_int @ B6 @ B )
% 5.01/5.27 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % division_decomp
% 5.01/5.27 thf(fact_5099_gcd__nat_Oextremum__uniqueI,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.01/5.27 => ( A = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat.extremum_uniqueI
% 5.01/5.27 thf(fact_5100_gcd__nat_Onot__eq__extremum,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( A != zero_zero_nat )
% 5.01/5.27 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 5.01/5.27 & ( A != zero_zero_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat.not_eq_extremum
% 5.01/5.27 thf(fact_5101_gcd__nat_Oextremum__unique,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.01/5.27 = ( A = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat.extremum_unique
% 5.01/5.27 thf(fact_5102_gcd__nat_Oextremum__strict,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.01/5.27 & ( zero_zero_nat != A ) ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat.extremum_strict
% 5.01/5.27 thf(fact_5103_gcd__nat_Oextremum,axiom,
% 5.01/5.27 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.01/5.27
% 5.01/5.27 % gcd_nat.extremum
% 5.01/5.27 thf(fact_5104_dvd__refl,axiom,
% 5.01/5.27 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_refl
% 5.01/5.27 thf(fact_5105_dvd__refl,axiom,
% 5.01/5.27 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_refl
% 5.01/5.27 thf(fact_5106_dvd__refl,axiom,
% 5.01/5.27 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_refl
% 5.01/5.27 thf(fact_5107_dvd__trans,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ B @ C )
% 5.01/5.27 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_trans
% 5.01/5.27 thf(fact_5108_dvd__trans,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ B @ C )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_trans
% 5.01/5.27 thf(fact_5109_dvd__trans,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_trans
% 5.01/5.27 thf(fact_5110_of__nat__dvd__iff,axiom,
% 5.01/5.27 ! [M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % of_nat_dvd_iff
% 5.01/5.27 thf(fact_5111_of__nat__dvd__iff,axiom,
% 5.01/5.27 ! [M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % of_nat_dvd_iff
% 5.01/5.27 thf(fact_5112_of__nat__dvd__iff,axiom,
% 5.01/5.27 ! [M: nat,N: nat] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.27 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.01/5.27
% 5.01/5.27 % of_nat_dvd_iff
% 5.01/5.27 thf(fact_5113_dvd__imp__le__int,axiom,
% 5.01/5.27 ! [I: int,D: int] :
% 5.01/5.27 ( ( I != zero_zero_int )
% 5.01/5.27 => ( ( dvd_dvd_int @ D @ I )
% 5.01/5.27 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_imp_le_int
% 5.01/5.27 thf(fact_5114_dvd__field__iff,axiom,
% 5.01/5.27 ( dvd_dvd_complex
% 5.01/5.27 = ( ^ [A4: complex,B3: complex] :
% 5.01/5.27 ( ( A4 = zero_zero_complex )
% 5.01/5.27 => ( B3 = zero_zero_complex ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_field_iff
% 5.01/5.27 thf(fact_5115_dvd__field__iff,axiom,
% 5.01/5.27 ( dvd_dvd_real
% 5.01/5.27 = ( ^ [A4: real,B3: real] :
% 5.01/5.27 ( ( A4 = zero_zero_real )
% 5.01/5.27 => ( B3 = zero_zero_real ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_field_iff
% 5.01/5.27 thf(fact_5116_dvd__field__iff,axiom,
% 5.01/5.27 ( dvd_dvd_rat
% 5.01/5.27 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.27 ( ( A4 = zero_zero_rat )
% 5.01/5.27 => ( B3 = zero_zero_rat ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_field_iff
% 5.01/5.27 thf(fact_5117_dvd__0__left,axiom,
% 5.01/5.27 ! [A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.01/5.27 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5118_dvd__0__left,axiom,
% 5.01/5.27 ! [A: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.01/5.27 => ( A = zero_zero_complex ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5119_dvd__0__left,axiom,
% 5.01/5.27 ! [A: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.01/5.27 => ( A = zero_zero_real ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5120_dvd__0__left,axiom,
% 5.01/5.27 ! [A: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.01/5.27 => ( A = zero_zero_rat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5121_dvd__0__left,axiom,
% 5.01/5.27 ! [A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.01/5.27 => ( A = zero_zero_nat ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5122_dvd__0__left,axiom,
% 5.01/5.27 ! [A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.01/5.27 => ( A = zero_zero_int ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_0_left
% 5.01/5.27 thf(fact_5123_dvdE,axiom,
% 5.01/5.27 ! [B: code_integer,A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.27 => ~ ! [K3: code_integer] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5124_dvdE,axiom,
% 5.01/5.27 ! [B: real,A: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ B @ A )
% 5.01/5.27 => ~ ! [K3: real] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5125_dvdE,axiom,
% 5.01/5.27 ! [B: rat,A: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ B @ A )
% 5.01/5.27 => ~ ! [K3: rat] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5126_dvdE,axiom,
% 5.01/5.27 ! [B: nat,A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.27 => ~ ! [K3: nat] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5127_dvdE,axiom,
% 5.01/5.27 ! [B: int,A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.27 => ~ ! [K3: int] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5128_dvdE,axiom,
% 5.01/5.27 ! [B: complex,A: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ B @ A )
% 5.01/5.27 => ~ ! [K3: complex] :
% 5.01/5.27 ( A
% 5.01/5.27 != ( times_times_complex @ B @ K3 ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdE
% 5.01/5.27 thf(fact_5129_dvdI,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5130_dvdI,axiom,
% 5.01/5.27 ! [A: real,B: real,K: real] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_real @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5131_dvdI,axiom,
% 5.01/5.27 ! [A: rat,B: rat,K: rat] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_rat @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5132_dvdI,axiom,
% 5.01/5.27 ! [A: nat,B: nat,K: nat] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_nat @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5133_dvdI,axiom,
% 5.01/5.27 ! [A: int,B: int,K: int] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_int @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5134_dvdI,axiom,
% 5.01/5.27 ! [A: complex,B: complex,K: complex] :
% 5.01/5.27 ( ( A
% 5.01/5.27 = ( times_times_complex @ B @ K ) )
% 5.01/5.27 => ( dvd_dvd_complex @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvdI
% 5.01/5.27 thf(fact_5135_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_Code_integer
% 5.01/5.27 = ( ^ [B3: code_integer,A4: code_integer] :
% 5.01/5.27 ? [K2: code_integer] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_3573771949741848930nteger @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5136_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_real
% 5.01/5.27 = ( ^ [B3: real,A4: real] :
% 5.01/5.27 ? [K2: real] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5137_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_rat
% 5.01/5.27 = ( ^ [B3: rat,A4: rat] :
% 5.01/5.27 ? [K2: rat] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_times_rat @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5138_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_nat
% 5.01/5.27 = ( ^ [B3: nat,A4: nat] :
% 5.01/5.27 ? [K2: nat] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5139_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_int
% 5.01/5.27 = ( ^ [B3: int,A4: int] :
% 5.01/5.27 ? [K2: int] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5140_dvd__def,axiom,
% 5.01/5.27 ( dvd_dvd_complex
% 5.01/5.27 = ( ^ [B3: complex,A4: complex] :
% 5.01/5.27 ? [K2: complex] :
% 5.01/5.27 ( A4
% 5.01/5.27 = ( times_times_complex @ B3 @ K2 ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_def
% 5.01/5.27 thf(fact_5141_dvd__mult,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5142_dvd__mult,axiom,
% 5.01/5.27 ! [A: real,C: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ C )
% 5.01/5.27 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5143_dvd__mult,axiom,
% 5.01/5.27 ! [A: rat,C: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ C )
% 5.01/5.27 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5144_dvd__mult,axiom,
% 5.01/5.27 ! [A: nat,C: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ C )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5145_dvd__mult,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ C )
% 5.01/5.27 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5146_dvd__mult,axiom,
% 5.01/5.27 ! [A: complex,C: complex,B: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ A @ C )
% 5.01/5.27 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult
% 5.01/5.27 thf(fact_5147_dvd__mult2,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5148_dvd__mult2,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ B )
% 5.01/5.27 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5149_dvd__mult2,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ B )
% 5.01/5.27 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5150_dvd__mult2,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5151_dvd__mult2,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5152_dvd__mult2,axiom,
% 5.01/5.27 ! [A: complex,B: complex,C: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ A @ B )
% 5.01/5.27 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult2
% 5.01/5.27 thf(fact_5153_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5154_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5155_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5156_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5157_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5158_dvd__mult__left,axiom,
% 5.01/5.27 ! [A: complex,B: complex,C: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_complex @ A @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_left
% 5.01/5.27 thf(fact_5159_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5160_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5161_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5162_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5163_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5164_dvd__triv__left,axiom,
% 5.01/5.27 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_left
% 5.01/5.27 thf(fact_5165_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5166_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_real @ C @ D )
% 5.01/5.27 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5167_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_rat @ C @ D )
% 5.01/5.27 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5168_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ C @ D )
% 5.01/5.27 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5169_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ C @ D )
% 5.01/5.27 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5170_mult__dvd__mono,axiom,
% 5.01/5.27 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_complex @ C @ D )
% 5.01/5.27 => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % mult_dvd_mono
% 5.01/5.27 thf(fact_5171_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5172_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5173_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5174_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5175_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5176_dvd__mult__right,axiom,
% 5.01/5.27 ! [A: complex,B: complex,C: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.01/5.27 => ( dvd_dvd_complex @ B @ C ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_mult_right
% 5.01/5.27 thf(fact_5177_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5178_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5179_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5180_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5181_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5182_dvd__triv__right,axiom,
% 5.01/5.27 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_triv_right
% 5.01/5.27 thf(fact_5183_dvd__add__right__iff,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_right_iff
% 5.01/5.27 thf(fact_5184_dvd__add__right__iff,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_right_iff
% 5.01/5.27 thf(fact_5185_dvd__add__right__iff,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_right_iff
% 5.01/5.27 thf(fact_5186_dvd__add__right__iff,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_right_iff
% 5.01/5.27 thf(fact_5187_dvd__add__right__iff,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_right_iff
% 5.01/5.27 thf(fact_5188_dvd__add__left__iff,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_left_iff
% 5.01/5.27 thf(fact_5189_dvd__add__left__iff,axiom,
% 5.01/5.27 ! [A: real,C: real,B: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_left_iff
% 5.01/5.27 thf(fact_5190_dvd__add__left__iff,axiom,
% 5.01/5.27 ! [A: rat,C: rat,B: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_left_iff
% 5.01/5.27 thf(fact_5191_dvd__add__left__iff,axiom,
% 5.01/5.27 ! [A: nat,C: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_left_iff
% 5.01/5.27 thf(fact_5192_dvd__add__left__iff,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ C )
% 5.01/5.27 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add_left_iff
% 5.01/5.27 thf(fact_5193_dvd__add,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add
% 5.01/5.27 thf(fact_5194_dvd__add,axiom,
% 5.01/5.27 ! [A: real,B: real,C: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_real @ A @ C )
% 5.01/5.27 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add
% 5.01/5.27 thf(fact_5195_dvd__add,axiom,
% 5.01/5.27 ! [A: rat,B: rat,C: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_rat @ A @ C )
% 5.01/5.27 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add
% 5.01/5.27 thf(fact_5196_dvd__add,axiom,
% 5.01/5.27 ! [A: nat,B: nat,C: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ A @ C )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add
% 5.01/5.27 thf(fact_5197_dvd__add,axiom,
% 5.01/5.27 ! [A: int,B: int,C: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ A @ C )
% 5.01/5.27 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_add
% 5.01/5.27 thf(fact_5198_dvd__unit__imp__unit,axiom,
% 5.01/5.27 ! [A: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_unit_imp_unit
% 5.01/5.27 thf(fact_5199_dvd__unit__imp__unit,axiom,
% 5.01/5.27 ! [A: nat,B: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.27 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_unit_imp_unit
% 5.01/5.27 thf(fact_5200_dvd__unit__imp__unit,axiom,
% 5.01/5.27 ! [A: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ B )
% 5.01/5.27 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.27 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_unit_imp_unit
% 5.01/5.27 thf(fact_5201_unit__imp__dvd,axiom,
% 5.01/5.27 ! [B: code_integer,A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_imp_dvd
% 5.01/5.27 thf(fact_5202_unit__imp__dvd,axiom,
% 5.01/5.27 ! [B: nat,A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.27 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_imp_dvd
% 5.01/5.27 thf(fact_5203_unit__imp__dvd,axiom,
% 5.01/5.27 ! [B: int,A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.27 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.01/5.27
% 5.01/5.27 % unit_imp_dvd
% 5.01/5.27 thf(fact_5204_one__dvd,axiom,
% 5.01/5.27 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5205_one__dvd,axiom,
% 5.01/5.27 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5206_one__dvd,axiom,
% 5.01/5.27 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5207_one__dvd,axiom,
% 5.01/5.27 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5208_one__dvd,axiom,
% 5.01/5.27 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5209_one__dvd,axiom,
% 5.01/5.27 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.01/5.27
% 5.01/5.27 % one_dvd
% 5.01/5.27 thf(fact_5210_dvd__diff,axiom,
% 5.01/5.27 ! [X2: code_integer,Y: code_integer,Z: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ X2 @ Z )
% 5.01/5.27 => ( dvd_dvd_Code_integer @ X2 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff
% 5.01/5.27 thf(fact_5211_dvd__diff,axiom,
% 5.01/5.27 ! [X2: real,Y: real,Z: real] :
% 5.01/5.27 ( ( dvd_dvd_real @ X2 @ Y )
% 5.01/5.27 => ( ( dvd_dvd_real @ X2 @ Z )
% 5.01/5.27 => ( dvd_dvd_real @ X2 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff
% 5.01/5.27 thf(fact_5212_dvd__diff,axiom,
% 5.01/5.27 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.27 ( ( dvd_dvd_rat @ X2 @ Y )
% 5.01/5.27 => ( ( dvd_dvd_rat @ X2 @ Z )
% 5.01/5.27 => ( dvd_dvd_rat @ X2 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff
% 5.01/5.27 thf(fact_5213_dvd__diff,axiom,
% 5.01/5.27 ! [X2: int,Y: int,Z: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ X2 @ Y )
% 5.01/5.27 => ( ( dvd_dvd_int @ X2 @ Z )
% 5.01/5.27 => ( dvd_dvd_int @ X2 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff
% 5.01/5.27 thf(fact_5214_dvd__diff,axiom,
% 5.01/5.27 ! [X2: complex,Y: complex,Z: complex] :
% 5.01/5.27 ( ( dvd_dvd_complex @ X2 @ Y )
% 5.01/5.27 => ( ( dvd_dvd_complex @ X2 @ Z )
% 5.01/5.27 => ( dvd_dvd_complex @ X2 @ ( minus_minus_complex @ Y @ Z ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff
% 5.01/5.27 thf(fact_5215_dvd__diff__commute,axiom,
% 5.01/5.27 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.01/5.27 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff_commute
% 5.01/5.27 thf(fact_5216_dvd__diff__commute,axiom,
% 5.01/5.27 ! [A: int,C: int,B: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.01/5.27 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % dvd_diff_commute
% 5.01/5.27 thf(fact_5217_div__div__div__same,axiom,
% 5.01/5.27 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.27 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.01/5.27 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.27 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.01/5.27 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_div_div_same
% 5.01/5.27 thf(fact_5218_div__div__div__same,axiom,
% 5.01/5.27 ! [D: nat,B: nat,A: nat] :
% 5.01/5.27 ( ( dvd_dvd_nat @ D @ B )
% 5.01/5.27 => ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.27 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.01/5.27 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.01/5.27
% 5.01/5.27 % div_div_div_same
% 5.01/5.27 thf(fact_5219_div__div__div__same,axiom,
% 5.01/5.27 ! [D: int,B: int,A: int] :
% 5.01/5.27 ( ( dvd_dvd_int @ D @ B )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.01/5.28 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_div_div_same
% 5.01/5.28 thf(fact_5220_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.28 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.01/5.28 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5221_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: complex,C: complex,B: complex] :
% 5.01/5.28 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.01/5.28 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_complex @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_complex @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5222_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: real,C: real,B: real] :
% 5.01/5.28 ( ( ( divide_divide_real @ A @ C )
% 5.01/5.28 = ( divide_divide_real @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_real @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_real @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5223_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: rat,C: rat,B: rat] :
% 5.01/5.28 ( ( ( divide_divide_rat @ A @ C )
% 5.01/5.28 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_rat @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_rat @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5224_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: nat,C: nat,B: nat] :
% 5.01/5.28 ( ( ( divide_divide_nat @ A @ C )
% 5.01/5.28 = ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5225_dvd__div__eq__cancel,axiom,
% 5.01/5.28 ! [A: int,C: int,B: int] :
% 5.01/5.28 ( ( ( divide_divide_int @ A @ C )
% 5.01/5.28 = ( divide_divide_int @ B @ C ) )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_cancel
% 5.01/5.28 thf(fact_5226_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.01/5.28 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5227_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: complex,A: complex,B: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_complex @ C @ B )
% 5.01/5.28 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.01/5.28 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5228_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: real,A: real,B: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_real @ C @ B )
% 5.01/5.28 => ( ( ( divide_divide_real @ A @ C )
% 5.01/5.28 = ( divide_divide_real @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5229_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: rat,A: rat,B: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_rat @ C @ B )
% 5.01/5.28 => ( ( ( divide_divide_rat @ A @ C )
% 5.01/5.28 = ( divide_divide_rat @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5230_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: nat,A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( ( divide_divide_nat @ A @ C )
% 5.01/5.28 = ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5231_dvd__div__eq__iff,axiom,
% 5.01/5.28 ! [C: int,A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ A )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( ( divide_divide_int @ A @ C )
% 5.01/5.28 = ( divide_divide_int @ B @ C ) )
% 5.01/5.28 = ( A = B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_iff
% 5.01/5.28 thf(fact_5232_dvd__power__same,axiom,
% 5.01/5.28 ! [X2: code_integer,Y: code_integer,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_same
% 5.01/5.28 thf(fact_5233_dvd__power__same,axiom,
% 5.01/5.28 ! [X2: real,Y: real,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_real @ X2 @ Y )
% 5.01/5.28 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_same
% 5.01/5.28 thf(fact_5234_dvd__power__same,axiom,
% 5.01/5.28 ! [X2: nat,Y: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ X2 @ Y )
% 5.01/5.28 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_same
% 5.01/5.28 thf(fact_5235_dvd__power__same,axiom,
% 5.01/5.28 ! [X2: int,Y: int,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ X2 @ Y )
% 5.01/5.28 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_same
% 5.01/5.28 thf(fact_5236_dvd__power__same,axiom,
% 5.01/5.28 ! [X2: complex,Y: complex,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_complex @ X2 @ Y )
% 5.01/5.28 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_same
% 5.01/5.28 thf(fact_5237_dvd__if__abs__eq,axiom,
% 5.01/5.28 ! [L: real,K: real] :
% 5.01/5.28 ( ( ( abs_abs_real @ L )
% 5.01/5.28 = ( abs_abs_real @ K ) )
% 5.01/5.28 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_if_abs_eq
% 5.01/5.28 thf(fact_5238_dvd__if__abs__eq,axiom,
% 5.01/5.28 ! [L: int,K: int] :
% 5.01/5.28 ( ( ( abs_abs_int @ L )
% 5.01/5.28 = ( abs_abs_int @ K ) )
% 5.01/5.28 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_if_abs_eq
% 5.01/5.28 thf(fact_5239_dvd__if__abs__eq,axiom,
% 5.01/5.28 ! [L: code_integer,K: code_integer] :
% 5.01/5.28 ( ( ( abs_abs_Code_integer @ L )
% 5.01/5.28 = ( abs_abs_Code_integer @ K ) )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_if_abs_eq
% 5.01/5.28 thf(fact_5240_dvd__if__abs__eq,axiom,
% 5.01/5.28 ! [L: rat,K: rat] :
% 5.01/5.28 ( ( ( abs_abs_rat @ L )
% 5.01/5.28 = ( abs_abs_rat @ K ) )
% 5.01/5.28 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_if_abs_eq
% 5.01/5.28 thf(fact_5241_dvd__mod,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ K @ M )
% 5.01/5.28 => ( ( dvd_dvd_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod
% 5.01/5.28 thf(fact_5242_dvd__mod,axiom,
% 5.01/5.28 ! [K: int,M: int,N: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ K @ M )
% 5.01/5.28 => ( ( dvd_dvd_int @ K @ N )
% 5.01/5.28 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod
% 5.01/5.28 thf(fact_5243_dvd__mod,axiom,
% 5.01/5.28 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod
% 5.01/5.28 thf(fact_5244_mod__mod__cancel,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.01/5.28 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_mod_cancel
% 5.01/5.28 thf(fact_5245_mod__mod__cancel,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.01/5.28 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_mod_cancel
% 5.01/5.28 thf(fact_5246_mod__mod__cancel,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.01/5.28 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_mod_cancel
% 5.01/5.28 thf(fact_5247_dvd__mod__iff,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.28 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_iff
% 5.01/5.28 thf(fact_5248_dvd__mod__iff,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.28 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_iff
% 5.01/5.28 thf(fact_5249_dvd__mod__iff,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_iff
% 5.01/5.28 thf(fact_5250_dvd__mod__imp__dvd,axiom,
% 5.01/5.28 ! [C: nat,A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_imp_dvd
% 5.01/5.28 thf(fact_5251_dvd__mod__imp__dvd,axiom,
% 5.01/5.28 ! [C: int,A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_imp_dvd
% 5.01/5.28 thf(fact_5252_dvd__mod__imp__dvd,axiom,
% 5.01/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mod_imp_dvd
% 5.01/5.28 thf(fact_5253_dvd__diff__nat,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ K @ M )
% 5.01/5.28 => ( ( dvd_dvd_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_diff_nat
% 5.01/5.28 thf(fact_5254_uminus__dvd__conv_I2_J,axiom,
% 5.01/5.28 ( dvd_dvd_int
% 5.01/5.28 = ( ^ [D3: int,T2: int] : ( dvd_dvd_int @ D3 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_dvd_conv(2)
% 5.01/5.28 thf(fact_5255_uminus__dvd__conv_I1_J,axiom,
% 5.01/5.28 ( dvd_dvd_int
% 5.01/5.28 = ( ^ [D3: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_dvd_conv(1)
% 5.01/5.28 thf(fact_5256_arctan__less__iff,axiom,
% 5.01/5.28 ! [X2: real,Y: real] :
% 5.01/5.28 ( ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y ) )
% 5.01/5.28 = ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_less_iff
% 5.01/5.28 thf(fact_5257_arctan__monotone,axiom,
% 5.01/5.28 ! [X2: real,Y: real] :
% 5.01/5.28 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.28 => ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_monotone
% 5.01/5.28 thf(fact_5258_arctan__monotone_H,axiom,
% 5.01/5.28 ! [X2: real,Y: real] :
% 5.01/5.28 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.28 => ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_monotone'
% 5.01/5.28 thf(fact_5259_arctan__le__iff,axiom,
% 5.01/5.28 ! [X2: real,Y: real] :
% 5.01/5.28 ( ( ord_less_eq_real @ ( arctan @ X2 ) @ ( arctan @ Y ) )
% 5.01/5.28 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_le_iff
% 5.01/5.28 thf(fact_5260_zdvd__zdiffD,axiom,
% 5.01/5.28 ! [K: int,M: int,N: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.01/5.28 => ( ( dvd_dvd_int @ K @ N )
% 5.01/5.28 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_zdiffD
% 5.01/5.28 thf(fact_5261_arctan__minus,axiom,
% 5.01/5.28 ! [X2: real] :
% 5.01/5.28 ( ( arctan @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.28 = ( uminus_uminus_real @ ( arctan @ X2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_minus
% 5.01/5.28 thf(fact_5262_dvd__pos__nat,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 => ( ( dvd_dvd_nat @ M @ N )
% 5.01/5.28 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_pos_nat
% 5.01/5.28 thf(fact_5263_bezout__lemma__nat,axiom,
% 5.01/5.28 ! [D: nat,A: nat,B: nat,X2: nat,Y: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D @ A )
% 5.01/5.28 => ( ( dvd_dvd_nat @ D @ B )
% 5.01/5.28 => ( ( ( ( times_times_nat @ A @ X2 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.01/5.28 | ( ( times_times_nat @ B @ X2 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.01/5.28 => ? [X4: nat,Y3: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D @ A )
% 5.01/5.28 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.01/5.28 & ( ( ( times_times_nat @ A @ X4 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.01/5.28 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bezout_lemma_nat
% 5.01/5.28 thf(fact_5264_bezout__add__nat,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ? [D2: nat,X4: nat,Y3: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D2 @ A )
% 5.01/5.28 & ( dvd_dvd_nat @ D2 @ B )
% 5.01/5.28 & ( ( ( times_times_nat @ A @ X4 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D2 ) )
% 5.01/5.28 | ( ( times_times_nat @ B @ X4 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bezout_add_nat
% 5.01/5.28 thf(fact_5265_bezout1__nat,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ? [D2: nat,X4: nat,Y3: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D2 @ A )
% 5.01/5.28 & ( dvd_dvd_nat @ D2 @ B )
% 5.01/5.28 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.01/5.28 = D2 )
% 5.01/5.28 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.01/5.28 = D2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bezout1_nat
% 5.01/5.28 thf(fact_5266_zdvd__mult__cancel1,axiom,
% 5.01/5.28 ! [M: int,N: int] :
% 5.01/5.28 ( ( M != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.01/5.28 = ( ( abs_abs_int @ N )
% 5.01/5.28 = one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_mult_cancel1
% 5.01/5.28 thf(fact_5267_concat__bit__assoc,axiom,
% 5.01/5.28 ! [N: nat,K: int,M: nat,L: int,R: int] :
% 5.01/5.28 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R ) )
% 5.01/5.28 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R ) ) ).
% 5.01/5.28
% 5.01/5.28 % concat_bit_assoc
% 5.01/5.28 thf(fact_5268_even__add__abs__iff,axiom,
% 5.01/5.28 ! [K: int,L: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_add_abs_iff
% 5.01/5.28 thf(fact_5269_even__abs__add__iff,axiom,
% 5.01/5.28 ! [K: int,L: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_abs_add_iff
% 5.01/5.28 thf(fact_5270_not__is__unit__0,axiom,
% 5.01/5.28 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.01/5.28
% 5.01/5.28 % not_is_unit_0
% 5.01/5.28 thf(fact_5271_not__is__unit__0,axiom,
% 5.01/5.28 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % not_is_unit_0
% 5.01/5.28 thf(fact_5272_not__is__unit__0,axiom,
% 5.01/5.28 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % not_is_unit_0
% 5.01/5.28 thf(fact_5273_minf_I10_J,axiom,
% 5.01/5.28 ! [D: code_integer,S2: code_integer] :
% 5.01/5.28 ? [Z3: code_integer] :
% 5.01/5.28 ! [X: code_integer] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ X @ Z3 )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(10)
% 5.01/5.28 thf(fact_5274_minf_I10_J,axiom,
% 5.01/5.28 ! [D: real,S2: real] :
% 5.01/5.28 ? [Z3: real] :
% 5.01/5.28 ! [X: real] :
% 5.01/5.28 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(10)
% 5.01/5.28 thf(fact_5275_minf_I10_J,axiom,
% 5.01/5.28 ! [D: rat,S2: rat] :
% 5.01/5.28 ? [Z3: rat] :
% 5.01/5.28 ! [X: rat] :
% 5.01/5.28 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(10)
% 5.01/5.28 thf(fact_5276_minf_I10_J,axiom,
% 5.01/5.28 ! [D: nat,S2: nat] :
% 5.01/5.28 ? [Z3: nat] :
% 5.01/5.28 ! [X: nat] :
% 5.01/5.28 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(10)
% 5.01/5.28 thf(fact_5277_minf_I10_J,axiom,
% 5.01/5.28 ! [D: int,S2: int] :
% 5.01/5.28 ? [Z3: int] :
% 5.01/5.28 ! [X: int] :
% 5.01/5.28 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(10)
% 5.01/5.28 thf(fact_5278_minf_I9_J,axiom,
% 5.01/5.28 ! [D: code_integer,S2: code_integer] :
% 5.01/5.28 ? [Z3: code_integer] :
% 5.01/5.28 ! [X: code_integer] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ X @ Z3 )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(9)
% 5.01/5.28 thf(fact_5279_minf_I9_J,axiom,
% 5.01/5.28 ! [D: real,S2: real] :
% 5.01/5.28 ? [Z3: real] :
% 5.01/5.28 ! [X: real] :
% 5.01/5.28 ( ( ord_less_real @ X @ Z3 )
% 5.01/5.28 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(9)
% 5.01/5.28 thf(fact_5280_minf_I9_J,axiom,
% 5.01/5.28 ! [D: rat,S2: rat] :
% 5.01/5.28 ? [Z3: rat] :
% 5.01/5.28 ! [X: rat] :
% 5.01/5.28 ( ( ord_less_rat @ X @ Z3 )
% 5.01/5.28 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(9)
% 5.01/5.28 thf(fact_5281_minf_I9_J,axiom,
% 5.01/5.28 ! [D: nat,S2: nat] :
% 5.01/5.28 ? [Z3: nat] :
% 5.01/5.28 ! [X: nat] :
% 5.01/5.28 ( ( ord_less_nat @ X @ Z3 )
% 5.01/5.28 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(9)
% 5.01/5.28 thf(fact_5282_minf_I9_J,axiom,
% 5.01/5.28 ! [D: int,S2: int] :
% 5.01/5.28 ? [Z3: int] :
% 5.01/5.28 ! [X: int] :
% 5.01/5.28 ( ( ord_less_int @ X @ Z3 )
% 5.01/5.28 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minf(9)
% 5.01/5.28 thf(fact_5283_pinf_I10_J,axiom,
% 5.01/5.28 ! [D: code_integer,S2: code_integer] :
% 5.01/5.28 ? [Z3: code_integer] :
% 5.01/5.28 ! [X: code_integer] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ Z3 @ X )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(10)
% 5.01/5.28 thf(fact_5284_pinf_I10_J,axiom,
% 5.01/5.28 ! [D: real,S2: real] :
% 5.01/5.28 ? [Z3: real] :
% 5.01/5.28 ! [X: real] :
% 5.01/5.28 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(10)
% 5.01/5.28 thf(fact_5285_pinf_I10_J,axiom,
% 5.01/5.28 ! [D: rat,S2: rat] :
% 5.01/5.28 ? [Z3: rat] :
% 5.01/5.28 ! [X: rat] :
% 5.01/5.28 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(10)
% 5.01/5.28 thf(fact_5286_pinf_I10_J,axiom,
% 5.01/5.28 ! [D: nat,S2: nat] :
% 5.01/5.28 ? [Z3: nat] :
% 5.01/5.28 ! [X: nat] :
% 5.01/5.28 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(10)
% 5.01/5.28 thf(fact_5287_pinf_I10_J,axiom,
% 5.01/5.28 ! [D: int,S2: int] :
% 5.01/5.28 ? [Z3: int] :
% 5.01/5.28 ! [X: int] :
% 5.01/5.28 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.28 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(10)
% 5.01/5.28 thf(fact_5288_pinf_I9_J,axiom,
% 5.01/5.28 ! [D: code_integer,S2: code_integer] :
% 5.01/5.28 ? [Z3: code_integer] :
% 5.01/5.28 ! [X: code_integer] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ Z3 @ X )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(9)
% 5.01/5.28 thf(fact_5289_pinf_I9_J,axiom,
% 5.01/5.28 ! [D: real,S2: real] :
% 5.01/5.28 ? [Z3: real] :
% 5.01/5.28 ! [X: real] :
% 5.01/5.28 ( ( ord_less_real @ Z3 @ X )
% 5.01/5.28 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(9)
% 5.01/5.28 thf(fact_5290_pinf_I9_J,axiom,
% 5.01/5.28 ! [D: rat,S2: rat] :
% 5.01/5.28 ? [Z3: rat] :
% 5.01/5.28 ! [X: rat] :
% 5.01/5.28 ( ( ord_less_rat @ Z3 @ X )
% 5.01/5.28 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(9)
% 5.01/5.28 thf(fact_5291_pinf_I9_J,axiom,
% 5.01/5.28 ! [D: nat,S2: nat] :
% 5.01/5.28 ? [Z3: nat] :
% 5.01/5.28 ! [X: nat] :
% 5.01/5.28 ( ( ord_less_nat @ Z3 @ X )
% 5.01/5.28 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(9)
% 5.01/5.28 thf(fact_5292_pinf_I9_J,axiom,
% 5.01/5.28 ! [D: int,S2: int] :
% 5.01/5.28 ? [Z3: int] :
% 5.01/5.28 ! [X: int] :
% 5.01/5.28 ( ( ord_less_int @ Z3 @ X )
% 5.01/5.28 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) )
% 5.01/5.28 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ S2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % pinf(9)
% 5.01/5.28 thf(fact_5293_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5294_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: complex,A: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ B @ A )
% 5.01/5.28 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.01/5.28 = zero_zero_complex )
% 5.01/5.28 = ( A = zero_zero_complex ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5295_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: real,A: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ B @ A )
% 5.01/5.28 => ( ( ( divide_divide_real @ A @ B )
% 5.01/5.28 = zero_zero_real )
% 5.01/5.28 = ( A = zero_zero_real ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5296_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: rat,A: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ B @ A )
% 5.01/5.28 => ( ( ( divide_divide_rat @ A @ B )
% 5.01/5.28 = zero_zero_rat )
% 5.01/5.28 = ( A = zero_zero_rat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5297_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( ( divide_divide_nat @ A @ B )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( A = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5298_dvd__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( ( divide_divide_int @ A @ B )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( A = zero_zero_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_0_iff
% 5.01/5.28 thf(fact_5299_unit__mult__right__cancel,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.01/5.28 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_right_cancel
% 5.01/5.28 thf(fact_5300_unit__mult__right__cancel,axiom,
% 5.01/5.28 ! [A: nat,B: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ( ( ( times_times_nat @ B @ A )
% 5.01/5.28 = ( times_times_nat @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_right_cancel
% 5.01/5.28 thf(fact_5301_unit__mult__right__cancel,axiom,
% 5.01/5.28 ! [A: int,B: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ( ( ( times_times_int @ B @ A )
% 5.01/5.28 = ( times_times_int @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_right_cancel
% 5.01/5.28 thf(fact_5302_unit__mult__left__cancel,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.01/5.28 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_left_cancel
% 5.01/5.28 thf(fact_5303_unit__mult__left__cancel,axiom,
% 5.01/5.28 ! [A: nat,B: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ( ( ( times_times_nat @ A @ B )
% 5.01/5.28 = ( times_times_nat @ A @ C ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_left_cancel
% 5.01/5.28 thf(fact_5304_unit__mult__left__cancel,axiom,
% 5.01/5.28 ! [A: int,B: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ( ( ( times_times_int @ A @ B )
% 5.01/5.28 = ( times_times_int @ A @ C ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_mult_left_cancel
% 5.01/5.28 thf(fact_5305_mult__unit__dvd__iff_H,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff'
% 5.01/5.28 thf(fact_5306_mult__unit__dvd__iff_H,axiom,
% 5.01/5.28 ! [A: nat,B: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff'
% 5.01/5.28 thf(fact_5307_mult__unit__dvd__iff_H,axiom,
% 5.01/5.28 ! [A: int,B: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff'
% 5.01/5.28 thf(fact_5308_dvd__mult__unit__iff_H,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff'
% 5.01/5.28 thf(fact_5309_dvd__mult__unit__iff_H,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff'
% 5.01/5.28 thf(fact_5310_dvd__mult__unit__iff_H,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff'
% 5.01/5.28 thf(fact_5311_mult__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff
% 5.01/5.28 thf(fact_5312_mult__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff
% 5.01/5.28 thf(fact_5313_mult__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mult_unit_dvd_iff
% 5.01/5.28 thf(fact_5314_dvd__mult__unit__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff
% 5.01/5.28 thf(fact_5315_dvd__mult__unit__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff
% 5.01/5.28 thf(fact_5316_dvd__mult__unit__iff,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_unit_iff
% 5.01/5.28 thf(fact_5317_is__unit__mult__iff,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_mult_iff
% 5.01/5.28 thf(fact_5318_is__unit__mult__iff,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.01/5.28 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_mult_iff
% 5.01/5.28 thf(fact_5319_is__unit__mult__iff,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.01/5.28 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_mult_iff
% 5.01/5.28 thf(fact_5320_dvd__div__mult,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult
% 5.01/5.28 thf(fact_5321_dvd__div__mult,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.01/5.28 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult
% 5.01/5.28 thf(fact_5322_dvd__div__mult,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.01/5.28 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult
% 5.01/5.28 thf(fact_5323_div__mult__swap,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_swap
% 5.01/5.28 thf(fact_5324_div__mult__swap,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_swap
% 5.01/5.28 thf(fact_5325_div__mult__swap,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.01/5.28 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_swap
% 5.01/5.28 thf(fact_5326_div__div__eq__right,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_div_eq_right
% 5.01/5.28 thf(fact_5327_div__div__eq__right,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_div_eq_right
% 5.01/5.28 thf(fact_5328_div__div__eq__right,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.01/5.28 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_div_eq_right
% 5.01/5.28 thf(fact_5329_dvd__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult2_eq
% 5.01/5.28 thf(fact_5330_dvd__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: nat,C: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.28 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult2_eq
% 5.01/5.28 thf(fact_5331_dvd__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: int,C: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.28 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_mult2_eq
% 5.01/5.28 thf(fact_5332_dvd__mult__imp__div,axiom,
% 5.01/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_imp_div
% 5.01/5.28 thf(fact_5333_dvd__mult__imp__div,axiom,
% 5.01/5.28 ! [A: nat,C: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.01/5.28 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_imp_div
% 5.01/5.28 thf(fact_5334_dvd__mult__imp__div,axiom,
% 5.01/5.28 ! [A: int,C: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.01/5.28 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_imp_div
% 5.01/5.28 thf(fact_5335_div__mult__div__if__dvd,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_div_if_dvd
% 5.01/5.28 thf(fact_5336_div__mult__div__if__dvd,axiom,
% 5.01/5.28 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_nat @ D @ C )
% 5.01/5.28 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.01/5.28 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_div_if_dvd
% 5.01/5.28 thf(fact_5337_div__mult__div__if__dvd,axiom,
% 5.01/5.28 ! [B: int,A: int,D: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_int @ D @ C )
% 5.01/5.28 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.01/5.28 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_div_if_dvd
% 5.01/5.28 thf(fact_5338_div__plus__div__distrib__dvd__right,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.01/5.28 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_right
% 5.01/5.28 thf(fact_5339_div__plus__div__distrib__dvd__right,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.01/5.28 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_right
% 5.01/5.28 thf(fact_5340_div__plus__div__distrib__dvd__right,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.01/5.28 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_right
% 5.01/5.28 thf(fact_5341_div__plus__div__distrib__dvd__left,axiom,
% 5.01/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.01/5.28 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_left
% 5.01/5.28 thf(fact_5342_div__plus__div__distrib__dvd__left,axiom,
% 5.01/5.28 ! [C: nat,A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ A )
% 5.01/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.01/5.28 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_left
% 5.01/5.28 thf(fact_5343_div__plus__div__distrib__dvd__left,axiom,
% 5.01/5.28 ! [C: int,A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ A )
% 5.01/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.01/5.28 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_plus_div_distrib_dvd_left
% 5.01/5.28 thf(fact_5344_dvd__div__unit__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_unit_iff
% 5.01/5.28 thf(fact_5345_dvd__div__unit__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_unit_iff
% 5.01/5.28 thf(fact_5346_dvd__div__unit__iff,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.01/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_unit_iff
% 5.01/5.28 thf(fact_5347_div__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_unit_dvd_iff
% 5.01/5.28 thf(fact_5348_div__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_unit_dvd_iff
% 5.01/5.28 thf(fact_5349_div__unit__dvd__iff,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_unit_dvd_iff
% 5.01/5.28 thf(fact_5350_unit__div__cancel,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.01/5.28 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_cancel
% 5.01/5.28 thf(fact_5351_unit__div__cancel,axiom,
% 5.01/5.28 ! [A: nat,B: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ( ( ( divide_divide_nat @ B @ A )
% 5.01/5.28 = ( divide_divide_nat @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_cancel
% 5.01/5.28 thf(fact_5352_unit__div__cancel,axiom,
% 5.01/5.28 ! [A: int,B: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ( ( ( divide_divide_int @ B @ A )
% 5.01/5.28 = ( divide_divide_int @ C @ A ) )
% 5.01/5.28 = ( B = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_cancel
% 5.01/5.28 thf(fact_5353_dvd__div__neg,axiom,
% 5.01/5.28 ! [B: real,A: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ B @ A )
% 5.01/5.28 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.01/5.28 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_neg
% 5.01/5.28 thf(fact_5354_dvd__div__neg,axiom,
% 5.01/5.28 ! [B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.01/5.28 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_neg
% 5.01/5.28 thf(fact_5355_dvd__div__neg,axiom,
% 5.01/5.28 ! [B: complex,A: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ B @ A )
% 5.01/5.28 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.01/5.28 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_neg
% 5.01/5.28 thf(fact_5356_dvd__div__neg,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.01/5.28 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_neg
% 5.01/5.28 thf(fact_5357_dvd__div__neg,axiom,
% 5.01/5.28 ! [B: rat,A: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ B @ A )
% 5.01/5.28 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.01/5.28 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_neg
% 5.01/5.28 thf(fact_5358_dvd__neg__div,axiom,
% 5.01/5.28 ! [B: real,A: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ B @ A )
% 5.01/5.28 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.01/5.28 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_neg_div
% 5.01/5.28 thf(fact_5359_dvd__neg__div,axiom,
% 5.01/5.28 ! [B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.01/5.28 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_neg_div
% 5.01/5.28 thf(fact_5360_dvd__neg__div,axiom,
% 5.01/5.28 ! [B: complex,A: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ B @ A )
% 5.01/5.28 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.01/5.28 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_neg_div
% 5.01/5.28 thf(fact_5361_dvd__neg__div,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.01/5.28 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_neg_div
% 5.01/5.28 thf(fact_5362_dvd__neg__div,axiom,
% 5.01/5.28 ! [B: rat,A: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ B @ A )
% 5.01/5.28 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.01/5.28 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_neg_div
% 5.01/5.28 thf(fact_5363_div__power,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_power
% 5.01/5.28 thf(fact_5364_div__power,axiom,
% 5.01/5.28 ! [B: nat,A: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.01/5.28 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_power
% 5.01/5.28 thf(fact_5365_div__power,axiom,
% 5.01/5.28 ! [B: int,A: int,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.01/5.28 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_power
% 5.01/5.28 thf(fact_5366_mod__0__imp__dvd,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( ( modulo_modulo_nat @ A @ B )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_0_imp_dvd
% 5.01/5.28 thf(fact_5367_mod__0__imp__dvd,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_0_imp_dvd
% 5.01/5.28 thf(fact_5368_mod__0__imp__dvd,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_0_imp_dvd
% 5.01/5.28 thf(fact_5369_dvd__eq__mod__eq__0,axiom,
% 5.01/5.28 ( dvd_dvd_nat
% 5.01/5.28 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.28 ( ( modulo_modulo_nat @ B3 @ A4 )
% 5.01/5.28 = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_eq_mod_eq_0
% 5.01/5.28 thf(fact_5370_dvd__eq__mod__eq__0,axiom,
% 5.01/5.28 ( dvd_dvd_int
% 5.01/5.28 = ( ^ [A4: int,B3: int] :
% 5.01/5.28 ( ( modulo_modulo_int @ B3 @ A4 )
% 5.01/5.28 = zero_zero_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_eq_mod_eq_0
% 5.01/5.28 thf(fact_5371_dvd__eq__mod__eq__0,axiom,
% 5.01/5.28 ( dvd_dvd_Code_integer
% 5.01/5.28 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.01/5.28 ( ( modulo364778990260209775nteger @ B3 @ A4 )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_eq_mod_eq_0
% 5.01/5.28 thf(fact_5372_mod__eq__0__iff__dvd,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( ( modulo_modulo_nat @ A @ B )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_0_iff_dvd
% 5.01/5.28 thf(fact_5373_mod__eq__0__iff__dvd,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( ( modulo_modulo_int @ A @ B )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_0_iff_dvd
% 5.01/5.28 thf(fact_5374_mod__eq__0__iff__dvd,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_0_iff_dvd
% 5.01/5.28 thf(fact_5375_le__imp__power__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: code_integer] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % le_imp_power_dvd
% 5.01/5.28 thf(fact_5376_le__imp__power__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: real] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % le_imp_power_dvd
% 5.01/5.28 thf(fact_5377_le__imp__power__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % le_imp_power_dvd
% 5.01/5.28 thf(fact_5378_le__imp__power__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: int] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % le_imp_power_dvd
% 5.01/5.28 thf(fact_5379_le__imp__power__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: complex] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % le_imp_power_dvd
% 5.01/5.28 thf(fact_5380_power__le__dvd,axiom,
% 5.01/5.28 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_dvd
% 5.01/5.28 thf(fact_5381_power__le__dvd,axiom,
% 5.01/5.28 ! [A: real,N: nat,B: real,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_dvd
% 5.01/5.28 thf(fact_5382_power__le__dvd,axiom,
% 5.01/5.28 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_dvd
% 5.01/5.28 thf(fact_5383_power__le__dvd,axiom,
% 5.01/5.28 ! [A: int,N: nat,B: int,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_dvd
% 5.01/5.28 thf(fact_5384_power__le__dvd,axiom,
% 5.01/5.28 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_dvd
% 5.01/5.28 thf(fact_5385_dvd__power__le,axiom,
% 5.01/5.28 ! [X2: code_integer,Y: code_integer,N: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_le
% 5.01/5.28 thf(fact_5386_dvd__power__le,axiom,
% 5.01/5.28 ! [X2: real,Y: real,N: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_real @ X2 @ Y )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_le
% 5.01/5.28 thf(fact_5387_dvd__power__le,axiom,
% 5.01/5.28 ! [X2: nat,Y: nat,N: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ X2 @ Y )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_le
% 5.01/5.28 thf(fact_5388_dvd__power__le,axiom,
% 5.01/5.28 ! [X2: int,Y: int,N: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ X2 @ Y )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_le
% 5.01/5.28 thf(fact_5389_dvd__power__le,axiom,
% 5.01/5.28 ! [X2: complex,Y: complex,N: nat,M: nat] :
% 5.01/5.28 ( ( dvd_dvd_complex @ X2 @ Y )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_le
% 5.01/5.28 thf(fact_5390_mod__eq__dvd__iff,axiom,
% 5.01/5.28 ! [A: int,C: int,B: int] :
% 5.01/5.28 ( ( ( modulo_modulo_int @ A @ C )
% 5.01/5.28 = ( modulo_modulo_int @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_dvd_iff
% 5.01/5.28 thf(fact_5391_mod__eq__dvd__iff,axiom,
% 5.01/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.01/5.28 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.01/5.28 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_dvd_iff
% 5.01/5.28 thf(fact_5392_dvd__minus__mod,axiom,
% 5.01/5.28 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_minus_mod
% 5.01/5.28 thf(fact_5393_dvd__minus__mod,axiom,
% 5.01/5.28 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_minus_mod
% 5.01/5.28 thf(fact_5394_dvd__minus__mod,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_minus_mod
% 5.01/5.28 thf(fact_5395_nat__dvd__not__less,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % nat_dvd_not_less
% 5.01/5.28 thf(fact_5396_bezout__add__strong__nat,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( A != zero_zero_nat )
% 5.01/5.28 => ? [D2: nat,X4: nat,Y3: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D2 @ A )
% 5.01/5.28 & ( dvd_dvd_nat @ D2 @ B )
% 5.01/5.28 & ( ( times_times_nat @ A @ X4 )
% 5.01/5.28 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D2 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bezout_add_strong_nat
% 5.01/5.28 thf(fact_5397_abs__zmult__eq__1,axiom,
% 5.01/5.28 ! [M: int,N: int] :
% 5.01/5.28 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.01/5.28 = one_one_int )
% 5.01/5.28 => ( ( abs_abs_int @ M )
% 5.01/5.28 = one_one_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_zmult_eq_1
% 5.01/5.28 thf(fact_5398_dvd__minus__self,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.28 = ( ( ord_less_nat @ N @ M )
% 5.01/5.28 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_minus_self
% 5.01/5.28 thf(fact_5399_zdvd__antisym__nonneg,axiom,
% 5.01/5.28 ! [M: int,N: int] :
% 5.01/5.28 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.01/5.28 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.01/5.28 => ( ( dvd_dvd_int @ M @ N )
% 5.01/5.28 => ( ( dvd_dvd_int @ N @ M )
% 5.01/5.28 => ( M = N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_antisym_nonneg
% 5.01/5.28 thf(fact_5400_less__eq__dvd__minus,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( dvd_dvd_nat @ M @ N )
% 5.01/5.28 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % less_eq_dvd_minus
% 5.01/5.28 thf(fact_5401_dvd__diffD1,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.28 => ( ( dvd_dvd_nat @ K @ M )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_diffD1
% 5.01/5.28 thf(fact_5402_dvd__diffD,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.01/5.28 => ( ( dvd_dvd_nat @ K @ N )
% 5.01/5.28 => ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_diffD
% 5.01/5.28 thf(fact_5403_zdvd__not__zless,axiom,
% 5.01/5.28 ! [M: int,N: int] :
% 5.01/5.28 ( ( ord_less_int @ zero_zero_int @ M )
% 5.01/5.28 => ( ( ord_less_int @ M @ N )
% 5.01/5.28 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_not_zless
% 5.01/5.28 thf(fact_5404_zdvd__mono,axiom,
% 5.01/5.28 ! [K: int,M: int,T: int] :
% 5.01/5.28 ( ( K != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ M @ T )
% 5.01/5.28 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_mono
% 5.01/5.28 thf(fact_5405_zdvd__mult__cancel,axiom,
% 5.01/5.28 ! [K: int,M: int,N: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.01/5.28 => ( ( K != zero_zero_int )
% 5.01/5.28 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_mult_cancel
% 5.01/5.28 thf(fact_5406_zdvd__reduce,axiom,
% 5.01/5.28 ! [K: int,N: int,M: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.01/5.28 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_reduce
% 5.01/5.28 thf(fact_5407_zdvd__period,axiom,
% 5.01/5.28 ! [A: int,D: int,X2: int,T: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ D )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X2 @ T ) )
% 5.01/5.28 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_period
% 5.01/5.28 thf(fact_5408_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: code_integer > $o,L: code_integer] :
% 5.01/5.28 ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5409_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: real > $o,L: real] :
% 5.01/5.28 ( ( ? [X3: real] : ( P @ ( times_times_real @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5410_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: rat > $o,L: rat] :
% 5.01/5.28 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5411_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: nat > $o,L: nat] :
% 5.01/5.28 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5412_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: int > $o,L: int] :
% 5.01/5.28 ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5413_unity__coeff__ex,axiom,
% 5.01/5.28 ! [P: complex > $o,L: complex] :
% 5.01/5.28 ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L @ X3 ) ) )
% 5.01/5.28 = ( ? [X3: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 5.01/5.28 & ( P @ X3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unity_coeff_ex
% 5.01/5.28 thf(fact_5414_unit__dvdE,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ! [C3: code_integer] :
% 5.01/5.28 ( B
% 5.01/5.28 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_dvdE
% 5.01/5.28 thf(fact_5415_unit__dvdE,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ~ ( ( A != zero_zero_nat )
% 5.01/5.28 => ! [C3: nat] :
% 5.01/5.28 ( B
% 5.01/5.28 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_dvdE
% 5.01/5.28 thf(fact_5416_unit__dvdE,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ~ ( ( A != zero_zero_int )
% 5.01/5.28 => ! [C3: int] :
% 5.01/5.28 ( B
% 5.01/5.28 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_dvdE
% 5.01/5.28 thf(fact_5417_dvd__div__div__eq__mult,axiom,
% 5.01/5.28 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.01/5.28 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( C != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.01/5.28 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.01/5.28 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.01/5.28 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_div_eq_mult
% 5.01/5.28 thf(fact_5418_dvd__div__div__eq__mult,axiom,
% 5.01/5.28 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.01/5.28 ( ( A != zero_zero_nat )
% 5.01/5.28 => ( ( C != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ D )
% 5.01/5.28 => ( ( ( divide_divide_nat @ B @ A )
% 5.01/5.28 = ( divide_divide_nat @ D @ C ) )
% 5.01/5.28 = ( ( times_times_nat @ B @ C )
% 5.01/5.28 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_div_eq_mult
% 5.01/5.28 thf(fact_5419_dvd__div__div__eq__mult,axiom,
% 5.01/5.28 ! [A: int,C: int,B: int,D: int] :
% 5.01/5.28 ( ( A != zero_zero_int )
% 5.01/5.28 => ( ( C != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ B )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ D )
% 5.01/5.28 => ( ( ( divide_divide_int @ B @ A )
% 5.01/5.28 = ( divide_divide_int @ D @ C ) )
% 5.01/5.28 = ( ( times_times_int @ B @ C )
% 5.01/5.28 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_div_eq_mult
% 5.01/5.28 thf(fact_5420_dvd__div__iff__mult,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( C != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_iff_mult
% 5.01/5.28 thf(fact_5421_dvd__div__iff__mult,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( C != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_iff_mult
% 5.01/5.28 thf(fact_5422_dvd__div__iff__mult,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( C != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ B )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_iff_mult
% 5.01/5.28 thf(fact_5423_div__dvd__iff__mult,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( B != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_dvd_iff_mult
% 5.01/5.28 thf(fact_5424_div__dvd__iff__mult,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( B != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_dvd_iff_mult
% 5.01/5.28 thf(fact_5425_div__dvd__iff__mult,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( B != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.01/5.28 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_dvd_iff_mult
% 5.01/5.28 thf(fact_5426_dvd__div__eq__mult,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.01/5.28 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.01/5.28 = C )
% 5.01/5.28 = ( B
% 5.01/5.28 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_mult
% 5.01/5.28 thf(fact_5427_dvd__div__eq__mult,axiom,
% 5.01/5.28 ! [A: nat,B: nat,C: nat] :
% 5.01/5.28 ( ( A != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.28 => ( ( ( divide_divide_nat @ B @ A )
% 5.01/5.28 = C )
% 5.01/5.28 = ( B
% 5.01/5.28 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_mult
% 5.01/5.28 thf(fact_5428_dvd__div__eq__mult,axiom,
% 5.01/5.28 ! [A: int,B: int,C: int] :
% 5.01/5.28 ( ( A != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ A @ B )
% 5.01/5.28 => ( ( ( divide_divide_int @ B @ A )
% 5.01/5.28 = C )
% 5.01/5.28 = ( B
% 5.01/5.28 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_div_eq_mult
% 5.01/5.28 thf(fact_5429_unit__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_eq_0_iff
% 5.01/5.28 thf(fact_5430_unit__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( ( divide_divide_nat @ A @ B )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( A = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_eq_0_iff
% 5.01/5.28 thf(fact_5431_unit__div__eq__0__iff,axiom,
% 5.01/5.28 ! [B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( ( divide_divide_int @ A @ B )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( A = zero_zero_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_eq_0_iff
% 5.01/5.28 thf(fact_5432_even__numeral,axiom,
% 5.01/5.28 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_numeral
% 5.01/5.28 thf(fact_5433_even__numeral,axiom,
% 5.01/5.28 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_numeral
% 5.01/5.28 thf(fact_5434_even__numeral,axiom,
% 5.01/5.28 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_numeral
% 5.01/5.28 thf(fact_5435_inf__period_I4_J,axiom,
% 5.01/5.28 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.01/5.28 => ! [X: code_integer,K4: code_integer] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ T ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(4)
% 5.01/5.28 thf(fact_5436_inf__period_I4_J,axiom,
% 5.01/5.28 ! [D: real,D4: real,T: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ D @ D4 )
% 5.01/5.28 => ! [X: real,K4: real] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(4)
% 5.01/5.28 thf(fact_5437_inf__period_I4_J,axiom,
% 5.01/5.28 ! [D: rat,D4: rat,T: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ D @ D4 )
% 5.01/5.28 => ! [X: rat,K4: rat] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(4)
% 5.01/5.28 thf(fact_5438_inf__period_I4_J,axiom,
% 5.01/5.28 ! [D: int,D4: int,T: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.28 => ! [X: int,K4: int] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(4)
% 5.01/5.28 thf(fact_5439_inf__period_I4_J,axiom,
% 5.01/5.28 ! [D: complex,D4: complex,T: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ D @ D4 )
% 5.01/5.28 => ! [X: complex,K4: complex] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X @ T ) ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(4)
% 5.01/5.28 thf(fact_5440_inf__period_I3_J,axiom,
% 5.01/5.28 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.01/5.28 => ! [X: code_integer,K4: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X @ T ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(3)
% 5.01/5.28 thf(fact_5441_inf__period_I3_J,axiom,
% 5.01/5.28 ! [D: real,D4: real,T: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ D @ D4 )
% 5.01/5.28 => ! [X: real,K4: real] :
% 5.01/5.28 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X @ T ) )
% 5.01/5.28 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(3)
% 5.01/5.28 thf(fact_5442_inf__period_I3_J,axiom,
% 5.01/5.28 ! [D: rat,D4: rat,T: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ D @ D4 )
% 5.01/5.28 => ! [X: rat,K4: rat] :
% 5.01/5.28 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X @ T ) )
% 5.01/5.28 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(3)
% 5.01/5.28 thf(fact_5443_inf__period_I3_J,axiom,
% 5.01/5.28 ! [D: int,D4: int,T: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.28 => ! [X: int,K4: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.01/5.28 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(3)
% 5.01/5.28 thf(fact_5444_inf__period_I3_J,axiom,
% 5.01/5.28 ! [D: complex,D4: complex,T: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ D @ D4 )
% 5.01/5.28 => ! [X: complex,K4: complex] :
% 5.01/5.28 ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X @ T ) )
% 5.01/5.28 = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X @ ( times_times_complex @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % inf_period(3)
% 5.01/5.28 thf(fact_5445_is__unit__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult2_eq
% 5.01/5.28 thf(fact_5446_is__unit__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: nat,C: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.28 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult2_eq
% 5.01/5.28 thf(fact_5447_is__unit__div__mult2__eq,axiom,
% 5.01/5.28 ! [B: int,C: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.28 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult2_eq
% 5.01/5.28 thf(fact_5448_unit__div__mult__swap,axiom,
% 5.01/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_mult_swap
% 5.01/5.28 thf(fact_5449_unit__div__mult__swap,axiom,
% 5.01/5.28 ! [C: nat,A: nat,B: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.01/5.28 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.01/5.28 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_mult_swap
% 5.01/5.28 thf(fact_5450_unit__div__mult__swap,axiom,
% 5.01/5.28 ! [C: int,A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.01/5.28 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.01/5.28 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_mult_swap
% 5.01/5.28 thf(fact_5451_unit__div__commute,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_commute
% 5.01/5.28 thf(fact_5452_unit__div__commute,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.01/5.28 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_commute
% 5.01/5.28 thf(fact_5453_unit__div__commute,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.01/5.28 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_div_commute
% 5.01/5.28 thf(fact_5454_div__mult__unit2,axiom,
% 5.01/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_unit2
% 5.01/5.28 thf(fact_5455_div__mult__unit2,axiom,
% 5.01/5.28 ! [C: nat,B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B @ A )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.01/5.28 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_unit2
% 5.01/5.28 thf(fact_5456_div__mult__unit2,axiom,
% 5.01/5.28 ! [C: int,B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ A )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.01/5.28 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div_mult_unit2
% 5.01/5.28 thf(fact_5457_unit__eq__div2,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( A
% 5.01/5.28 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.01/5.28 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.01/5.28 = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div2
% 5.01/5.28 thf(fact_5458_unit__eq__div2,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( A
% 5.01/5.28 = ( divide_divide_nat @ C @ B ) )
% 5.01/5.28 = ( ( times_times_nat @ A @ B )
% 5.01/5.28 = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div2
% 5.01/5.28 thf(fact_5459_unit__eq__div2,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( A
% 5.01/5.28 = ( divide_divide_int @ C @ B ) )
% 5.01/5.28 = ( ( times_times_int @ A @ B )
% 5.01/5.28 = C ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div2
% 5.01/5.28 thf(fact_5460_unit__eq__div1,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.01/5.28 = C )
% 5.01/5.28 = ( A
% 5.01/5.28 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div1
% 5.01/5.28 thf(fact_5461_unit__eq__div1,axiom,
% 5.01/5.28 ! [B: nat,A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( ( divide_divide_nat @ A @ B )
% 5.01/5.28 = C )
% 5.01/5.28 = ( A
% 5.01/5.28 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div1
% 5.01/5.28 thf(fact_5462_unit__eq__div1,axiom,
% 5.01/5.28 ! [B: int,A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( ( divide_divide_int @ A @ B )
% 5.01/5.28 = C )
% 5.01/5.28 = ( A
% 5.01/5.28 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_eq_div1
% 5.01/5.28 thf(fact_5463_unit__imp__mod__eq__0,axiom,
% 5.01/5.28 ! [B: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( modulo_modulo_nat @ A @ B )
% 5.01/5.28 = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_imp_mod_eq_0
% 5.01/5.28 thf(fact_5464_unit__imp__mod__eq__0,axiom,
% 5.01/5.28 ! [B: int,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( modulo_modulo_int @ A @ B )
% 5.01/5.28 = zero_zero_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_imp_mod_eq_0
% 5.01/5.28 thf(fact_5465_unit__imp__mod__eq__0,axiom,
% 5.01/5.28 ! [B: code_integer,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.28
% 5.01/5.28 % unit_imp_mod_eq_0
% 5.01/5.28 thf(fact_5466_is__unit__power__iff,axiom,
% 5.01/5.28 ! [A: code_integer,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_power_iff
% 5.01/5.28 thf(fact_5467_is__unit__power__iff,axiom,
% 5.01/5.28 ! [A: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.01/5.28 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_power_iff
% 5.01/5.28 thf(fact_5468_is__unit__power__iff,axiom,
% 5.01/5.28 ! [A: int,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.01/5.28 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_power_iff
% 5.01/5.28 thf(fact_5469_zabs__def,axiom,
% 5.01/5.28 ( abs_abs_int
% 5.01/5.28 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zabs_def
% 5.01/5.28 thf(fact_5470_dvd__imp__le,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ K @ N )
% 5.01/5.28 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_imp_le
% 5.01/5.28 thf(fact_5471_nat__mult__dvd__cancel1,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.28 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % nat_mult_dvd_cancel1
% 5.01/5.28 thf(fact_5472_dvd__mult__cancel,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.01/5.28 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.28 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_cancel
% 5.01/5.28 thf(fact_5473_abs__mod__less,axiom,
% 5.01/5.28 ! [L: int,K: int] :
% 5.01/5.28 ( ( L != zero_zero_int )
% 5.01/5.28 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_mod_less
% 5.01/5.28 thf(fact_5474_zdvd__imp__le,axiom,
% 5.01/5.28 ! [Z: int,N: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ Z @ N )
% 5.01/5.28 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.01/5.28 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zdvd_imp_le
% 5.01/5.28 thf(fact_5475_mod__greater__zero__iff__not__dvd,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_greater_zero_iff_not_dvd
% 5.01/5.28 thf(fact_5476_mod__eq__dvd__iff__nat,axiom,
% 5.01/5.28 ! [N: nat,M: nat,Q2: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.01/5.28 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.01/5.28 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_eq_dvd_iff_nat
% 5.01/5.28 thf(fact_5477_real__of__nat__div,axiom,
% 5.01/5.28 ! [D: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ D @ N )
% 5.01/5.28 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.01/5.28 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % real_of_nat_div
% 5.01/5.28 thf(fact_5478_even__zero,axiom,
% 5.01/5.28 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.01/5.28
% 5.01/5.28 % even_zero
% 5.01/5.28 thf(fact_5479_even__zero,axiom,
% 5.01/5.28 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.01/5.28
% 5.01/5.28 % even_zero
% 5.01/5.28 thf(fact_5480_even__zero,axiom,
% 5.01/5.28 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.01/5.28
% 5.01/5.28 % even_zero
% 5.01/5.28 thf(fact_5481_is__unit__div__mult__cancel__right,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_right
% 5.01/5.28 thf(fact_5482_is__unit__div__mult__cancel__right,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( A != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.01/5.28 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_right
% 5.01/5.28 thf(fact_5483_is__unit__div__mult__cancel__right,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( A != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.01/5.28 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_right
% 5.01/5.28 thf(fact_5484_is__unit__div__mult__cancel__left,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_left
% 5.01/5.28 thf(fact_5485_is__unit__div__mult__cancel__left,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ( A != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.01/5.28 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.01/5.28 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_left
% 5.01/5.28 thf(fact_5486_is__unit__div__mult__cancel__left,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ( A != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.01/5.28 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.01/5.28 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unit_div_mult_cancel_left
% 5.01/5.28 thf(fact_5487_is__unitE,axiom,
% 5.01/5.28 ! [A: code_integer,C: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.01/5.28 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.28 => ! [B2: code_integer] :
% 5.01/5.28 ( ( B2 != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.01/5.28 = B2 )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 5.01/5.28 = A )
% 5.01/5.28 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 5.01/5.28 = one_one_Code_integer )
% 5.01/5.28 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.01/5.28 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unitE
% 5.01/5.28 thf(fact_5488_is__unitE,axiom,
% 5.01/5.28 ! [A: nat,C: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.01/5.28 => ~ ( ( A != zero_zero_nat )
% 5.01/5.28 => ! [B2: nat] :
% 5.01/5.28 ( ( B2 != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 5.01/5.28 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.01/5.28 = B2 )
% 5.01/5.28 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 5.01/5.28 = A )
% 5.01/5.28 => ( ( ( times_times_nat @ A @ B2 )
% 5.01/5.28 = one_one_nat )
% 5.01/5.28 => ( ( divide_divide_nat @ C @ A )
% 5.01/5.28 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unitE
% 5.01/5.28 thf(fact_5489_is__unitE,axiom,
% 5.01/5.28 ! [A: int,C: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.01/5.28 => ~ ( ( A != zero_zero_int )
% 5.01/5.28 => ! [B2: int] :
% 5.01/5.28 ( ( B2 != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 5.01/5.28 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.01/5.28 = B2 )
% 5.01/5.28 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 5.01/5.28 = A )
% 5.01/5.28 => ( ( ( times_times_int @ A @ B2 )
% 5.01/5.28 = one_one_int )
% 5.01/5.28 => ( ( divide_divide_int @ C @ A )
% 5.01/5.28 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % is_unitE
% 5.01/5.28 thf(fact_5490_evenE,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: code_integer] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % evenE
% 5.01/5.28 thf(fact_5491_evenE,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: nat] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % evenE
% 5.01/5.28 thf(fact_5492_evenE,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: int] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % evenE
% 5.01/5.28 thf(fact_5493_odd__even__add,axiom,
% 5.01/5.28 ! [A: code_integer,B: code_integer] :
% 5.01/5.28 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_even_add
% 5.01/5.28 thf(fact_5494_odd__even__add,axiom,
% 5.01/5.28 ! [A: nat,B: nat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.01/5.28 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_even_add
% 5.01/5.28 thf(fact_5495_odd__even__add,axiom,
% 5.01/5.28 ! [A: int,B: int] :
% 5.01/5.28 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.01/5.28 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_even_add
% 5.01/5.28 thf(fact_5496_odd__one,axiom,
% 5.01/5.28 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.01/5.28
% 5.01/5.28 % odd_one
% 5.01/5.28 thf(fact_5497_odd__one,axiom,
% 5.01/5.28 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % odd_one
% 5.01/5.28 thf(fact_5498_odd__one,axiom,
% 5.01/5.28 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % odd_one
% 5.01/5.28 thf(fact_5499_bit__eq__rec,axiom,
% 5.01/5.28 ( ( ^ [Y5: code_integer,Z4: code_integer] : ( Y5 = Z4 ) )
% 5.01/5.28 = ( ^ [A4: code_integer,B3: code_integer] :
% 5.01/5.28 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.01/5.28 & ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bit_eq_rec
% 5.01/5.28 thf(fact_5500_bit__eq__rec,axiom,
% 5.01/5.28 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.01/5.28 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 )
% 5.01/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.01/5.28 & ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bit_eq_rec
% 5.01/5.28 thf(fact_5501_bit__eq__rec,axiom,
% 5.01/5.28 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.01/5.28 = ( ^ [A4: int,B3: int] :
% 5.01/5.28 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.01/5.28 & ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bit_eq_rec
% 5.01/5.28 thf(fact_5502_even__minus,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_minus
% 5.01/5.28 thf(fact_5503_even__minus,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_minus
% 5.01/5.28 thf(fact_5504_dvd__power__iff,axiom,
% 5.01/5.28 ! [X2: code_integer,M: nat,N: nat] :
% 5.01/5.28 ( ( X2 != zero_z3403309356797280102nteger )
% 5.01/5.28 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_iff
% 5.01/5.28 thf(fact_5505_dvd__power__iff,axiom,
% 5.01/5.28 ! [X2: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( X2 != zero_zero_nat )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_iff
% 5.01/5.28 thf(fact_5506_dvd__power__iff,axiom,
% 5.01/5.28 ! [X2: int,M: nat,N: nat] :
% 5.01/5.28 ( ( X2 != zero_zero_int )
% 5.01/5.28 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_iff
% 5.01/5.28 thf(fact_5507_odd__numeral,axiom,
% 5.01/5.28 ! [N: num] :
% 5.01/5.28 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral
% 5.01/5.28 thf(fact_5508_odd__numeral,axiom,
% 5.01/5.28 ! [N: num] :
% 5.01/5.28 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral
% 5.01/5.28 thf(fact_5509_odd__numeral,axiom,
% 5.01/5.28 ! [N: num] :
% 5.01/5.28 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral
% 5.01/5.28 thf(fact_5510_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: code_integer] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_Code_integer ) )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5511_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: rat] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_rat ) )
% 5.01/5.28 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5512_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: real] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_real ) )
% 5.01/5.28 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5513_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: nat] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_nat ) )
% 5.01/5.28 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5514_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: int] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_int ) )
% 5.01/5.28 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5515_dvd__power,axiom,
% 5.01/5.28 ! [N: nat,X2: complex] :
% 5.01/5.28 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 | ( X2 = one_one_complex ) )
% 5.01/5.28 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power
% 5.01/5.28 thf(fact_5516_even__signed__take__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_signed_take_bit_iff
% 5.01/5.28 thf(fact_5517_even__signed__take__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_signed_take_bit_iff
% 5.01/5.28 thf(fact_5518_div2__even__ext__nat,axiom,
% 5.01/5.28 ! [X2: nat,Y: nat] :
% 5.01/5.28 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.28 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.01/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.01/5.28 => ( X2 = Y ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % div2_even_ext_nat
% 5.01/5.28 thf(fact_5519_even__even__mod__4__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_even_mod_4_iff
% 5.01/5.28 thf(fact_5520_odd__numeral__BitM,axiom,
% 5.01/5.28 ! [W: num] :
% 5.01/5.28 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral_BitM
% 5.01/5.28 thf(fact_5521_odd__numeral__BitM,axiom,
% 5.01/5.28 ! [W: num] :
% 5.01/5.28 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral_BitM
% 5.01/5.28 thf(fact_5522_odd__numeral__BitM,axiom,
% 5.01/5.28 ! [W: num] :
% 5.01/5.28 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_numeral_BitM
% 5.01/5.28 thf(fact_5523_dvd__mult__cancel1,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.01/5.28 = ( N = one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_cancel1
% 5.01/5.28 thf(fact_5524_dvd__mult__cancel2,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.01/5.28 = ( N = one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_mult_cancel2
% 5.01/5.28 thf(fact_5525_dvd__minus__add,axiom,
% 5.01/5.28 ! [Q2: nat,N: nat,R: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.01/5.28 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 5.01/5.28 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.01/5.28 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_minus_add
% 5.01/5.28 thf(fact_5526_power__dvd__imp__le,axiom,
% 5.01/5.28 ! [I: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.01/5.28 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.01/5.28 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_dvd_imp_le
% 5.01/5.28 thf(fact_5527_mod__nat__eqI,axiom,
% 5.01/5.28 ! [R: nat,N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_nat @ R @ N )
% 5.01/5.28 => ( ( ord_less_eq_nat @ R @ M )
% 5.01/5.28 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 5.01/5.28 => ( ( modulo_modulo_nat @ M @ N )
% 5.01/5.28 = R ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_nat_eqI
% 5.01/5.28 thf(fact_5528_mod__int__pos__iff,axiom,
% 5.01/5.28 ! [K: int,L: int] :
% 5.01/5.28 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.01/5.28 = ( ( dvd_dvd_int @ L @ K )
% 5.01/5.28 | ( ( L = zero_zero_int )
% 5.01/5.28 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.01/5.28 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod_int_pos_iff
% 5.01/5.28 thf(fact_5529_even__two__times__div__two,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.01/5.28 = A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_two_times_div_two
% 5.01/5.28 thf(fact_5530_even__two__times__div__two,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.28 = A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_two_times_div_two
% 5.01/5.28 thf(fact_5531_even__two__times__div__two,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.01/5.28 = A ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_two_times_div_two
% 5.01/5.28 thf(fact_5532_even__iff__mod__2__eq__zero,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_iff_mod_2_eq_zero
% 5.01/5.28 thf(fact_5533_even__iff__mod__2__eq__zero,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_iff_mod_2_eq_zero
% 5.01/5.28 thf(fact_5534_even__iff__mod__2__eq__zero,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_iff_mod_2_eq_zero
% 5.01/5.28 thf(fact_5535_odd__iff__mod__2__eq__one,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_iff_mod_2_eq_one
% 5.01/5.28 thf(fact_5536_odd__iff__mod__2__eq__one,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_iff_mod_2_eq_one
% 5.01/5.28 thf(fact_5537_odd__iff__mod__2__eq__one,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_Code_integer ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_iff_mod_2_eq_one
% 5.01/5.28 thf(fact_5538_power__mono__odd,axiom,
% 5.01/5.28 ! [N: nat,A: real,B: real] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_real @ A @ B )
% 5.01/5.28 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_odd
% 5.01/5.28 thf(fact_5539_power__mono__odd,axiom,
% 5.01/5.28 ! [N: nat,A: rat,B: rat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.28 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_odd
% 5.01/5.28 thf(fact_5540_power__mono__odd,axiom,
% 5.01/5.28 ! [N: nat,A: int,B: int] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_int @ A @ B )
% 5.01/5.28 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_odd
% 5.01/5.28 thf(fact_5541_uminus__power__if,axiom,
% 5.01/5.28 ! [N: nat,A: real] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.01/5.28 = ( power_power_real @ A @ N ) ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.01/5.28 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_power_if
% 5.01/5.28 thf(fact_5542_uminus__power__if,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.01/5.28 = ( power_power_int @ A @ N ) ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.01/5.28 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_power_if
% 5.01/5.28 thf(fact_5543_uminus__power__if,axiom,
% 5.01/5.28 ! [N: nat,A: complex] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.01/5.28 = ( power_power_complex @ A @ N ) ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.01/5.28 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_power_if
% 5.01/5.28 thf(fact_5544_uminus__power__if,axiom,
% 5.01/5.28 ! [N: nat,A: code_integer] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.01/5.28 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.01/5.28 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_power_if
% 5.01/5.28 thf(fact_5545_uminus__power__if,axiom,
% 5.01/5.28 ! [N: nat,A: rat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.01/5.28 = ( power_power_rat @ A @ N ) ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.01/5.28 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % uminus_power_if
% 5.01/5.28 thf(fact_5546_odd__pos,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_pos
% 5.01/5.28 thf(fact_5547_power__even__abs,axiom,
% 5.01/5.28 ! [N: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.01/5.28 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_even_abs
% 5.01/5.28 thf(fact_5548_power__even__abs,axiom,
% 5.01/5.28 ! [N: nat,A: rat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.01/5.28 = ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_even_abs
% 5.01/5.28 thf(fact_5549_power__even__abs,axiom,
% 5.01/5.28 ! [N: nat,A: real] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.01/5.28 = ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_even_abs
% 5.01/5.28 thf(fact_5550_power__even__abs,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.01/5.28 = ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_even_abs
% 5.01/5.28 thf(fact_5551_dvd__power__iff__le,axiom,
% 5.01/5.28 ! [K: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.01/5.28 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.01/5.28 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_power_iff_le
% 5.01/5.28 thf(fact_5552_even__unset__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 | ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_unset_bit_iff
% 5.01/5.28 thf(fact_5553_even__unset__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 | ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_unset_bit_iff
% 5.01/5.28 thf(fact_5554_even__unset__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 | ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_unset_bit_iff
% 5.01/5.28 thf(fact_5555_even__set__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 & ( M != zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_set_bit_iff
% 5.01/5.28 thf(fact_5556_even__set__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 & ( M != zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_set_bit_iff
% 5.01/5.28 thf(fact_5557_even__set__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 & ( M != zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_set_bit_iff
% 5.01/5.28 thf(fact_5558_even__flip__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 != ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_flip_bit_iff
% 5.01/5.28 thf(fact_5559_even__flip__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 != ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_flip_bit_iff
% 5.01/5.28 thf(fact_5560_even__flip__bit__iff,axiom,
% 5.01/5.28 ! [M: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 != ( M = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_flip_bit_iff
% 5.01/5.28 thf(fact_5561_even__diff__iff,axiom,
% 5.01/5.28 ! [K: int,L: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_diff_iff
% 5.01/5.28 thf(fact_5562_oddE,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: code_integer] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % oddE
% 5.01/5.28 thf(fact_5563_oddE,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: nat] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % oddE
% 5.01/5.28 thf(fact_5564_oddE,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ~ ! [B2: int] :
% 5.01/5.28 ( A
% 5.01/5.28 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % oddE
% 5.01/5.28 thf(fact_5565_mod2__eq__if,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_nat ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod2_eq_if
% 5.01/5.28 thf(fact_5566_mod2__eq__if,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_int ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod2_eq_if
% 5.01/5.28 thf(fact_5567_mod2__eq__if,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_z3403309356797280102nteger ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = one_one_Code_integer ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mod2_eq_if
% 5.01/5.28 thf(fact_5568_parity__cases,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 != zero_zero_nat ) )
% 5.01/5.28 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 != one_one_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % parity_cases
% 5.01/5.28 thf(fact_5569_parity__cases,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 != zero_zero_int ) )
% 5.01/5.28 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 != one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % parity_cases
% 5.01/5.28 thf(fact_5570_parity__cases,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 != zero_z3403309356797280102nteger ) )
% 5.01/5.28 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 != one_one_Code_integer ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % parity_cases
% 5.01/5.28 thf(fact_5571_zero__le__power__eq,axiom,
% 5.01/5.28 ! [A: real,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_power_eq
% 5.01/5.28 thf(fact_5572_zero__le__power__eq,axiom,
% 5.01/5.28 ! [A: rat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_power_eq
% 5.01/5.28 thf(fact_5573_zero__le__power__eq,axiom,
% 5.01/5.28 ! [A: int,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.01/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_power_eq
% 5.01/5.28 thf(fact_5574_zero__le__odd__power,axiom,
% 5.01/5.28 ! [N: nat,A: real] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.01/5.28 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_odd_power
% 5.01/5.28 thf(fact_5575_zero__le__odd__power,axiom,
% 5.01/5.28 ! [N: nat,A: rat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.01/5.28 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_odd_power
% 5.01/5.28 thf(fact_5576_zero__le__odd__power,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.01/5.28 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_odd_power
% 5.01/5.28 thf(fact_5577_zero__le__even__power,axiom,
% 5.01/5.28 ! [N: nat,A: real] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_even_power
% 5.01/5.28 thf(fact_5578_zero__le__even__power,axiom,
% 5.01/5.28 ! [N: nat,A: rat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_even_power
% 5.01/5.28 thf(fact_5579_zero__le__even__power,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_le_even_power
% 5.01/5.28 thf(fact_5580_minus__one__power__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.01/5.28 = one_one_real ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.01/5.28 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minus_one_power_iff
% 5.01/5.28 thf(fact_5581_minus__one__power__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.01/5.28 = one_one_int ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.01/5.28 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minus_one_power_iff
% 5.01/5.28 thf(fact_5582_minus__one__power__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.01/5.28 = one_one_complex ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.01/5.28 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minus_one_power_iff
% 5.01/5.28 thf(fact_5583_minus__one__power__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.01/5.28 = one_one_Code_integer ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.01/5.28 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minus_one_power_iff
% 5.01/5.28 thf(fact_5584_minus__one__power__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.01/5.28 = one_one_rat ) )
% 5.01/5.28 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.01/5.28 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % minus_one_power_iff
% 5.01/5.28 thf(fact_5585_nat__intermed__int__val,axiom,
% 5.01/5.28 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.01/5.28 ( ! [I3: nat] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.01/5.28 & ( ord_less_nat @ I3 @ N ) )
% 5.01/5.28 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.01/5.28 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.01/5.28 => ? [I3: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ I3 )
% 5.01/5.28 & ( ord_less_eq_nat @ I3 @ N )
% 5.01/5.28 & ( ( F @ I3 )
% 5.01/5.28 = K ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % nat_intermed_int_val
% 5.01/5.28 thf(fact_5586_power__mono__even,axiom,
% 5.01/5.28 ! [N: nat,A: code_integer,B: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.01/5.28 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_even
% 5.01/5.28 thf(fact_5587_power__mono__even,axiom,
% 5.01/5.28 ! [N: nat,A: real,B: real] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.01/5.28 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_even
% 5.01/5.28 thf(fact_5588_power__mono__even,axiom,
% 5.01/5.28 ! [N: nat,A: rat,B: rat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.01/5.28 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_even
% 5.01/5.28 thf(fact_5589_power__mono__even,axiom,
% 5.01/5.28 ! [N: nat,A: int,B: int] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.01/5.28 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_mono_even
% 5.01/5.28 thf(fact_5590_incr__lemma,axiom,
% 5.01/5.28 ! [D: int,Z: int,X2: int] :
% 5.01/5.28 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.28 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % incr_lemma
% 5.01/5.28 thf(fact_5591_decr__lemma,axiom,
% 5.01/5.28 ! [D: int,X2: int,Z: int] :
% 5.01/5.28 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.28 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.01/5.28
% 5.01/5.28 % decr_lemma
% 5.01/5.28 thf(fact_5592_central__binomial__odd,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.28 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % central_binomial_odd
% 5.01/5.28 thf(fact_5593_zero__less__power__eq,axiom,
% 5.01/5.28 ! [A: real,N: nat] :
% 5.01/5.28 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A != zero_zero_real ) )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_power_eq
% 5.01/5.28 thf(fact_5594_zero__less__power__eq,axiom,
% 5.01/5.28 ! [A: rat,N: nat] :
% 5.01/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A != zero_zero_rat ) )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_power_eq
% 5.01/5.28 thf(fact_5595_zero__less__power__eq,axiom,
% 5.01/5.28 ! [A: int,N: nat] :
% 5.01/5.28 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A != zero_zero_int ) )
% 5.01/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_power_eq
% 5.01/5.28 thf(fact_5596_nat__ivt__aux,axiom,
% 5.01/5.28 ! [N: nat,F: nat > int,K: int] :
% 5.01/5.28 ( ! [I3: nat] :
% 5.01/5.28 ( ( ord_less_nat @ I3 @ N )
% 5.01/5.28 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.01/5.28 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.01/5.28 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.01/5.28 => ? [I3: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ I3 @ N )
% 5.01/5.28 & ( ( F @ I3 )
% 5.01/5.28 = K ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % nat_ivt_aux
% 5.01/5.28 thf(fact_5597_Euclid__induct,axiom,
% 5.01/5.28 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.01/5.28 ( ! [A3: nat,B2: nat] :
% 5.01/5.28 ( ( P @ A3 @ B2 )
% 5.01/5.28 = ( P @ B2 @ A3 ) )
% 5.01/5.28 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 5.01/5.28 => ( ! [A3: nat,B2: nat] :
% 5.01/5.28 ( ( P @ A3 @ B2 )
% 5.01/5.28 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
% 5.01/5.28 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % Euclid_induct
% 5.01/5.28 thf(fact_5598_complex__mod__minus__le__complex__mod,axiom,
% 5.01/5.28 ! [X2: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.28
% 5.01/5.28 % complex_mod_minus_le_complex_mod
% 5.01/5.28 thf(fact_5599_complex__mod__triangle__ineq2,axiom,
% 5.01/5.28 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % complex_mod_triangle_ineq2
% 5.01/5.28 thf(fact_5600_even__mask__div__iff_H,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff'
% 5.01/5.28 thf(fact_5601_even__mask__div__iff_H,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff'
% 5.01/5.28 thf(fact_5602_even__mask__div__iff_H,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff'
% 5.01/5.28 thf(fact_5603_power__le__zero__eq,axiom,
% 5.01/5.28 ! [A: real,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.01/5.28 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_zero_eq
% 5.01/5.28 thf(fact_5604_power__le__zero__eq,axiom,
% 5.01/5.28 ! [A: rat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.01/5.28 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_zero_eq
% 5.01/5.28 thf(fact_5605_power__le__zero__eq,axiom,
% 5.01/5.28 ! [A: int,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.01/5.28 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.01/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % power_le_zero_eq
% 5.01/5.28 thf(fact_5606_nat0__intermed__int__val,axiom,
% 5.01/5.28 ! [N: nat,F: nat > int,K: int] :
% 5.01/5.28 ( ! [I3: nat] :
% 5.01/5.28 ( ( ord_less_nat @ I3 @ N )
% 5.01/5.28 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.01/5.28 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.01/5.28 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.01/5.28 => ? [I3: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ I3 @ N )
% 5.01/5.28 & ( ( F @ I3 )
% 5.01/5.28 = K ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % nat0_intermed_int_val
% 5.01/5.28 thf(fact_5607_option_Osize__gen_I1_J,axiom,
% 5.01/5.28 ! [X2: product_prod_nat_nat > nat] :
% 5.01/5.28 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 5.01/5.28 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % option.size_gen(1)
% 5.01/5.28 thf(fact_5608_option_Osize__gen_I1_J,axiom,
% 5.01/5.28 ! [X2: num > nat] :
% 5.01/5.28 ( ( size_option_num @ X2 @ none_num )
% 5.01/5.28 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % option.size_gen(1)
% 5.01/5.28 thf(fact_5609_even__mod__4__div__2,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.28 = ( suc @ zero_zero_nat ) )
% 5.01/5.28 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mod_4_div_2
% 5.01/5.28 thf(fact_5610_arctan__add,axiom,
% 5.01/5.28 ! [X2: real,Y: real] :
% 5.01/5.28 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.28 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.28 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y ) )
% 5.01/5.28 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % arctan_add
% 5.01/5.28 thf(fact_5611_even__mask__div__iff,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff
% 5.01/5.28 thf(fact_5612_even__mask__div__iff,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff
% 5.01/5.28 thf(fact_5613_even__mask__div__iff,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mask_div_iff
% 5.01/5.28 thf(fact_5614_odd__mod__4__div__2,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.28 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.01/5.28 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % odd_mod_4_div_2
% 5.01/5.28 thf(fact_5615_Bernoulli__inequality__even,axiom,
% 5.01/5.28 ! [N: nat,X2: real] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % Bernoulli_inequality_even
% 5.01/5.28 thf(fact_5616_even__mult__exp__div__exp__iff,axiom,
% 5.01/5.28 ! [A: code_integer,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ord_less_nat @ N @ M )
% 5.01/5.28 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 | ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mult_exp_div_exp_iff
% 5.01/5.28 thf(fact_5617_even__mult__exp__div__exp__iff,axiom,
% 5.01/5.28 ! [A: nat,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ord_less_nat @ N @ M )
% 5.01/5.28 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 | ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mult_exp_div_exp_iff
% 5.01/5.28 thf(fact_5618_even__mult__exp__div__exp__iff,axiom,
% 5.01/5.28 ! [A: int,M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.28 = ( ( ord_less_nat @ N @ M )
% 5.01/5.28 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 | ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_mult_exp_div_exp_iff
% 5.01/5.28 thf(fact_5619_flip__bit__0,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.01/5.28 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % flip_bit_0
% 5.01/5.28 thf(fact_5620_flip__bit__0,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.01/5.28 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % flip_bit_0
% 5.01/5.28 thf(fact_5621_flip__bit__0,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.01/5.28 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % flip_bit_0
% 5.01/5.28 thf(fact_5622_set__decode__Suc,axiom,
% 5.01/5.28 ! [N: nat,X2: nat] :
% 5.01/5.28 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X2 ) )
% 5.01/5.28 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % set_decode_Suc
% 5.01/5.28 thf(fact_5623_add__scale__eq__noteq,axiom,
% 5.01/5.28 ! [R: real,A: real,B: real,C: real,D: real] :
% 5.01/5.28 ( ( R != zero_zero_real )
% 5.01/5.28 => ( ( ( A = B )
% 5.01/5.28 & ( C != D ) )
% 5.01/5.28 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 5.01/5.28 != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % add_scale_eq_noteq
% 5.01/5.28 thf(fact_5624_add__scale__eq__noteq,axiom,
% 5.01/5.28 ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.28 ( ( R != zero_zero_rat )
% 5.01/5.28 => ( ( ( A = B )
% 5.01/5.28 & ( C != D ) )
% 5.01/5.28 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 5.01/5.28 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % add_scale_eq_noteq
% 5.01/5.28 thf(fact_5625_add__scale__eq__noteq,axiom,
% 5.01/5.28 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.28 ( ( R != zero_zero_nat )
% 5.01/5.28 => ( ( ( A = B )
% 5.01/5.28 & ( C != D ) )
% 5.01/5.28 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 5.01/5.28 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % add_scale_eq_noteq
% 5.01/5.28 thf(fact_5626_add__scale__eq__noteq,axiom,
% 5.01/5.28 ! [R: int,A: int,B: int,C: int,D: int] :
% 5.01/5.28 ( ( R != zero_zero_int )
% 5.01/5.28 => ( ( ( A = B )
% 5.01/5.28 & ( C != D ) )
% 5.01/5.28 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 5.01/5.28 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % add_scale_eq_noteq
% 5.01/5.28 thf(fact_5627_add__scale__eq__noteq,axiom,
% 5.01/5.28 ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.01/5.28 ( ( R != zero_zero_complex )
% 5.01/5.28 => ( ( ( A = B )
% 5.01/5.28 & ( C != D ) )
% 5.01/5.28 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 5.01/5.28 != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % add_scale_eq_noteq
% 5.01/5.28 thf(fact_5628_fact__double,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_double
% 5.01/5.28 thf(fact_5629_fact__double,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_double
% 5.01/5.28 thf(fact_5630_fact__double,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_double
% 5.01/5.28 thf(fact_5631_mask__numeral,axiom,
% 5.01/5.28 ! [N: num] :
% 5.01/5.28 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.01/5.28 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_numeral
% 5.01/5.28 thf(fact_5632_mask__numeral,axiom,
% 5.01/5.28 ! [N: num] :
% 5.01/5.28 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.01/5.28 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_numeral
% 5.01/5.28 thf(fact_5633_num_Osize__gen_I3_J,axiom,
% 5.01/5.28 ! [X33: num] :
% 5.01/5.28 ( ( size_num @ ( bit1 @ X33 ) )
% 5.01/5.28 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % num.size_gen(3)
% 5.01/5.28 thf(fact_5634_take__bit__rec,axiom,
% 5.01/5.28 ( bit_se1745604003318907178nteger
% 5.01/5.28 = ( ^ [N4: nat,A4: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_rec
% 5.01/5.28 thf(fact_5635_take__bit__rec,axiom,
% 5.01/5.28 ( bit_se2923211474154528505it_int
% 5.01/5.28 = ( ^ [N4: nat,A4: int] : ( if_int @ ( N4 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_rec
% 5.01/5.28 thf(fact_5636_take__bit__rec,axiom,
% 5.01/5.28 ( bit_se2925701944663578781it_nat
% 5.01/5.28 = ( ^ [N4: nat,A4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_rec
% 5.01/5.28 thf(fact_5637_mask__nat__positive__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.28 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_nat_positive_iff
% 5.01/5.28 thf(fact_5638_take__bit__of__0,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.01/5.28 = zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_0
% 5.01/5.28 thf(fact_5639_take__bit__of__0,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_0
% 5.01/5.28 thf(fact_5640_of__bool__less__eq__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.01/5.28 = ( P
% 5.01/5.28 => Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_iff
% 5.01/5.28 thf(fact_5641_of__bool__less__eq__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.01/5.28 = ( P
% 5.01/5.28 => Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_iff
% 5.01/5.28 thf(fact_5642_of__bool__less__eq__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.01/5.28 = ( P
% 5.01/5.28 => Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_iff
% 5.01/5.28 thf(fact_5643_of__bool__less__eq__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.01/5.28 = ( P
% 5.01/5.28 => Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_iff
% 5.01/5.28 thf(fact_5644_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.01/5.28 = zero_zero_complex )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5645_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.01/5.28 = zero_zero_real )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5646_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.01/5.28 = zero_zero_rat )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5647_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5648_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5649_of__bool__eq__0__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n356916108424825756nteger @ P )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_0_iff
% 5.01/5.28 thf(fact_5650_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n1201886186963655149omplex @ $false )
% 5.01/5.28 = zero_zero_complex ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5651_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n3304061248610475627l_real @ $false )
% 5.01/5.28 = zero_zero_real ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5652_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.01/5.28 = zero_zero_rat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5653_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5654_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.01/5.28 = zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5655_of__bool__eq_I1_J,axiom,
% 5.01/5.28 ( ( zero_n356916108424825756nteger @ $false )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(1)
% 5.01/5.28 thf(fact_5656_of__bool__less__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.01/5.28 = ( ~ P
% 5.01/5.28 & Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_iff
% 5.01/5.28 thf(fact_5657_of__bool__less__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.01/5.28 = ( ~ P
% 5.01/5.28 & Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_iff
% 5.01/5.28 thf(fact_5658_of__bool__less__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.01/5.28 = ( ~ P
% 5.01/5.28 & Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_iff
% 5.01/5.28 thf(fact_5659_of__bool__less__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.01/5.28 = ( ~ P
% 5.01/5.28 & Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_iff
% 5.01/5.28 thf(fact_5660_of__bool__less__iff,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.01/5.28 = ( ~ P
% 5.01/5.28 & Q ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_iff
% 5.01/5.28 thf(fact_5661_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n1201886186963655149omplex @ $true )
% 5.01/5.28 = one_one_complex ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5662_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n3304061248610475627l_real @ $true )
% 5.01/5.28 = one_one_real ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5663_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.01/5.28 = one_one_rat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5664_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5665_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5666_of__bool__eq_I2_J,axiom,
% 5.01/5.28 ( ( zero_n356916108424825756nteger @ $true )
% 5.01/5.28 = one_one_Code_integer ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq(2)
% 5.01/5.28 thf(fact_5667_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.01/5.28 = one_one_complex )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5668_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.01/5.28 = one_one_real )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5669_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.01/5.28 = one_one_rat )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5670_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.01/5.28 = one_one_nat )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5671_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.01/5.28 = one_one_int )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5672_of__bool__eq__1__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ( zero_n356916108424825756nteger @ P )
% 5.01/5.28 = one_one_Code_integer )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_1_iff
% 5.01/5.28 thf(fact_5673_of__nat__fact,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1314217659103216013at_int @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.28 = ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_fact
% 5.01/5.28 thf(fact_5674_of__nat__fact,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri4939895301339042750nteger @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.28 = ( semiri3624122377584611663nteger @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_fact
% 5.01/5.28 thf(fact_5675_of__nat__fact,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1316708129612266289at_nat @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.28 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_fact
% 5.01/5.28 thf(fact_5676_of__nat__fact,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri5074537144036343181t_real @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.28 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_fact
% 5.01/5.28 thf(fact_5677_of__nat__fact,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri8010041392384452111omplex @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.28 = ( semiri5044797733671781792omplex @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_fact
% 5.01/5.28 thf(fact_5678_of__nat__of__bool,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_of_bool
% 5.01/5.28 thf(fact_5679_of__nat__of__bool,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_of_bool
% 5.01/5.28 thf(fact_5680_of__nat__of__bool,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_of_bool
% 5.01/5.28 thf(fact_5681_of__nat__of__bool,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_of_bool
% 5.01/5.28 thf(fact_5682_of__nat__of__bool,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_of_bool
% 5.01/5.28 thf(fact_5683_abs__bool__eq,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.01/5.28 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_bool_eq
% 5.01/5.28 thf(fact_5684_abs__bool__eq,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.01/5.28 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_bool_eq
% 5.01/5.28 thf(fact_5685_abs__bool__eq,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_bool_eq
% 5.01/5.28 thf(fact_5686_abs__bool__eq,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % abs_bool_eq
% 5.01/5.28 thf(fact_5687_concat__bit__of__zero__2,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % concat_bit_of_zero_2
% 5.01/5.28 thf(fact_5688_take__bit__of__Suc__0,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_Suc_0
% 5.01/5.28 thf(fact_5689_zero__less__of__bool__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_of_bool_iff
% 5.01/5.28 thf(fact_5690_zero__less__of__bool__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_of_bool_iff
% 5.01/5.28 thf(fact_5691_zero__less__of__bool__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_of_bool_iff
% 5.01/5.28 thf(fact_5692_zero__less__of__bool__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_of_bool_iff
% 5.01/5.28 thf(fact_5693_zero__less__of__bool__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.01/5.28 = P ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_of_bool_iff
% 5.01/5.28 thf(fact_5694_take__bit__0,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.01/5.28 = zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_0
% 5.01/5.28 thf(fact_5695_take__bit__0,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_0
% 5.01/5.28 thf(fact_5696_of__bool__less__one__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_one_iff
% 5.01/5.28 thf(fact_5697_of__bool__less__one__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_one_iff
% 5.01/5.28 thf(fact_5698_of__bool__less__one__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_one_iff
% 5.01/5.28 thf(fact_5699_of__bool__less__one__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_one_iff
% 5.01/5.28 thf(fact_5700_of__bool__less__one__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.01/5.28 = ~ P ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_one_iff
% 5.01/5.28 thf(fact_5701_take__bit__Suc__1,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_1
% 5.01/5.28 thf(fact_5702_take__bit__Suc__1,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_1
% 5.01/5.28 thf(fact_5703_take__bit__numeral__1,axiom,
% 5.01/5.28 ! [L: num] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_numeral_1
% 5.01/5.28 thf(fact_5704_take__bit__numeral__1,axiom,
% 5.01/5.28 ! [L: num] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_numeral_1
% 5.01/5.28 thf(fact_5705_fact__0,axiom,
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.01/5.28 = one_one_rat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_0
% 5.01/5.28 thf(fact_5706_fact__0,axiom,
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % fact_0
% 5.01/5.28 thf(fact_5707_fact__0,axiom,
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_0
% 5.01/5.28 thf(fact_5708_fact__0,axiom,
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.01/5.28 = one_one_real ) ).
% 5.01/5.28
% 5.01/5.28 % fact_0
% 5.01/5.28 thf(fact_5709_fact__0,axiom,
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.01/5.28 = one_one_complex ) ).
% 5.01/5.28
% 5.01/5.28 % fact_0
% 5.01/5.28 thf(fact_5710_of__bool__not__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.01/5.28 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_not_iff
% 5.01/5.28 thf(fact_5711_of__bool__not__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.01/5.28 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_not_iff
% 5.01/5.28 thf(fact_5712_of__bool__not__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.01/5.28 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_not_iff
% 5.01/5.28 thf(fact_5713_of__bool__not__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.01/5.28 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_not_iff
% 5.01/5.28 thf(fact_5714_of__bool__not__iff,axiom,
% 5.01/5.28 ! [P: $o] :
% 5.01/5.28 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.01/5.28 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_not_iff
% 5.01/5.28 thf(fact_5715_Suc__0__mod__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat
% 5.01/5.28 @ ( N
% 5.01/5.28 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % Suc_0_mod_eq
% 5.01/5.28 thf(fact_5716_mask__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( N = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_eq_0_iff
% 5.01/5.28 thf(fact_5717_mask__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( N = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_eq_0_iff
% 5.01/5.28 thf(fact_5718_mask__0,axiom,
% 5.01/5.28 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % mask_0
% 5.01/5.28 thf(fact_5719_mask__0,axiom,
% 5.01/5.28 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.01/5.28 = zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % mask_0
% 5.01/5.28 thf(fact_5720_fact__1,axiom,
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.01/5.28 = one_one_rat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_1
% 5.01/5.28 thf(fact_5721_fact__1,axiom,
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % fact_1
% 5.01/5.28 thf(fact_5722_fact__1,axiom,
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_1
% 5.01/5.28 thf(fact_5723_fact__1,axiom,
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.01/5.28 = one_one_real ) ).
% 5.01/5.28
% 5.01/5.28 % fact_1
% 5.01/5.28 thf(fact_5724_fact__1,axiom,
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.01/5.28 = one_one_complex ) ).
% 5.01/5.28
% 5.01/5.28 % fact_1
% 5.01/5.28 thf(fact_5725_take__bit__of__1__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( N = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_1_eq_0_iff
% 5.01/5.28 thf(fact_5726_take__bit__of__1__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( N = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_1_eq_0_iff
% 5.01/5.28 thf(fact_5727_fact__Suc__0,axiom,
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_rat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc_0
% 5.01/5.28 thf(fact_5728_fact__Suc__0,axiom,
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc_0
% 5.01/5.28 thf(fact_5729_fact__Suc__0,axiom,
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc_0
% 5.01/5.28 thf(fact_5730_fact__Suc__0,axiom,
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_real ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc_0
% 5.01/5.28 thf(fact_5731_fact__Suc__0,axiom,
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_complex ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc_0
% 5.01/5.28 thf(fact_5732_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.01/5.28 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5733_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.01/5.28 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5734_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 5.01/5.28 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5735_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.01/5.28 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5736_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.01/5.28 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5737_fact__Suc,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.01/5.28 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_Suc
% 5.01/5.28 thf(fact_5738_mask__Suc__0,axiom,
% 5.01/5.28 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % mask_Suc_0
% 5.01/5.28 thf(fact_5739_mask__Suc__0,axiom,
% 5.01/5.28 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.01/5.28 = one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % mask_Suc_0
% 5.01/5.28 thf(fact_5740_take__bit__minus__one__eq__mask,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.28 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_minus_one_eq_mask
% 5.01/5.28 thf(fact_5741_take__bit__minus__one__eq__mask,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.28 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_minus_one_eq_mask
% 5.01/5.28 thf(fact_5742_Divides_Oadjust__div__eq,axiom,
% 5.01/5.28 ! [Q2: int,R: int] :
% 5.01/5.28 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.01/5.28 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % Divides.adjust_div_eq
% 5.01/5.28 thf(fact_5743_fact__2,axiom,
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_2
% 5.01/5.28 thf(fact_5744_fact__2,axiom,
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_2
% 5.01/5.28 thf(fact_5745_fact__2,axiom,
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_2
% 5.01/5.28 thf(fact_5746_fact__2,axiom,
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_2
% 5.01/5.28 thf(fact_5747_fact__2,axiom,
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_2
% 5.01/5.28 thf(fact_5748_odd__of__bool__self,axiom,
% 5.01/5.28 ! [P4: $o] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P4 ) ) )
% 5.01/5.28 = P4 ) ).
% 5.01/5.28
% 5.01/5.28 % odd_of_bool_self
% 5.01/5.28 thf(fact_5749_odd__of__bool__self,axiom,
% 5.01/5.28 ! [P4: $o] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P4 ) ) )
% 5.01/5.28 = P4 ) ).
% 5.01/5.28
% 5.01/5.28 % odd_of_bool_self
% 5.01/5.28 thf(fact_5750_odd__of__bool__self,axiom,
% 5.01/5.28 ! [P4: $o] :
% 5.01/5.28 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P4 ) ) )
% 5.01/5.28 = P4 ) ).
% 5.01/5.28
% 5.01/5.28 % odd_of_bool_self
% 5.01/5.28 thf(fact_5751_take__bit__of__1,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_1
% 5.01/5.28 thf(fact_5752_take__bit__of__1,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_1
% 5.01/5.28 thf(fact_5753_take__bit__of__1,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_1
% 5.01/5.28 thf(fact_5754_of__bool__half__eq__0,axiom,
% 5.01/5.28 ! [B: $o] :
% 5.01/5.28 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_half_eq_0
% 5.01/5.28 thf(fact_5755_of__bool__half__eq__0,axiom,
% 5.01/5.28 ! [B: $o] :
% 5.01/5.28 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_half_eq_0
% 5.01/5.28 thf(fact_5756_of__bool__half__eq__0,axiom,
% 5.01/5.28 ! [B: $o] :
% 5.01/5.28 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_half_eq_0
% 5.01/5.28 thf(fact_5757_even__take__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,A: code_integer] :
% 5.01/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_take_bit_eq
% 5.01/5.28 thf(fact_5758_even__take__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_take_bit_eq
% 5.01/5.28 thf(fact_5759_even__take__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,A: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.01/5.28 = ( ( N = zero_zero_nat )
% 5.01/5.28 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % even_take_bit_eq
% 5.01/5.28 thf(fact_5760_set__decode__0,axiom,
% 5.01/5.28 ! [X2: nat] :
% 5.01/5.28 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.01/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % set_decode_0
% 5.01/5.28 thf(fact_5761_take__bit__Suc__0,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.01/5.28 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_0
% 5.01/5.28 thf(fact_5762_take__bit__Suc__0,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.01/5.28 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_0
% 5.01/5.28 thf(fact_5763_take__bit__Suc__0,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.01/5.28 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_0
% 5.01/5.28 thf(fact_5764_one__div__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_div_2_pow_eq
% 5.01/5.28 thf(fact_5765_one__div__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_div_2_pow_eq
% 5.01/5.28 thf(fact_5766_one__div__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_div_2_pow_eq
% 5.01/5.28 thf(fact_5767_bits__1__div__exp,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_1_div_exp
% 5.01/5.28 thf(fact_5768_bits__1__div__exp,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_1_div_exp
% 5.01/5.28 thf(fact_5769_bits__1__div__exp,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_1_div_exp
% 5.01/5.28 thf(fact_5770_take__bit__of__exp,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_exp
% 5.01/5.28 thf(fact_5771_take__bit__of__exp,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_exp
% 5.01/5.28 thf(fact_5772_take__bit__of__exp,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_exp
% 5.01/5.28 thf(fact_5773_take__bit__of__2,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_2
% 5.01/5.28 thf(fact_5774_take__bit__of__2,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_2
% 5.01/5.28 thf(fact_5775_take__bit__of__2,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_2
% 5.01/5.28 thf(fact_5776_one__mod__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_mod_2_pow_eq
% 5.01/5.28 thf(fact_5777_one__mod__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_mod_2_pow_eq
% 5.01/5.28 thf(fact_5778_one__mod__2__pow__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % one_mod_2_pow_eq
% 5.01/5.28 thf(fact_5779_dvd__antisym,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( dvd_dvd_nat @ M @ N )
% 5.01/5.28 => ( ( dvd_dvd_nat @ N @ M )
% 5.01/5.28 => ( M = N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_antisym
% 5.01/5.28 thf(fact_5780_take__bit__of__nat,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( bit_se1745604003318907178nteger @ N @ ( semiri4939895301339042750nteger @ M ) )
% 5.01/5.28 = ( semiri4939895301339042750nteger @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_nat
% 5.01/5.28 thf(fact_5781_take__bit__of__nat,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.01/5.28 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_nat
% 5.01/5.28 thf(fact_5782_take__bit__of__nat,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.01/5.28 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_of_nat
% 5.01/5.28 thf(fact_5783_of__nat__mask__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri4939895301339042750nteger @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.28 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_mask_eq
% 5.01/5.28 thf(fact_5784_of__nat__mask__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.28 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_mask_eq
% 5.01/5.28 thf(fact_5785_of__nat__mask__eq,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.28 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_nat_mask_eq
% 5.01/5.28 thf(fact_5786_of__bool__eq__iff,axiom,
% 5.01/5.28 ! [P4: $o,Q2: $o] :
% 5.01/5.28 ( ( ( zero_n2687167440665602831ol_nat @ P4 )
% 5.01/5.28 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.01/5.28 = ( P4 = Q2 ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_iff
% 5.01/5.28 thf(fact_5787_of__bool__eq__iff,axiom,
% 5.01/5.28 ! [P4: $o,Q2: $o] :
% 5.01/5.28 ( ( ( zero_n2684676970156552555ol_int @ P4 )
% 5.01/5.28 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.01/5.28 = ( P4 = Q2 ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_iff
% 5.01/5.28 thf(fact_5788_of__bool__eq__iff,axiom,
% 5.01/5.28 ! [P4: $o,Q2: $o] :
% 5.01/5.28 ( ( ( zero_n356916108424825756nteger @ P4 )
% 5.01/5.28 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.01/5.28 = ( P4 = Q2 ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_eq_iff
% 5.01/5.28 thf(fact_5789_take__bit__add,axiom,
% 5.01/5.28 ! [N: nat,A: int,B: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_add
% 5.01/5.28 thf(fact_5790_take__bit__add,axiom,
% 5.01/5.28 ! [N: nat,A: nat,B: nat] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_add
% 5.01/5.28 thf(fact_5791_take__bit__tightened,axiom,
% 5.01/5.28 ! [N: nat,A: int,B: int,M: nat] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_tightened
% 5.01/5.28 thf(fact_5792_take__bit__tightened,axiom,
% 5.01/5.28 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.01/5.28 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_tightened
% 5.01/5.28 thf(fact_5793_take__bit__nat__less__eq__self,axiom,
% 5.01/5.28 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_less_eq_self
% 5.01/5.28 thf(fact_5794_take__bit__tightened__less__eq__nat,axiom,
% 5.01/5.28 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_tightened_less_eq_nat
% 5.01/5.28 thf(fact_5795_fact__mono__nat,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mono_nat
% 5.01/5.28 thf(fact_5796_fact__ge__self,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_self
% 5.01/5.28 thf(fact_5797_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n3304061248610475627l_real
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5798_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n2052037380579107095ol_rat
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5799_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n1201886186963655149omplex
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5800_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n2687167440665602831ol_nat
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5801_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n2684676970156552555ol_int
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5802_of__bool__conj,axiom,
% 5.01/5.28 ! [P: $o,Q: $o] :
% 5.01/5.28 ( ( zero_n356916108424825756nteger
% 5.01/5.28 @ ( P
% 5.01/5.28 & Q ) )
% 5.01/5.28 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_conj
% 5.01/5.28 thf(fact_5803_fact__nonzero,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ N )
% 5.01/5.28 != zero_zero_rat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_nonzero
% 5.01/5.28 thf(fact_5804_fact__nonzero,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ N )
% 5.01/5.28 != zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % fact_nonzero
% 5.01/5.28 thf(fact_5805_fact__nonzero,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ N )
% 5.01/5.28 != zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_nonzero
% 5.01/5.28 thf(fact_5806_fact__nonzero,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ N )
% 5.01/5.28 != zero_zero_real ) ).
% 5.01/5.28
% 5.01/5.28 % fact_nonzero
% 5.01/5.28 thf(fact_5807_fact__nonzero,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ N )
% 5.01/5.28 != zero_zero_complex ) ).
% 5.01/5.28
% 5.01/5.28 % fact_nonzero
% 5.01/5.28 thf(fact_5808_take__bit__minus,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_minus
% 5.01/5.28 thf(fact_5809_take__bit__mult,axiom,
% 5.01/5.28 ! [N: nat,K: int,L: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_mult
% 5.01/5.28 thf(fact_5810_take__bit__diff,axiom,
% 5.01/5.28 ! [N: nat,K: int,L: int] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_diff
% 5.01/5.28 thf(fact_5811_concat__bit__take__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,B: int] :
% 5.01/5.28 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.01/5.28 = ( bit_concat_bit @ N @ B ) ) ).
% 5.01/5.28
% 5.01/5.28 % concat_bit_take_bit_eq
% 5.01/5.28 thf(fact_5812_concat__bit__eq__iff,axiom,
% 5.01/5.28 ! [N: nat,K: int,L: int,R: int,S2: int] :
% 5.01/5.28 ( ( ( bit_concat_bit @ N @ K @ L )
% 5.01/5.28 = ( bit_concat_bit @ N @ R @ S2 ) )
% 5.01/5.28 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ R ) )
% 5.01/5.28 & ( L = S2 ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % concat_bit_eq_iff
% 5.01/5.28 thf(fact_5813_less__eq__mask,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % less_eq_mask
% 5.01/5.28 thf(fact_5814_take__bit__eq__mask__iff,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.28 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.28 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.01/5.28 = zero_zero_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_mask_iff
% 5.01/5.28 thf(fact_5815_subset__decode__imp__le,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.01/5.28 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % subset_decode_imp_le
% 5.01/5.28 thf(fact_5816_fact__less__mono__nat,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_less_mono_nat
% 5.01/5.28 thf(fact_5817_zero__less__eq__of__bool,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_eq_of_bool
% 5.01/5.28 thf(fact_5818_zero__less__eq__of__bool,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_eq_of_bool
% 5.01/5.28 thf(fact_5819_zero__less__eq__of__bool,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_eq_of_bool
% 5.01/5.28 thf(fact_5820_zero__less__eq__of__bool,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_eq_of_bool
% 5.01/5.28 thf(fact_5821_zero__less__eq__of__bool,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.01/5.28
% 5.01/5.28 % zero_less_eq_of_bool
% 5.01/5.28 thf(fact_5822_of__bool__less__eq__one,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_one
% 5.01/5.28 thf(fact_5823_of__bool__less__eq__one,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_one
% 5.01/5.28 thf(fact_5824_of__bool__less__eq__one,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_one
% 5.01/5.28 thf(fact_5825_of__bool__less__eq__one,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_one
% 5.01/5.28 thf(fact_5826_of__bool__less__eq__one,axiom,
% 5.01/5.28 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_less_eq_one
% 5.01/5.28 thf(fact_5827_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: complex > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_complex ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5828_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: real > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_real ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5829_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: rat > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_rat ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5830_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: nat > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_nat ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5831_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: int > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_int ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5832_split__of__bool__asm,axiom,
% 5.01/5.28 ! [P: code_integer > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 5.01/5.28 = ( ~ ( ( P4
% 5.01/5.28 & ~ ( P @ one_one_Code_integer ) )
% 5.01/5.28 | ( ~ P4
% 5.01/5.28 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool_asm
% 5.01/5.28 thf(fact_5833_split__of__bool,axiom,
% 5.01/5.28 ! [P: complex > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_complex ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5834_split__of__bool,axiom,
% 5.01/5.28 ! [P: real > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_real ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_zero_real ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5835_split__of__bool,axiom,
% 5.01/5.28 ! [P: rat > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_rat ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5836_split__of__bool,axiom,
% 5.01/5.28 ! [P: nat > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_nat ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5837_split__of__bool,axiom,
% 5.01/5.28 ! [P: int > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_int ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_zero_int ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5838_split__of__bool,axiom,
% 5.01/5.28 ! [P: code_integer > $o,P4: $o] :
% 5.01/5.28 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 5.01/5.28 = ( ( P4
% 5.01/5.28 => ( P @ one_one_Code_integer ) )
% 5.01/5.28 & ( ~ P4
% 5.01/5.28 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % split_of_bool
% 5.01/5.28 thf(fact_5839_of__bool__def,axiom,
% 5.01/5.28 ( zero_n1201886186963655149omplex
% 5.01/5.28 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5840_of__bool__def,axiom,
% 5.01/5.28 ( zero_n3304061248610475627l_real
% 5.01/5.28 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5841_of__bool__def,axiom,
% 5.01/5.28 ( zero_n2052037380579107095ol_rat
% 5.01/5.28 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5842_of__bool__def,axiom,
% 5.01/5.28 ( zero_n2687167440665602831ol_nat
% 5.01/5.28 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5843_of__bool__def,axiom,
% 5.01/5.28 ( zero_n2684676970156552555ol_int
% 5.01/5.28 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5844_of__bool__def,axiom,
% 5.01/5.28 ( zero_n356916108424825756nteger
% 5.01/5.28 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_def
% 5.01/5.28 thf(fact_5845_dvd__fact,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.01/5.28 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % dvd_fact
% 5.01/5.28 thf(fact_5846_take__bit__tightened__less__eq__int,axiom,
% 5.01/5.28 ! [M: nat,N: nat,K: int] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_tightened_less_eq_int
% 5.01/5.28 thf(fact_5847_take__bit__nonnegative,axiom,
% 5.01/5.28 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nonnegative
% 5.01/5.28 thf(fact_5848_take__bit__int__less__eq__self__iff,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.01/5.28 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_less_eq_self_iff
% 5.01/5.28 thf(fact_5849_not__take__bit__negative,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % not_take_bit_negative
% 5.01/5.28 thf(fact_5850_take__bit__int__greater__self__iff,axiom,
% 5.01/5.28 ! [K: int,N: nat] :
% 5.01/5.28 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.01/5.28 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_greater_self_iff
% 5.01/5.28 thf(fact_5851_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,A: int,B: int] :
% 5.01/5.28 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.01/5.28 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.01/5.28 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % signed_take_bit_eq_iff_take_bit_eq
% 5.01/5.28 thf(fact_5852_fact__ge__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_zero
% 5.01/5.28 thf(fact_5853_fact__ge__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_zero
% 5.01/5.28 thf(fact_5854_fact__ge__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_zero
% 5.01/5.28 thf(fact_5855_fact__ge__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_zero
% 5.01/5.28 thf(fact_5856_fact__not__neg,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_not_neg
% 5.01/5.28 thf(fact_5857_fact__not__neg,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % fact_not_neg
% 5.01/5.28 thf(fact_5858_fact__not__neg,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % fact_not_neg
% 5.01/5.28 thf(fact_5859_fact__not__neg,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.01/5.28
% 5.01/5.28 % fact_not_neg
% 5.01/5.28 thf(fact_5860_fact__gt__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_gt_zero
% 5.01/5.28 thf(fact_5861_fact__gt__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_gt_zero
% 5.01/5.28 thf(fact_5862_fact__gt__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_gt_zero
% 5.01/5.28 thf(fact_5863_fact__gt__zero,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_gt_zero
% 5.01/5.28 thf(fact_5864_signed__take__bit__take__bit,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: int] :
% 5.01/5.28 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.01/5.28 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % signed_take_bit_take_bit
% 5.01/5.28 thf(fact_5865_fact__ge__1,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_1
% 5.01/5.28 thf(fact_5866_fact__ge__1,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_1
% 5.01/5.28 thf(fact_5867_fact__ge__1,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_1
% 5.01/5.28 thf(fact_5868_fact__ge__1,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_1
% 5.01/5.28 thf(fact_5869_fact__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mono
% 5.01/5.28 thf(fact_5870_fact__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mono
% 5.01/5.28 thf(fact_5871_fact__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mono
% 5.01/5.28 thf(fact_5872_fact__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mono
% 5.01/5.28 thf(fact_5873_take__bit__unset__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: int] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_unset_bit_eq
% 5.01/5.28 thf(fact_5874_take__bit__unset__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: nat] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_unset_bit_eq
% 5.01/5.28 thf(fact_5875_take__bit__set__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: int] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_set_bit_eq
% 5.01/5.28 thf(fact_5876_take__bit__set__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: nat] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_set_bit_eq
% 5.01/5.28 thf(fact_5877_take__bit__flip__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: int] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.01/5.28 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_flip_bit_eq
% 5.01/5.28 thf(fact_5878_take__bit__flip__bit__eq,axiom,
% 5.01/5.28 ! [N: nat,M: nat,A: nat] :
% 5.01/5.28 ( ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.01/5.28 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.01/5.28 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_flip_bit_eq
% 5.01/5.28 thf(fact_5879_fact__dvd,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_dvd
% 5.01/5.28 thf(fact_5880_fact__dvd,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_dvd
% 5.01/5.28 thf(fact_5881_fact__dvd,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_dvd
% 5.01/5.28 thf(fact_5882_fact__dvd,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.28 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_dvd
% 5.01/5.28 thf(fact_5883_pochhammer__fact,axiom,
% 5.01/5.28 ( semiri773545260158071498ct_rat
% 5.01/5.28 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.01/5.28
% 5.01/5.28 % pochhammer_fact
% 5.01/5.28 thf(fact_5884_pochhammer__fact,axiom,
% 5.01/5.28 ( semiri1406184849735516958ct_int
% 5.01/5.28 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % pochhammer_fact
% 5.01/5.28 thf(fact_5885_pochhammer__fact,axiom,
% 5.01/5.28 ( semiri1408675320244567234ct_nat
% 5.01/5.28 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % pochhammer_fact
% 5.01/5.28 thf(fact_5886_pochhammer__fact,axiom,
% 5.01/5.28 ( semiri2265585572941072030t_real
% 5.01/5.28 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.01/5.28
% 5.01/5.28 % pochhammer_fact
% 5.01/5.28 thf(fact_5887_pochhammer__fact,axiom,
% 5.01/5.28 ( semiri5044797733671781792omplex
% 5.01/5.28 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.01/5.28
% 5.01/5.28 % pochhammer_fact
% 5.01/5.28 thf(fact_5888_mask__nonnegative__int,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_nonnegative_int
% 5.01/5.28 thf(fact_5889_not__mask__negative__int,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.01/5.28
% 5.01/5.28 % not_mask_negative_int
% 5.01/5.28 thf(fact_5890_fact__ge__Suc__0__nat,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_ge_Suc_0_nat
% 5.01/5.28 thf(fact_5891_take__bit__signed__take__bit,axiom,
% 5.01/5.28 ! [M: nat,N: nat,A: int] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.01/5.28 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_signed_take_bit
% 5.01/5.28 thf(fact_5892_take__bit__decr__eq,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.28 != zero_zero_int )
% 5.01/5.28 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.01/5.28 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_decr_eq
% 5.01/5.28 thf(fact_5893_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.28 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.28 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_mask_iff_exp_dvd
% 5.01/5.28 thf(fact_5894_fact__less__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_less_mono
% 5.01/5.28 thf(fact_5895_fact__less__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_less_mono
% 5.01/5.28 thf(fact_5896_fact__less__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_less_mono
% 5.01/5.28 thf(fact_5897_fact__less__mono,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.28 => ( ( ord_less_nat @ M @ N )
% 5.01/5.28 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_less_mono
% 5.01/5.28 thf(fact_5898_fact__fact__dvd__fact,axiom,
% 5.01/5.28 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_fact_dvd_fact
% 5.01/5.28 thf(fact_5899_fact__fact__dvd__fact,axiom,
% 5.01/5.28 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_fact_dvd_fact
% 5.01/5.28 thf(fact_5900_fact__fact__dvd__fact,axiom,
% 5.01/5.28 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_fact_dvd_fact
% 5.01/5.28 thf(fact_5901_fact__fact__dvd__fact,axiom,
% 5.01/5.28 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_fact_dvd_fact
% 5.01/5.28 thf(fact_5902_fact__fact__dvd__fact,axiom,
% 5.01/5.28 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_fact_dvd_fact
% 5.01/5.28 thf(fact_5903_fact__mod,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.01/5.28 = zero_zero_int ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mod
% 5.01/5.28 thf(fact_5904_fact__mod,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.01/5.28 = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mod
% 5.01/5.28 thf(fact_5905_fact__mod,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.28 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.01/5.28 = zero_zero_nat ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_mod
% 5.01/5.28 thf(fact_5906_fact__le__power,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_le_power
% 5.01/5.28 thf(fact_5907_fact__le__power,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_le_power
% 5.01/5.28 thf(fact_5908_fact__le__power,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_le_power
% 5.01/5.28 thf(fact_5909_fact__le__power,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_le_power
% 5.01/5.28 thf(fact_5910_fact__le__power,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_le_power
% 5.01/5.28 thf(fact_5911_less__mask,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.28 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % less_mask
% 5.01/5.28 thf(fact_5912_fact__diff__Suc,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.01/5.28 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.01/5.28 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_diff_Suc
% 5.01/5.28 thf(fact_5913_fact__div__fact__le__pow,axiom,
% 5.01/5.28 ! [R: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ R @ N )
% 5.01/5.28 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_div_fact_le_pow
% 5.01/5.28 thf(fact_5914_binomial__fact__lemma,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.01/5.28 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % binomial_fact_lemma
% 5.01/5.28 thf(fact_5915_choose__dvd,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % choose_dvd
% 5.01/5.28 thf(fact_5916_choose__dvd,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % choose_dvd
% 5.01/5.28 thf(fact_5917_choose__dvd,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % choose_dvd
% 5.01/5.28 thf(fact_5918_choose__dvd,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % choose_dvd
% 5.01/5.28 thf(fact_5919_choose__dvd,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % choose_dvd
% 5.01/5.28 thf(fact_5920_fact__numeral,axiom,
% 5.01/5.28 ! [K: num] :
% 5.01/5.28 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.01/5.28 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_numeral
% 5.01/5.28 thf(fact_5921_fact__numeral,axiom,
% 5.01/5.28 ! [K: num] :
% 5.01/5.28 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.01/5.28 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_numeral
% 5.01/5.28 thf(fact_5922_fact__numeral,axiom,
% 5.01/5.28 ! [K: num] :
% 5.01/5.28 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.01/5.28 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_numeral
% 5.01/5.28 thf(fact_5923_fact__numeral,axiom,
% 5.01/5.28 ! [K: num] :
% 5.01/5.28 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.01/5.28 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_numeral
% 5.01/5.28 thf(fact_5924_fact__numeral,axiom,
% 5.01/5.28 ! [K: num] :
% 5.01/5.28 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.01/5.28 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_numeral
% 5.01/5.28 thf(fact_5925_take__bit__Suc__bit0,axiom,
% 5.01/5.28 ! [N: nat,K: num] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.01/5.28 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_bit0
% 5.01/5.28 thf(fact_5926_take__bit__Suc__bit0,axiom,
% 5.01/5.28 ! [N: nat,K: num] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.01/5.28 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_bit0
% 5.01/5.28 thf(fact_5927_take__bit__eq__mod,axiom,
% 5.01/5.28 ( bit_se1745604003318907178nteger
% 5.01/5.28 = ( ^ [N4: nat,A4: code_integer] : ( modulo364778990260209775nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_mod
% 5.01/5.28 thf(fact_5928_take__bit__eq__mod,axiom,
% 5.01/5.28 ( bit_se2923211474154528505it_int
% 5.01/5.28 = ( ^ [N4: nat,A4: int] : ( modulo_modulo_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_mod
% 5.01/5.28 thf(fact_5929_take__bit__eq__mod,axiom,
% 5.01/5.28 ( bit_se2925701944663578781it_nat
% 5.01/5.28 = ( ^ [N4: nat,A4: nat] : ( modulo_modulo_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_mod
% 5.01/5.28 thf(fact_5930_take__bit__nat__eq__self,axiom,
% 5.01/5.28 ! [M: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.28 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.01/5.28 = M ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_eq_self
% 5.01/5.28 thf(fact_5931_take__bit__nat__less__exp,axiom,
% 5.01/5.28 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_less_exp
% 5.01/5.28 thf(fact_5932_take__bit__nat__eq__self__iff,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.01/5.28 = M )
% 5.01/5.28 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_eq_self_iff
% 5.01/5.28 thf(fact_5933_take__bit__nat__def,axiom,
% 5.01/5.28 ( bit_se2925701944663578781it_nat
% 5.01/5.28 = ( ^ [N4: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_def
% 5.01/5.28 thf(fact_5934_of__bool__odd__eq__mod__2,axiom,
% 5.01/5.28 ! [A: nat] :
% 5.01/5.28 ( ( zero_n2687167440665602831ol_nat
% 5.01/5.28 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_odd_eq_mod_2
% 5.01/5.28 thf(fact_5935_of__bool__odd__eq__mod__2,axiom,
% 5.01/5.28 ! [A: int] :
% 5.01/5.28 ( ( zero_n2684676970156552555ol_int
% 5.01/5.28 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_odd_eq_mod_2
% 5.01/5.28 thf(fact_5936_of__bool__odd__eq__mod__2,axiom,
% 5.01/5.28 ! [A: code_integer] :
% 5.01/5.28 ( ( zero_n356916108424825756nteger
% 5.01/5.28 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.28 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % of_bool_odd_eq_mod_2
% 5.01/5.28 thf(fact_5937_take__bit__int__less__exp,axiom,
% 5.01/5.28 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_less_exp
% 5.01/5.28 thf(fact_5938_binomial__altdef__nat,axiom,
% 5.01/5.28 ! [K: nat,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.28 => ( ( binomial @ N @ K )
% 5.01/5.28 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % binomial_altdef_nat
% 5.01/5.28 thf(fact_5939_take__bit__int__def,axiom,
% 5.01/5.28 ( bit_se2923211474154528505it_int
% 5.01/5.28 = ( ^ [N4: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_def
% 5.01/5.28 thf(fact_5940_num_Osize__gen_I1_J,axiom,
% 5.01/5.28 ( ( size_num @ one )
% 5.01/5.28 = zero_zero_nat ) ).
% 5.01/5.28
% 5.01/5.28 % num.size_gen(1)
% 5.01/5.28 thf(fact_5941_take__bit__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat,A: code_integer] :
% 5.01/5.28 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.01/5.28 = zero_z3403309356797280102nteger )
% 5.01/5.28 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_0_iff
% 5.01/5.28 thf(fact_5942_take__bit__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat,A: int] :
% 5.01/5.28 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.01/5.28 = zero_zero_int )
% 5.01/5.28 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_0_iff
% 5.01/5.28 thf(fact_5943_take__bit__eq__0__iff,axiom,
% 5.01/5.28 ! [N: nat,A: nat] :
% 5.01/5.28 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.01/5.28 = zero_zero_nat )
% 5.01/5.28 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_eq_0_iff
% 5.01/5.28 thf(fact_5944_take__bit__numeral__bit0,axiom,
% 5.01/5.28 ! [L: num,K: num] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.01/5.28 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_numeral_bit0
% 5.01/5.28 thf(fact_5945_take__bit__numeral__bit0,axiom,
% 5.01/5.28 ! [L: num,K: num] :
% 5.01/5.28 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.01/5.28 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_numeral_bit0
% 5.01/5.28 thf(fact_5946_take__bit__nat__less__self__iff,axiom,
% 5.01/5.28 ! [N: nat,M: nat] :
% 5.01/5.28 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.01/5.28 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_nat_less_self_iff
% 5.01/5.28 thf(fact_5947_square__fact__le__2__fact,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % square_fact_le_2_fact
% 5.01/5.28 thf(fact_5948_Suc__mask__eq__exp,axiom,
% 5.01/5.28 ! [N: nat] :
% 5.01/5.28 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.28 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % Suc_mask_eq_exp
% 5.01/5.28 thf(fact_5949_mask__nat__less__exp,axiom,
% 5.01/5.28 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.28
% 5.01/5.28 % mask_nat_less_exp
% 5.01/5.28 thf(fact_5950_bits__induct,axiom,
% 5.01/5.28 ! [P: nat > $o,A: nat] :
% 5.01/5.28 ( ! [A3: nat] :
% 5.01/5.28 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ A3 ) )
% 5.01/5.28 => ( ! [A3: nat,B2: $o] :
% 5.01/5.28 ( ( P @ A3 )
% 5.01/5.28 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.01/5.28 => ( P @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_induct
% 5.01/5.28 thf(fact_5951_bits__induct,axiom,
% 5.01/5.28 ! [P: int > $o,A: int] :
% 5.01/5.28 ( ! [A3: int] :
% 5.01/5.28 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ A3 ) )
% 5.01/5.28 => ( ! [A3: int,B2: $o] :
% 5.01/5.28 ( ( P @ A3 )
% 5.01/5.28 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.01/5.28 => ( P @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_induct
% 5.01/5.28 thf(fact_5952_bits__induct,axiom,
% 5.01/5.28 ! [P: code_integer > $o,A: code_integer] :
% 5.01/5.28 ( ! [A3: code_integer] :
% 5.01/5.28 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ A3 ) )
% 5.01/5.28 => ( ! [A3: code_integer,B2: $o] :
% 5.01/5.28 ( ( P @ A3 )
% 5.01/5.28 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.28 = A3 )
% 5.01/5.28 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 5.01/5.28 => ( P @ A ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % bits_induct
% 5.01/5.28 thf(fact_5953_take__bit__Suc__minus__bit0,axiom,
% 5.01/5.28 ! [N: nat,K: num] :
% 5.01/5.28 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.28 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_Suc_minus_bit0
% 5.01/5.28 thf(fact_5954_take__bit__int__less__self__iff,axiom,
% 5.01/5.28 ! [N: nat,K: int] :
% 5.01/5.28 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.01/5.28 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_less_self_iff
% 5.01/5.28 thf(fact_5955_take__bit__int__greater__eq__self__iff,axiom,
% 5.01/5.28 ! [K: int,N: nat] :
% 5.01/5.28 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.01/5.28 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % take_bit_int_greater_eq_self_iff
% 5.01/5.28 thf(fact_5956_fact__num__eq__if,axiom,
% 5.01/5.28 ( semiri773545260158071498ct_rat
% 5.01/5.28 = ( ^ [M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M3 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_num_eq_if
% 5.01/5.28 thf(fact_5957_fact__num__eq__if,axiom,
% 5.01/5.28 ( semiri1406184849735516958ct_int
% 5.01/5.28 = ( ^ [M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.28
% 5.01/5.28 % fact_num_eq_if
% 5.01/5.28 thf(fact_5958_fact__num__eq__if,axiom,
% 5.01/5.28 ( semiri3624122377584611663nteger
% 5.01/5.29 = ( ^ [M3: nat] : ( if_Code_integer @ ( M3 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M3 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_num_eq_if
% 5.01/5.29 thf(fact_5959_fact__num__eq__if,axiom,
% 5.01/5.29 ( semiri1408675320244567234ct_nat
% 5.01/5.29 = ( ^ [M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_num_eq_if
% 5.01/5.29 thf(fact_5960_fact__num__eq__if,axiom,
% 5.01/5.29 ( semiri2265585572941072030t_real
% 5.01/5.29 = ( ^ [M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_num_eq_if
% 5.01/5.29 thf(fact_5961_fact__num__eq__if,axiom,
% 5.01/5.29 ( semiri5044797733671781792omplex
% 5.01/5.29 = ( ^ [M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M3 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_num_eq_if
% 5.01/5.29 thf(fact_5962_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri773545260158071498ct_rat @ N )
% 5.01/5.29 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5963_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri1406184849735516958ct_int @ N )
% 5.01/5.29 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5964_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri3624122377584611663nteger @ N )
% 5.01/5.29 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5965_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.01/5.29 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5966_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri2265585572941072030t_real @ N )
% 5.01/5.29 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5967_fact__reduce,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( semiri5044797733671781792omplex @ N )
% 5.01/5.29 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_reduce
% 5.01/5.29 thf(fact_5968_pochhammer__same,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.01/5.29 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pochhammer_same
% 5.01/5.29 thf(fact_5969_pochhammer__same,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.01/5.29 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pochhammer_same
% 5.01/5.29 thf(fact_5970_pochhammer__same,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.01/5.29 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pochhammer_same
% 5.01/5.29 thf(fact_5971_pochhammer__same,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.01/5.29 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pochhammer_same
% 5.01/5.29 thf(fact_5972_pochhammer__same,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.01/5.29 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pochhammer_same
% 5.01/5.29 thf(fact_5973_binomial__fact,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.01/5.29 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % binomial_fact
% 5.01/5.29 thf(fact_5974_binomial__fact,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.01/5.29 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % binomial_fact
% 5.01/5.29 thf(fact_5975_binomial__fact,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.01/5.29 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % binomial_fact
% 5.01/5.29 thf(fact_5976_fact__binomial,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.01/5.29 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_binomial
% 5.01/5.29 thf(fact_5977_fact__binomial,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.01/5.29 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_binomial
% 5.01/5.29 thf(fact_5978_fact__binomial,axiom,
% 5.01/5.29 ! [K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.29 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.01/5.29 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_binomial
% 5.01/5.29 thf(fact_5979_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % semiring_bit_operations_class.even_mask_iff
% 5.01/5.29 thf(fact_5980_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % semiring_bit_operations_class.even_mask_iff
% 5.01/5.29 thf(fact_5981_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % semiring_bit_operations_class.even_mask_iff
% 5.01/5.29 thf(fact_5982_add__0__iff,axiom,
% 5.01/5.29 ! [B: complex,A: complex] :
% 5.01/5.29 ( ( B
% 5.01/5.29 = ( plus_plus_complex @ B @ A ) )
% 5.01/5.29 = ( A = zero_zero_complex ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_0_iff
% 5.01/5.29 thf(fact_5983_add__0__iff,axiom,
% 5.01/5.29 ! [B: real,A: real] :
% 5.01/5.29 ( ( B
% 5.01/5.29 = ( plus_plus_real @ B @ A ) )
% 5.01/5.29 = ( A = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_0_iff
% 5.01/5.29 thf(fact_5984_add__0__iff,axiom,
% 5.01/5.29 ! [B: rat,A: rat] :
% 5.01/5.29 ( ( B
% 5.01/5.29 = ( plus_plus_rat @ B @ A ) )
% 5.01/5.29 = ( A = zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_0_iff
% 5.01/5.29 thf(fact_5985_add__0__iff,axiom,
% 5.01/5.29 ! [B: nat,A: nat] :
% 5.01/5.29 ( ( B
% 5.01/5.29 = ( plus_plus_nat @ B @ A ) )
% 5.01/5.29 = ( A = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_0_iff
% 5.01/5.29 thf(fact_5986_add__0__iff,axiom,
% 5.01/5.29 ! [B: int,A: int] :
% 5.01/5.29 ( ( B
% 5.01/5.29 = ( plus_plus_int @ B @ A ) )
% 5.01/5.29 = ( A = zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_0_iff
% 5.01/5.29 thf(fact_5987_exp__mod__exp,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_mod_exp
% 5.01/5.29 thf(fact_5988_exp__mod__exp,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_mod_exp
% 5.01/5.29 thf(fact_5989_exp__mod__exp,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_mod_exp
% 5.01/5.29 thf(fact_5990_crossproduct__noteq,axiom,
% 5.01/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.29 ( ( ( A != B )
% 5.01/5.29 & ( C != D ) )
% 5.01/5.29 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.01/5.29 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_noteq
% 5.01/5.29 thf(fact_5991_crossproduct__noteq,axiom,
% 5.01/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.01/5.29 ( ( ( A != B )
% 5.01/5.29 & ( C != D ) )
% 5.01/5.29 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.01/5.29 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_noteq
% 5.01/5.29 thf(fact_5992_crossproduct__noteq,axiom,
% 5.01/5.29 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.01/5.29 ( ( ( A != B )
% 5.01/5.29 & ( C != D ) )
% 5.01/5.29 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.01/5.29 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_noteq
% 5.01/5.29 thf(fact_5993_crossproduct__noteq,axiom,
% 5.01/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.01/5.29 ( ( ( A != B )
% 5.01/5.29 & ( C != D ) )
% 5.01/5.29 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.01/5.29 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_noteq
% 5.01/5.29 thf(fact_5994_crossproduct__noteq,axiom,
% 5.01/5.29 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.01/5.29 ( ( ( A != B )
% 5.01/5.29 & ( C != D ) )
% 5.01/5.29 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 5.01/5.29 != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_noteq
% 5.01/5.29 thf(fact_5995_crossproduct__eq,axiom,
% 5.01/5.29 ! [W: real,Y: real,X2: real,Z: real] :
% 5.01/5.29 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X2 @ Z ) )
% 5.01/5.29 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X2 @ Y ) ) )
% 5.01/5.29 = ( ( W = X2 )
% 5.01/5.29 | ( Y = Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_eq
% 5.01/5.29 thf(fact_5996_crossproduct__eq,axiom,
% 5.01/5.29 ! [W: rat,Y: rat,X2: rat,Z: rat] :
% 5.01/5.29 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X2 @ Z ) )
% 5.01/5.29 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X2 @ Y ) ) )
% 5.01/5.29 = ( ( W = X2 )
% 5.01/5.29 | ( Y = Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_eq
% 5.01/5.29 thf(fact_5997_crossproduct__eq,axiom,
% 5.01/5.29 ! [W: nat,Y: nat,X2: nat,Z: nat] :
% 5.01/5.29 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X2 @ Z ) )
% 5.01/5.29 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X2 @ Y ) ) )
% 5.01/5.29 = ( ( W = X2 )
% 5.01/5.29 | ( Y = Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_eq
% 5.01/5.29 thf(fact_5998_crossproduct__eq,axiom,
% 5.01/5.29 ! [W: int,Y: int,X2: int,Z: int] :
% 5.01/5.29 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X2 @ Z ) )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X2 @ Y ) ) )
% 5.01/5.29 = ( ( W = X2 )
% 5.01/5.29 | ( Y = Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_eq
% 5.01/5.29 thf(fact_5999_crossproduct__eq,axiom,
% 5.01/5.29 ! [W: complex,Y: complex,X2: complex,Z: complex] :
% 5.01/5.29 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X2 @ Z ) )
% 5.01/5.29 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X2 @ Y ) ) )
% 5.01/5.29 = ( ( W = X2 )
% 5.01/5.29 | ( Y = Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % crossproduct_eq
% 5.01/5.29 thf(fact_6000_take__bit__int__eq__self,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.29 = K ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_int_eq_self
% 5.01/5.29 thf(fact_6001_take__bit__int__eq__self__iff,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.29 = K )
% 5.01/5.29 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_int_eq_self_iff
% 5.01/5.29 thf(fact_6002_take__bit__numeral__minus__bit0,axiom,
% 5.01/5.29 ! [L: num,K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.29 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_minus_bit0
% 5.01/5.29 thf(fact_6003_mask__nat__def,axiom,
% 5.01/5.29 ( bit_se2002935070580805687sk_nat
% 5.01/5.29 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mask_nat_def
% 5.01/5.29 thf(fact_6004_mask__half__int,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.29 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mask_half_int
% 5.01/5.29 thf(fact_6005_take__bit__incr__eq,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.01/5.29 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.01/5.29 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.01/5.29 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_incr_eq
% 5.01/5.29 thf(fact_6006_mask__int__def,axiom,
% 5.01/5.29 ( bit_se2000444600071755411sk_int
% 5.01/5.29 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mask_int_def
% 5.01/5.29 thf(fact_6007_take__bit__Suc__minus__1__eq,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_minus_1_eq
% 5.01/5.29 thf(fact_6008_take__bit__Suc__minus__1__eq,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_minus_1_eq
% 5.01/5.29 thf(fact_6009_take__bit__Suc__bit1,axiom,
% 5.01/5.29 ! [N: nat,K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_bit1
% 5.01/5.29 thf(fact_6010_take__bit__Suc__bit1,axiom,
% 5.01/5.29 ! [N: nat,K: num] :
% 5.01/5.29 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.01/5.29 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_bit1
% 5.01/5.29 thf(fact_6011_take__bit__numeral__minus__1__eq,axiom,
% 5.01/5.29 ! [K: num] :
% 5.01/5.29 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_minus_1_eq
% 5.01/5.29 thf(fact_6012_take__bit__numeral__minus__1__eq,axiom,
% 5.01/5.29 ! [K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_minus_1_eq
% 5.01/5.29 thf(fact_6013_take__bit__Suc,axiom,
% 5.01/5.29 ! [N: nat,A: code_integer] :
% 5.01/5.29 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.01/5.29 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc
% 5.01/5.29 thf(fact_6014_take__bit__Suc,axiom,
% 5.01/5.29 ! [N: nat,A: int] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc
% 5.01/5.29 thf(fact_6015_take__bit__Suc,axiom,
% 5.01/5.29 ! [N: nat,A: nat] :
% 5.01/5.29 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.01/5.29 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc
% 5.01/5.29 thf(fact_6016_mask__eq__exp__minus__1,axiom,
% 5.01/5.29 ( bit_se2002935070580805687sk_nat
% 5.01/5.29 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mask_eq_exp_minus_1
% 5.01/5.29 thf(fact_6017_mask__eq__exp__minus__1,axiom,
% 5.01/5.29 ( bit_se2000444600071755411sk_int
% 5.01/5.29 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mask_eq_exp_minus_1
% 5.01/5.29 thf(fact_6018_take__bit__int__less__eq,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_int_less_eq
% 5.01/5.29 thf(fact_6019_take__bit__int__greater__eq,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.29 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_int_greater_eq
% 5.01/5.29 thf(fact_6020_signed__take__bit__eq__take__bit__shift,axiom,
% 5.01/5.29 ( bit_ri631733984087533419it_int
% 5.01/5.29 = ( ^ [N4: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_eq_take_bit_shift
% 5.01/5.29 thf(fact_6021_stable__imp__take__bit__eq,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.01/5.29 = zero_z3403309356797280102nteger ) )
% 5.01/5.29 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.01/5.29 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_take_bit_eq
% 5.01/5.29 thf(fact_6022_stable__imp__take__bit__eq,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.01/5.29 = zero_zero_int ) )
% 5.01/5.29 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.01/5.29 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_take_bit_eq
% 5.01/5.29 thf(fact_6023_stable__imp__take__bit__eq,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.01/5.29 = zero_zero_nat ) )
% 5.01/5.29 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.01/5.29 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_take_bit_eq
% 5.01/5.29 thf(fact_6024_take__bit__numeral__bit1,axiom,
% 5.01/5.29 ! [L: num,K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_bit1
% 5.01/5.29 thf(fact_6025_take__bit__numeral__bit1,axiom,
% 5.01/5.29 ! [L: num,K: num] :
% 5.01/5.29 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.01/5.29 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_bit1
% 5.01/5.29 thf(fact_6026_exp__div__exp__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_times_nat
% 5.01/5.29 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.29 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.01/5.29 != zero_zero_nat )
% 5.01/5.29 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.01/5.29 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_div_exp_eq
% 5.01/5.29 thf(fact_6027_exp__div__exp__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_times_int
% 5.01/5.29 @ ( zero_n2684676970156552555ol_int
% 5.01/5.29 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.01/5.29 != zero_zero_int )
% 5.01/5.29 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.01/5.29 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_div_exp_eq
% 5.01/5.29 thf(fact_6028_exp__div__exp__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( times_3573771949741848930nteger
% 5.01/5.29 @ ( zero_n356916108424825756nteger
% 5.01/5.29 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.01/5.29 != zero_z3403309356797280102nteger )
% 5.01/5.29 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.01/5.29 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_div_exp_eq
% 5.01/5.29 thf(fact_6029_take__bit__minus__small__eq,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.01/5.29 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_minus_small_eq
% 5.01/5.29 thf(fact_6030_num_Osize__gen_I2_J,axiom,
% 5.01/5.29 ! [X23: num] :
% 5.01/5.29 ( ( size_num @ ( bit0 @ X23 ) )
% 5.01/5.29 = ( plus_plus_nat @ ( size_num @ X23 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % num.size_gen(2)
% 5.01/5.29 thf(fact_6031_sin__coeff__def,axiom,
% 5.01/5.29 ( sin_coeff
% 5.01/5.29 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_coeff_def
% 5.01/5.29 thf(fact_6032_binomial__code,axiom,
% 5.01/5.29 ( binomial
% 5.01/5.29 = ( ^ [N4: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K2 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % binomial_code
% 5.01/5.29 thf(fact_6033_cos__coeff__def,axiom,
% 5.01/5.29 ( cos_coeff
% 5.01/5.29 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) @ zero_zero_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_coeff_def
% 5.01/5.29 thf(fact_6034_take__bit__numeral__minus__bit1,axiom,
% 5.01/5.29 ! [L: num,K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_numeral_minus_bit1
% 5.01/5.29 thf(fact_6035_take__bit__Suc__minus__bit1,axiom,
% 5.01/5.29 ! [N: nat,K: num] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_minus_bit1
% 5.01/5.29 thf(fact_6036_fact__code,axiom,
% 5.01/5.29 ( semiri1406184849735516958ct_int
% 5.01/5.29 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_code
% 5.01/5.29 thf(fact_6037_fact__code,axiom,
% 5.01/5.29 ( semiri3624122377584611663nteger
% 5.01/5.29 = ( ^ [N4: nat] : ( semiri4939895301339042750nteger @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_code
% 5.01/5.29 thf(fact_6038_fact__code,axiom,
% 5.01/5.29 ( semiri1408675320244567234ct_nat
% 5.01/5.29 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_code
% 5.01/5.29 thf(fact_6039_fact__code,axiom,
% 5.01/5.29 ( semiri2265585572941072030t_real
% 5.01/5.29 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_code
% 5.01/5.29 thf(fact_6040_fact__code,axiom,
% 5.01/5.29 ( semiri5044797733671781792omplex
% 5.01/5.29 = ( ^ [N4: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fact_code
% 5.01/5.29 thf(fact_6041_sin__coeff__0,axiom,
% 5.01/5.29 ( ( sin_coeff @ zero_zero_nat )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_coeff_0
% 5.01/5.29 thf(fact_6042_cos__coeff__0,axiom,
% 5.01/5.29 ( ( cos_coeff @ zero_zero_nat )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % cos_coeff_0
% 5.01/5.29 thf(fact_6043_pred__numeral__inc,axiom,
% 5.01/5.29 ! [K: num] :
% 5.01/5.29 ( ( pred_numeral @ ( inc @ K ) )
% 5.01/5.29 = ( numeral_numeral_nat @ K ) ) ).
% 5.01/5.29
% 5.01/5.29 % pred_numeral_inc
% 5.01/5.29 thf(fact_6044_add__neg__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(5)
% 5.01/5.29 thf(fact_6045_add__neg__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(5)
% 5.01/5.29 thf(fact_6046_add__neg__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(5)
% 5.01/5.29 thf(fact_6047_add__neg__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(5)
% 5.01/5.29 thf(fact_6048_add__neg__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.01/5.29 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(5)
% 5.01/5.29 thf(fact_6049_add__neg__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(6)
% 5.01/5.29 thf(fact_6050_add__neg__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(6)
% 5.01/5.29 thf(fact_6051_add__neg__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(6)
% 5.01/5.29 thf(fact_6052_add__neg__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(6)
% 5.01/5.29 thf(fact_6053_add__neg__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.29 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_neg_numeral_special(6)
% 5.01/5.29 thf(fact_6054_diff__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.29 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(6)
% 5.01/5.29 thf(fact_6055_diff__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(6)
% 5.01/5.29 thf(fact_6056_diff__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.01/5.29 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(6)
% 5.01/5.29 thf(fact_6057_diff__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(6)
% 5.01/5.29 thf(fact_6058_diff__numeral__special_I6_J,axiom,
% 5.01/5.29 ! [M: num] :
% 5.01/5.29 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.29 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(6)
% 5.01/5.29 thf(fact_6059_diff__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(5)
% 5.01/5.29 thf(fact_6060_diff__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(5)
% 5.01/5.29 thf(fact_6061_diff__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(5)
% 5.01/5.29 thf(fact_6062_diff__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(5)
% 5.01/5.29 thf(fact_6063_diff__numeral__special_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.01/5.29 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_numeral_special(5)
% 5.01/5.29 thf(fact_6064_num__induct,axiom,
% 5.01/5.29 ! [P: num > $o,X2: num] :
% 5.01/5.29 ( ( P @ one )
% 5.01/5.29 => ( ! [X4: num] :
% 5.01/5.29 ( ( P @ X4 )
% 5.01/5.29 => ( P @ ( inc @ X4 ) ) )
% 5.01/5.29 => ( P @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % num_induct
% 5.01/5.29 thf(fact_6065_add__inc,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( plus_plus_num @ X2 @ ( inc @ Y ) )
% 5.01/5.29 = ( inc @ ( plus_plus_num @ X2 @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_inc
% 5.01/5.29 thf(fact_6066_sin__coeff__Suc,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sin_coeff @ ( suc @ N ) )
% 5.01/5.29 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_coeff_Suc
% 5.01/5.29 thf(fact_6067_inc_Osimps_I1_J,axiom,
% 5.01/5.29 ( ( inc @ one )
% 5.01/5.29 = ( bit0 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % inc.simps(1)
% 5.01/5.29 thf(fact_6068_inc_Osimps_I3_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( inc @ ( bit1 @ X2 ) )
% 5.01/5.29 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % inc.simps(3)
% 5.01/5.29 thf(fact_6069_inc_Osimps_I2_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( inc @ ( bit0 @ X2 ) )
% 5.01/5.29 = ( bit1 @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % inc.simps(2)
% 5.01/5.29 thf(fact_6070_add__One,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( plus_plus_num @ X2 @ one )
% 5.01/5.29 = ( inc @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % add_One
% 5.01/5.29 thf(fact_6071_inc__BitM__eq,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( inc @ ( bitM @ N ) )
% 5.01/5.29 = ( bit0 @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % inc_BitM_eq
% 5.01/5.29 thf(fact_6072_BitM__inc__eq,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( bitM @ ( inc @ N ) )
% 5.01/5.29 = ( bit1 @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % BitM_inc_eq
% 5.01/5.29 thf(fact_6073_cos__coeff__Suc,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( cos_coeff @ ( suc @ N ) )
% 5.01/5.29 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_coeff_Suc
% 5.01/5.29 thf(fact_6074_mult__inc,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( times_times_num @ X2 @ ( inc @ Y ) )
% 5.01/5.29 = ( plus_plus_num @ ( times_times_num @ X2 @ Y ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % mult_inc
% 5.01/5.29 thf(fact_6075_numeral__inc,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( numera6690914467698888265omplex @ ( inc @ X2 ) )
% 5.01/5.29 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_inc
% 5.01/5.29 thf(fact_6076_numeral__inc,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( numeral_numeral_real @ ( inc @ X2 ) )
% 5.01/5.29 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_inc
% 5.01/5.29 thf(fact_6077_numeral__inc,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( numeral_numeral_rat @ ( inc @ X2 ) )
% 5.01/5.29 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_inc
% 5.01/5.29 thf(fact_6078_numeral__inc,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( numeral_numeral_nat @ ( inc @ X2 ) )
% 5.01/5.29 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_inc
% 5.01/5.29 thf(fact_6079_numeral__inc,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( numeral_numeral_int @ ( inc @ X2 ) )
% 5.01/5.29 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_inc
% 5.01/5.29 thf(fact_6080_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.01/5.29 ! [X2: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.01/5.29 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa @ Xb @ Xc )
% 5.01/5.29 = Y )
% 5.01/5.29 => ( ( ( ord_less_nat @ Xb @ Xa )
% 5.01/5.29 => ( Y = Xc ) )
% 5.01/5.29 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.01/5.29 => ( Y
% 5.01/5.29 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X2 @ Xa @ Xc ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fold_atLeastAtMost_nat.elims
% 5.01/5.29 thf(fact_6081_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.01/5.29 ( set_fo2584398358068434914at_nat
% 5.01/5.29 = ( ^ [F3: nat > nat > nat,A4: nat,B3: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A4 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A4 @ one_one_nat ) @ B3 @ ( F3 @ A4 @ Acc ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % fold_atLeastAtMost_nat.simps
% 5.01/5.29 thf(fact_6082_signed__take__bit__eq__take__bit__minus,axiom,
% 5.01/5.29 ( bit_ri631733984087533419it_int
% 5.01/5.29 = ( ^ [N4: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N4 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_eq_take_bit_minus
% 5.01/5.29 thf(fact_6083_modulo__int__unfold,axiom,
% 5.01/5.29 ! [L: int,K: int,N: nat,M: nat] :
% 5.01/5.29 ( ( ( ( ( sgn_sgn_int @ L )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( ( sgn_sgn_int @ K )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( N = zero_zero_nat ) )
% 5.01/5.29 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.01/5.29 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( ( sgn_sgn_int @ K )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( N = zero_zero_nat ) )
% 5.01/5.29 => ( ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 = ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.01/5.29 & ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 != ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.01/5.29 @ ( minus_minus_int
% 5.01/5.29 @ ( semiri1314217659103216013at_int
% 5.01/5.29 @ ( times_times_nat @ N
% 5.01/5.29 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.29 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.01/5.29 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % modulo_int_unfold
% 5.01/5.29 thf(fact_6084_divide__int__unfold,axiom,
% 5.01/5.29 ! [L: int,K: int,N: nat,M: nat] :
% 5.01/5.29 ( ( ( ( ( sgn_sgn_int @ L )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( ( sgn_sgn_int @ K )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( N = zero_zero_nat ) )
% 5.01/5.29 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = zero_zero_int ) )
% 5.01/5.29 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( ( sgn_sgn_int @ K )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 | ( N = zero_zero_nat ) )
% 5.01/5.29 => ( ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 = ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.01/5.29 & ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 != ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = ( uminus_uminus_int
% 5.01/5.29 @ ( semiri1314217659103216013at_int
% 5.01/5.29 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.01/5.29 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.29 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % divide_int_unfold
% 5.01/5.29 thf(fact_6085_tanh__real__altdef,axiom,
% 5.01/5.29 ( tanh_real
% 5.01/5.29 = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % tanh_real_altdef
% 5.01/5.29 thf(fact_6086_power__numeral,axiom,
% 5.01/5.29 ! [K: num,L: num] :
% 5.01/5.29 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.01/5.29 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_numeral
% 5.01/5.29 thf(fact_6087_power__numeral,axiom,
% 5.01/5.29 ! [K: num,L: num] :
% 5.01/5.29 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.01/5.29 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_numeral
% 5.01/5.29 thf(fact_6088_power__numeral,axiom,
% 5.01/5.29 ! [K: num,L: num] :
% 5.01/5.29 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.01/5.29 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_numeral
% 5.01/5.29 thf(fact_6089_power__numeral,axiom,
% 5.01/5.29 ! [K: num,L: num] :
% 5.01/5.29 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.01/5.29 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_numeral
% 5.01/5.29 thf(fact_6090_power__numeral,axiom,
% 5.01/5.29 ! [K: num,L: num] :
% 5.01/5.29 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.01/5.29 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_numeral
% 5.01/5.29 thf(fact_6091_and__int__unfold,axiom,
% 5.01/5.29 ( bit_se725231765392027082nd_int
% 5.01/5.29 = ( ^ [K2: int,L2: int] :
% 5.01/5.29 ( if_int
% 5.01/5.29 @ ( ( K2 = zero_zero_int )
% 5.01/5.29 | ( L2 = zero_zero_int ) )
% 5.01/5.29 @ zero_zero_int
% 5.01/5.29 @ ( if_int
% 5.01/5.29 @ ( K2
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 @ L2
% 5.01/5.29 @ ( if_int
% 5.01/5.29 @ ( L2
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 @ K2
% 5.01/5.29 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_int_unfold
% 5.01/5.29 thf(fact_6092_and_Oright__idem,axiom,
% 5.01/5.29 ! [A: int,B: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.right_idem
% 5.01/5.29 thf(fact_6093_and_Oright__idem,axiom,
% 5.01/5.29 ! [A: nat,B: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.right_idem
% 5.01/5.29 thf(fact_6094_and_Oleft__idem,axiom,
% 5.01/5.29 ! [A: int,B: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_idem
% 5.01/5.29 thf(fact_6095_and_Oleft__idem,axiom,
% 5.01/5.29 ! [A: nat,B: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_idem
% 5.01/5.29 thf(fact_6096_and_Oidem,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.idem
% 5.01/5.29 thf(fact_6097_and_Oidem,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.idem
% 5.01/5.29 thf(fact_6098_sgn__sgn,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = ( sgn_sgn_int @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_sgn
% 5.01/5.29 thf(fact_6099_sgn__sgn,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = ( sgn_sgn_real @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_sgn
% 5.01/5.29 thf(fact_6100_sgn__sgn,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 5.01/5.29 = ( sgn_sgn_complex @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_sgn
% 5.01/5.29 thf(fact_6101_sgn__sgn,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = ( sgn_sgn_Code_integer @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_sgn
% 5.01/5.29 thf(fact_6102_sgn__sgn,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = ( sgn_sgn_rat @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_sgn
% 5.01/5.29 thf(fact_6103_bit_Oconj__zero__right,axiom,
% 5.01/5.29 ! [X2: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ X2 @ zero_zero_int )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % bit.conj_zero_right
% 5.01/5.29 thf(fact_6104_bit_Oconj__zero__left,axiom,
% 5.01/5.29 ! [X2: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X2 )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % bit.conj_zero_left
% 5.01/5.29 thf(fact_6105_zero__and__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % zero_and_eq
% 5.01/5.29 thf(fact_6106_zero__and__eq,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % zero_and_eq
% 5.01/5.29 thf(fact_6107_and__zero__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_zero_eq
% 5.01/5.29 thf(fact_6108_and__zero__eq,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_zero_eq
% 5.01/5.29 thf(fact_6109_sgn__0,axiom,
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.01/5.29 = zero_z3403309356797280102nteger ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0
% 5.01/5.29 thf(fact_6110_sgn__0,axiom,
% 5.01/5.29 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.01/5.29 = zero_zero_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0
% 5.01/5.29 thf(fact_6111_sgn__0,axiom,
% 5.01/5.29 ( ( sgn_sgn_real @ zero_zero_real )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0
% 5.01/5.29 thf(fact_6112_sgn__0,axiom,
% 5.01/5.29 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.01/5.29 = zero_zero_rat ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0
% 5.01/5.29 thf(fact_6113_sgn__0,axiom,
% 5.01/5.29 ( ( sgn_sgn_int @ zero_zero_int )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0
% 5.01/5.29 thf(fact_6114_sgn__zero,axiom,
% 5.01/5.29 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.01/5.29 = zero_zero_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_zero
% 5.01/5.29 thf(fact_6115_sgn__zero,axiom,
% 5.01/5.29 ( ( sgn_sgn_real @ zero_zero_real )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_zero
% 5.01/5.29 thf(fact_6116_sgn__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_int @ one_one_int )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1
% 5.01/5.29 thf(fact_6117_sgn__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_real @ one_one_real )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1
% 5.01/5.29 thf(fact_6118_sgn__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_complex @ one_one_complex )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1
% 5.01/5.29 thf(fact_6119_sgn__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 5.01/5.29 = one_one_Code_integer ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1
% 5.01/5.29 thf(fact_6120_sgn__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_rat @ one_one_rat )
% 5.01/5.29 = one_one_rat ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1
% 5.01/5.29 thf(fact_6121_sgn__one,axiom,
% 5.01/5.29 ( ( sgn_sgn_real @ one_one_real )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_one
% 5.01/5.29 thf(fact_6122_sgn__one,axiom,
% 5.01/5.29 ( ( sgn_sgn_complex @ one_one_complex )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_one
% 5.01/5.29 thf(fact_6123_sgn__divide,axiom,
% 5.01/5.29 ! [A: complex,B: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.29 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_divide
% 5.01/5.29 thf(fact_6124_sgn__divide,axiom,
% 5.01/5.29 ! [A: real,B: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.29 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_divide
% 5.01/5.29 thf(fact_6125_sgn__divide,axiom,
% 5.01/5.29 ! [A: rat,B: rat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.29 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_divide
% 5.01/5.29 thf(fact_6126_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.sgn_minus
% 5.01/5.29 thf(fact_6127_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.sgn_minus
% 5.01/5.29 thf(fact_6128_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.sgn_minus
% 5.01/5.29 thf(fact_6129_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.sgn_minus
% 5.01/5.29 thf(fact_6130_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 5.01/5.29 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.sgn_minus
% 5.01/5.29 thf(fact_6131_power__sgn,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.01/5.29 = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_sgn
% 5.01/5.29 thf(fact_6132_power__sgn,axiom,
% 5.01/5.29 ! [A: rat,N: nat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N ) )
% 5.01/5.29 = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_sgn
% 5.01/5.29 thf(fact_6133_power__sgn,axiom,
% 5.01/5.29 ! [A: real,N: nat] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( power_power_real @ A @ N ) )
% 5.01/5.29 = ( power_power_real @ ( sgn_sgn_real @ A ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_sgn
% 5.01/5.29 thf(fact_6134_power__sgn,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( power_power_int @ A @ N ) )
% 5.01/5.29 = ( power_power_int @ ( sgn_sgn_int @ A ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % power_sgn
% 5.01/5.29 thf(fact_6135_exp__less__cancel__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) )
% 5.01/5.29 = ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_less_cancel_iff
% 5.01/5.29 thf(fact_6136_exp__less__mono,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.29 => ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_less_mono
% 5.01/5.29 thf(fact_6137_take__bit__and,axiom,
% 5.01/5.29 ! [N: nat,A: int,B: int] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_and
% 5.01/5.29 thf(fact_6138_take__bit__and,axiom,
% 5.01/5.29 ! [N: nat,A: nat,B: nat] :
% 5.01/5.29 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_and
% 5.01/5.29 thf(fact_6139_exp__le__cancel__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_le_cancel_iff
% 5.01/5.29 thf(fact_6140_sgn__less,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.01/5.29 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_less
% 5.01/5.29 thf(fact_6141_sgn__less,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_less
% 5.01/5.29 thf(fact_6142_sgn__less,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.01/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_less
% 5.01/5.29 thf(fact_6143_sgn__less,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_less
% 5.01/5.29 thf(fact_6144_sgn__greater,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_greater
% 5.01/5.29 thf(fact_6145_sgn__greater,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_greater
% 5.01/5.29 thf(fact_6146_sgn__greater,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_greater
% 5.01/5.29 thf(fact_6147_sgn__greater,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_greater
% 5.01/5.29 thf(fact_6148_exp__zero,axiom,
% 5.01/5.29 ( ( exp_complex @ zero_zero_complex )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % exp_zero
% 5.01/5.29 thf(fact_6149_exp__zero,axiom,
% 5.01/5.29 ( ( exp_real @ zero_zero_real )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % exp_zero
% 5.01/5.29 thf(fact_6150_bit_Oconj__one__right,axiom,
% 5.01/5.29 ! [X2: code_integer] :
% 5.01/5.29 ( ( bit_se3949692690581998587nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % bit.conj_one_right
% 5.01/5.29 thf(fact_6151_bit_Oconj__one__right,axiom,
% 5.01/5.29 ! [X2: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % bit.conj_one_right
% 5.01/5.29 thf(fact_6152_and_Oright__neutral,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.right_neutral
% 5.01/5.29 thf(fact_6153_and_Oright__neutral,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.right_neutral
% 5.01/5.29 thf(fact_6154_and_Oleft__neutral,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_neutral
% 5.01/5.29 thf(fact_6155_and_Oleft__neutral,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_neutral
% 5.01/5.29 thf(fact_6156_divide__sgn,axiom,
% 5.01/5.29 ! [A: real,B: real] :
% 5.01/5.29 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 5.01/5.29 = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % divide_sgn
% 5.01/5.29 thf(fact_6157_divide__sgn,axiom,
% 5.01/5.29 ! [A: rat,B: rat] :
% 5.01/5.29 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 5.01/5.29 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % divide_sgn
% 5.01/5.29 thf(fact_6158_exp__eq__one__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( exp_real @ X2 )
% 5.01/5.29 = one_one_real )
% 5.01/5.29 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_eq_one_iff
% 5.01/5.29 thf(fact_6159_and__nonnegative__int__iff,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.01/5.29 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_nonnegative_int_iff
% 5.01/5.29 thf(fact_6160_and__negative__int__iff,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.01/5.29 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.29 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_negative_int_iff
% 5.01/5.29 thf(fact_6161_sgn__pos,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.01/5.29 => ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = one_one_Code_integer ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_pos
% 5.01/5.29 thf(fact_6162_sgn__pos,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( sgn_sgn_real @ A )
% 5.01/5.29 = one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_pos
% 5.01/5.29 thf(fact_6163_sgn__pos,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.29 => ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_pos
% 5.01/5.29 thf(fact_6164_sgn__pos,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.29 => ( ( sgn_sgn_int @ A )
% 5.01/5.29 = one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_pos
% 5.01/5.29 thf(fact_6165_bit__numeral__Bit0__Suc__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_Bit0_Suc_iff
% 5.01/5.29 thf(fact_6166_bit__numeral__Bit0__Suc__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_Bit0_Suc_iff
% 5.01/5.29 thf(fact_6167_and__numerals_I8_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(8)
% 5.01/5.29 thf(fact_6168_and__numerals_I8_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.01/5.29 = one_one_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(8)
% 5.01/5.29 thf(fact_6169_and__numerals_I2_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(2)
% 5.01/5.29 thf(fact_6170_and__numerals_I2_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.29 = one_one_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(2)
% 5.01/5.29 thf(fact_6171_abs__sgn__eq__1,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = one_one_Code_integer ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq_1
% 5.01/5.29 thf(fact_6172_abs__sgn__eq__1,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( A != zero_zero_real )
% 5.01/5.29 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq_1
% 5.01/5.29 thf(fact_6173_abs__sgn__eq__1,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( A != zero_zero_rat )
% 5.01/5.29 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq_1
% 5.01/5.29 thf(fact_6174_abs__sgn__eq__1,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( A != zero_zero_int )
% 5.01/5.29 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq_1
% 5.01/5.29 thf(fact_6175_bit__numeral__Bit1__Suc__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_Bit1_Suc_iff
% 5.01/5.29 thf(fact_6176_bit__numeral__Bit1__Suc__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_Bit1_Suc_iff
% 5.01/5.29 thf(fact_6177_sgn__mult__self__eq,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_self_eq
% 5.01/5.29 thf(fact_6178_sgn__mult__self__eq,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_self_eq
% 5.01/5.29 thf(fact_6179_sgn__mult__self__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_self_eq
% 5.01/5.29 thf(fact_6180_sgn__mult__self__eq,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_self_eq
% 5.01/5.29 thf(fact_6181_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 5.01/5.29 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.abs_sgn
% 5.01/5.29 thf(fact_6182_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 5.01/5.29 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.abs_sgn
% 5.01/5.29 thf(fact_6183_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 5.01/5.29 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.abs_sgn
% 5.01/5.29 thf(fact_6184_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 5.01/5.29 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.abs_sgn
% 5.01/5.29 thf(fact_6185_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.29 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % idom_abs_sgn_class.abs_sgn
% 5.01/5.29 thf(fact_6186_sgn__abs,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 5.01/5.29 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_abs
% 5.01/5.29 thf(fact_6187_sgn__abs,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_abs
% 5.01/5.29 thf(fact_6188_sgn__abs,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_abs
% 5.01/5.29 thf(fact_6189_sgn__abs,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_abs
% 5.01/5.29 thf(fact_6190_sgn__abs,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_abs
% 5.01/5.29 thf(fact_6191_one__less__exp__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_exp_iff
% 5.01/5.29 thf(fact_6192_exp__less__one__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_less_one_iff
% 5.01/5.29 thf(fact_6193_exp__le__one__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_le_one_iff
% 5.01/5.29 thf(fact_6194_one__le__exp__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_exp_iff
% 5.01/5.29 thf(fact_6195_exp__ln,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.29 = X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ln
% 5.01/5.29 thf(fact_6196_exp__ln__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.29 = X2 )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ln_iff
% 5.01/5.29 thf(fact_6197_dvd__mult__sgn__iff,axiom,
% 5.01/5.29 ! [L: int,K: int,R: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 5.01/5.29 = ( ( dvd_dvd_int @ L @ K )
% 5.01/5.29 | ( R = zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % dvd_mult_sgn_iff
% 5.01/5.29 thf(fact_6198_dvd__sgn__mult__iff,axiom,
% 5.01/5.29 ! [L: int,R: int,K: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 5.01/5.29 = ( ( dvd_dvd_int @ L @ K )
% 5.01/5.29 | ( R = zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % dvd_sgn_mult_iff
% 5.01/5.29 thf(fact_6199_mult__sgn__dvd__iff,axiom,
% 5.01/5.29 ! [L: int,R: int,K: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R ) ) @ K )
% 5.01/5.29 = ( ( dvd_dvd_int @ L @ K )
% 5.01/5.29 & ( ( R = zero_zero_int )
% 5.01/5.29 => ( K = zero_zero_int ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mult_sgn_dvd_iff
% 5.01/5.29 thf(fact_6200_sgn__mult__dvd__iff,axiom,
% 5.01/5.29 ! [R: int,L: int,K: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L ) @ K )
% 5.01/5.29 = ( ( dvd_dvd_int @ L @ K )
% 5.01/5.29 & ( ( R = zero_zero_int )
% 5.01/5.29 => ( K = zero_zero_int ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_dvd_iff
% 5.01/5.29 thf(fact_6201_signed__take__bit__nonnegative__iff,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_nonnegative_iff
% 5.01/5.29 thf(fact_6202_signed__take__bit__negative__iff,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_negative_iff
% 5.01/5.29 thf(fact_6203_and__numerals_I1_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(1)
% 5.01/5.29 thf(fact_6204_and__numerals_I1_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(1)
% 5.01/5.29 thf(fact_6205_and__numerals_I5_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(5)
% 5.01/5.29 thf(fact_6206_and__numerals_I5_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(5)
% 5.01/5.29 thf(fact_6207_sgn__neg,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.29 => ( ( sgn_sgn_real @ A )
% 5.01/5.29 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_neg
% 5.01/5.29 thf(fact_6208_sgn__neg,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ord_less_int @ A @ zero_zero_int )
% 5.01/5.29 => ( ( sgn_sgn_int @ A )
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_neg
% 5.01/5.29 thf(fact_6209_sgn__neg,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_neg
% 5.01/5.29 thf(fact_6210_sgn__neg,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.29 => ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_neg
% 5.01/5.29 thf(fact_6211_and__numerals_I3_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.29 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(3)
% 5.01/5.29 thf(fact_6212_and__numerals_I3_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.29 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(3)
% 5.01/5.29 thf(fact_6213_sgn__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.01/5.29 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_of_nat
% 5.01/5.29 thf(fact_6214_sgn__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.29 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_of_nat
% 5.01/5.29 thf(fact_6215_sgn__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.29 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_of_nat
% 5.01/5.29 thf(fact_6216_sgn__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.29 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_of_nat
% 5.01/5.29 thf(fact_6217_bit__numeral__simps_I2_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(2)
% 5.01/5.29 thf(fact_6218_bit__numeral__simps_I2_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(2)
% 5.01/5.29 thf(fact_6219_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.01/5.29 ! [W: num,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_minus_numeral_Bit0_Suc_iff
% 5.01/5.29 thf(fact_6220_bit__numeral__simps_I3_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(3)
% 5.01/5.29 thf(fact_6221_bit__numeral__simps_I3_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(3)
% 5.01/5.29 thf(fact_6222_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.01/5.29 ! [W: num,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_minus_numeral_Bit1_Suc_iff
% 5.01/5.29 thf(fact_6223_and__minus__numerals_I2_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_minus_numerals(2)
% 5.01/5.29 thf(fact_6224_and__minus__numerals_I6_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_minus_numerals(6)
% 5.01/5.29 thf(fact_6225_and__numerals_I4_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.29 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(4)
% 5.01/5.29 thf(fact_6226_and__numerals_I4_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.29 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(4)
% 5.01/5.29 thf(fact_6227_and__numerals_I6_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.29 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(6)
% 5.01/5.29 thf(fact_6228_and__numerals_I6_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.29 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(6)
% 5.01/5.29 thf(fact_6229_bit__0,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.01/5.29 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_0
% 5.01/5.29 thf(fact_6230_bit__0,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.01/5.29 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_0
% 5.01/5.29 thf(fact_6231_bit__0,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.01/5.29 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_0
% 5.01/5.29 thf(fact_6232_and__minus__numerals_I5_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_minus_numerals(5)
% 5.01/5.29 thf(fact_6233_and__minus__numerals_I1_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % and_minus_numerals(1)
% 5.01/5.29 thf(fact_6234_bit__minus__numeral__int_I1_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_minus_numeral_int(1)
% 5.01/5.29 thf(fact_6235_bit__minus__numeral__int_I2_J,axiom,
% 5.01/5.29 ! [W: num,N: num] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_minus_numeral_int(2)
% 5.01/5.29 thf(fact_6236_bit__mod__2__iff,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.01/5.29 = ( ( N = zero_zero_nat )
% 5.01/5.29 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_mod_2_iff
% 5.01/5.29 thf(fact_6237_bit__mod__2__iff,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.01/5.29 = ( ( N = zero_zero_nat )
% 5.01/5.29 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_mod_2_iff
% 5.01/5.29 thf(fact_6238_bit__mod__2__iff,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.01/5.29 = ( ( N = zero_zero_nat )
% 5.01/5.29 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_mod_2_iff
% 5.01/5.29 thf(fact_6239_and__numerals_I7_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.29 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(7)
% 5.01/5.29 thf(fact_6240_and__numerals_I7_J,axiom,
% 5.01/5.29 ! [X2: num,Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.29 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_numerals(7)
% 5.01/5.29 thf(fact_6241_norm__exp,axiom,
% 5.01/5.29 ! [X2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X2 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % norm_exp
% 5.01/5.29 thf(fact_6242_norm__exp,axiom,
% 5.01/5.29 ! [X2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X2 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % norm_exp
% 5.01/5.29 thf(fact_6243_of__nat__and__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( semiri4939895301339042750nteger @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.01/5.29 = ( bit_se3949692690581998587nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % of_nat_and_eq
% 5.01/5.29 thf(fact_6244_of__nat__and__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % of_nat_and_eq
% 5.01/5.29 thf(fact_6245_of__nat__and__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % of_nat_and_eq
% 5.01/5.29 thf(fact_6246_bit__of__nat__iff__bit,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( bit_se9216721137139052372nteger @ ( semiri4939895301339042750nteger @ M ) @ N )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_nat_iff_bit
% 5.01/5.29 thf(fact_6247_bit__of__nat__iff__bit,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_nat_iff_bit
% 5.01/5.29 thf(fact_6248_bit__of__nat__iff__bit,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_nat_iff_bit
% 5.01/5.29 thf(fact_6249_bit__and__int__iff,axiom,
% 5.01/5.29 ! [K: int,L: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_and_int_iff
% 5.01/5.29 thf(fact_6250_and_Oleft__commute,axiom,
% 5.01/5.29 ! [B: int,A: int,C: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_commute
% 5.01/5.29 thf(fact_6251_and_Oleft__commute,axiom,
% 5.01/5.29 ! [B: nat,A: nat,C: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.left_commute
% 5.01/5.29 thf(fact_6252_bit__and__iff,axiom,
% 5.01/5.29 ! [A: int,B: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_and_iff
% 5.01/5.29 thf(fact_6253_bit__and__iff,axiom,
% 5.01/5.29 ! [A: nat,B: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N )
% 5.01/5.29 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 & ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_and_iff
% 5.01/5.29 thf(fact_6254_and_Ocommute,axiom,
% 5.01/5.29 ( bit_se725231765392027082nd_int
% 5.01/5.29 = ( ^ [A4: int,B3: int] : ( bit_se725231765392027082nd_int @ B3 @ A4 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.commute
% 5.01/5.29 thf(fact_6255_and_Ocommute,axiom,
% 5.01/5.29 ( bit_se727722235901077358nd_nat
% 5.01/5.29 = ( ^ [A4: nat,B3: nat] : ( bit_se727722235901077358nd_nat @ B3 @ A4 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.commute
% 5.01/5.29 thf(fact_6256_and_Oassoc,axiom,
% 5.01/5.29 ! [A: int,B: int,C: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.01/5.29 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.assoc
% 5.01/5.29 thf(fact_6257_and_Oassoc,axiom,
% 5.01/5.29 ! [A: nat,B: nat,C: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.01/5.29 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and.assoc
% 5.01/5.29 thf(fact_6258_bit__numeral__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_iff
% 5.01/5.29 thf(fact_6259_bit__numeral__iff,axiom,
% 5.01/5.29 ! [M: num,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_iff
% 5.01/5.29 thf(fact_6260_bit__disjunctive__add__iff,axiom,
% 5.01/5.29 ! [A: int,B: int,N: nat] :
% 5.01/5.29 ( ! [N3: nat] :
% 5.01/5.29 ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.01/5.29 | ~ ( bit_se1146084159140164899it_int @ B @ N3 ) )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 | ( bit_se1146084159140164899it_int @ B @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_disjunctive_add_iff
% 5.01/5.29 thf(fact_6261_bit__disjunctive__add__iff,axiom,
% 5.01/5.29 ! [A: nat,B: nat,N: nat] :
% 5.01/5.29 ( ! [N3: nat] :
% 5.01/5.29 ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.01/5.29 | ~ ( bit_se1148574629649215175it_nat @ B @ N3 ) )
% 5.01/5.29 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.01/5.29 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 | ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_disjunctive_add_iff
% 5.01/5.29 thf(fact_6262_exp__less__cancel,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) )
% 5.01/5.29 => ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_less_cancel
% 5.01/5.29 thf(fact_6263_sgn__eq__0__iff,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = zero_z3403309356797280102nteger )
% 5.01/5.29 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_eq_0_iff
% 5.01/5.29 thf(fact_6264_sgn__eq__0__iff,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( ( sgn_sgn_complex @ A )
% 5.01/5.29 = zero_zero_complex )
% 5.01/5.29 = ( A = zero_zero_complex ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_eq_0_iff
% 5.01/5.29 thf(fact_6265_sgn__eq__0__iff,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ A )
% 5.01/5.29 = zero_zero_real )
% 5.01/5.29 = ( A = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_eq_0_iff
% 5.01/5.29 thf(fact_6266_sgn__eq__0__iff,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = zero_zero_rat )
% 5.01/5.29 = ( A = zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_eq_0_iff
% 5.01/5.29 thf(fact_6267_sgn__eq__0__iff,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ A )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 = ( A = zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_eq_0_iff
% 5.01/5.29 thf(fact_6268_sgn__0__0,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = zero_z3403309356797280102nteger )
% 5.01/5.29 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0_0
% 5.01/5.29 thf(fact_6269_sgn__0__0,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ A )
% 5.01/5.29 = zero_zero_real )
% 5.01/5.29 = ( A = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0_0
% 5.01/5.29 thf(fact_6270_sgn__0__0,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = zero_zero_rat )
% 5.01/5.29 = ( A = zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0_0
% 5.01/5.29 thf(fact_6271_sgn__0__0,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ A )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 = ( A = zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_0_0
% 5.01/5.29 thf(fact_6272_sgn__zero__iff,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( ( sgn_sgn_complex @ X2 )
% 5.01/5.29 = zero_zero_complex )
% 5.01/5.29 = ( X2 = zero_zero_complex ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_zero_iff
% 5.01/5.29 thf(fact_6273_sgn__zero__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ X2 )
% 5.01/5.29 = zero_zero_real )
% 5.01/5.29 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_zero_iff
% 5.01/5.29 thf(fact_6274_sgn__mult,axiom,
% 5.01/5.29 ! [A: code_integer,B: code_integer] :
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.01/5.29 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult
% 5.01/5.29 thf(fact_6275_sgn__mult,axiom,
% 5.01/5.29 ! [A: real,B: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 5.01/5.29 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult
% 5.01/5.29 thf(fact_6276_sgn__mult,axiom,
% 5.01/5.29 ! [A: rat,B: rat] :
% 5.01/5.29 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.29 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult
% 5.01/5.29 thf(fact_6277_sgn__mult,axiom,
% 5.01/5.29 ! [A: int,B: int] :
% 5.01/5.29 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 5.01/5.29 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult
% 5.01/5.29 thf(fact_6278_sgn__mult,axiom,
% 5.01/5.29 ! [A: complex,B: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 5.01/5.29 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult
% 5.01/5.29 thf(fact_6279_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.29 = ( times_times_real @ ( sgn_sgn_real @ X2 ) @ ( sgn_sgn_real @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Real_Vector_Spaces.sgn_mult
% 5.01/5.29 thf(fact_6280_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.01/5.29 ! [X2: complex,Y: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( times_times_complex @ X2 @ Y ) )
% 5.01/5.29 = ( times_times_complex @ ( sgn_sgn_complex @ X2 ) @ ( sgn_sgn_complex @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Real_Vector_Spaces.sgn_mult
% 5.01/5.29 thf(fact_6281_same__sgn__sgn__add,axiom,
% 5.01/5.29 ! [B: code_integer,A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ B )
% 5.01/5.29 = ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.01/5.29 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_sgn_add
% 5.01/5.29 thf(fact_6282_same__sgn__sgn__add,axiom,
% 5.01/5.29 ! [B: real,A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ B )
% 5.01/5.29 = ( sgn_sgn_real @ A ) )
% 5.01/5.29 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 5.01/5.29 = ( sgn_sgn_real @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_sgn_add
% 5.01/5.29 thf(fact_6283_same__sgn__sgn__add,axiom,
% 5.01/5.29 ! [B: rat,A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ B )
% 5.01/5.29 = ( sgn_sgn_rat @ A ) )
% 5.01/5.29 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 5.01/5.29 = ( sgn_sgn_rat @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_sgn_add
% 5.01/5.29 thf(fact_6284_same__sgn__sgn__add,axiom,
% 5.01/5.29 ! [B: int,A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ B )
% 5.01/5.29 = ( sgn_sgn_int @ A ) )
% 5.01/5.29 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 5.01/5.29 = ( sgn_sgn_int @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_sgn_add
% 5.01/5.29 thf(fact_6285_Real__Vector__Spaces_Osgn__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sgn_sgn_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sgn_sgn_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Real_Vector_Spaces.sgn_minus
% 5.01/5.29 thf(fact_6286_Real__Vector__Spaces_Osgn__minus,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Real_Vector_Spaces.sgn_minus
% 5.01/5.29 thf(fact_6287_exp__not__eq__zero,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( exp_complex @ X2 )
% 5.01/5.29 != zero_zero_complex ) ).
% 5.01/5.29
% 5.01/5.29 % exp_not_eq_zero
% 5.01/5.29 thf(fact_6288_exp__not__eq__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( exp_real @ X2 )
% 5.01/5.29 != zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % exp_not_eq_zero
% 5.01/5.29 thf(fact_6289_exp__times__arg__commute,axiom,
% 5.01/5.29 ! [A2: real] :
% 5.01/5.29 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.01/5.29 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_times_arg_commute
% 5.01/5.29 thf(fact_6290_exp__times__arg__commute,axiom,
% 5.01/5.29 ! [A2: complex] :
% 5.01/5.29 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.01/5.29 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_times_arg_commute
% 5.01/5.29 thf(fact_6291_bit__unset__bit__iff,axiom,
% 5.01/5.29 ! [M: nat,A: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 & ( M != N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_unset_bit_iff
% 5.01/5.29 thf(fact_6292_bit__unset__bit__iff,axiom,
% 5.01/5.29 ! [M: nat,A: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N )
% 5.01/5.29 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 & ( M != N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_unset_bit_iff
% 5.01/5.29 thf(fact_6293_and__eq__minus__1__iff,axiom,
% 5.01/5.29 ! [A: code_integer,B: code_integer] :
% 5.01/5.29 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( ( A
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 & ( B
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_eq_minus_1_iff
% 5.01/5.29 thf(fact_6294_and__eq__minus__1__iff,axiom,
% 5.01/5.29 ! [A: int,B: int] :
% 5.01/5.29 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( ( A
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 & ( B
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_eq_minus_1_iff
% 5.01/5.29 thf(fact_6295_not__bit__1__Suc,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % not_bit_1_Suc
% 5.01/5.29 thf(fact_6296_not__bit__1__Suc,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % not_bit_1_Suc
% 5.01/5.29 thf(fact_6297_bit__1__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_1_iff
% 5.01/5.29 thf(fact_6298_bit__1__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_1_iff
% 5.01/5.29 thf(fact_6299_bit__numeral__simps_I1_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(1)
% 5.01/5.29 thf(fact_6300_bit__numeral__simps_I1_J,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_numeral_simps(1)
% 5.01/5.29 thf(fact_6301_not__exp__less__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ~ ( ord_less_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % not_exp_less_zero
% 5.01/5.29 thf(fact_6302_exp__gt__zero,axiom,
% 5.01/5.29 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_gt_zero
% 5.01/5.29 thf(fact_6303_exp__total,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.29 => ? [X4: real] :
% 5.01/5.29 ( ( exp_real @ X4 )
% 5.01/5.29 = Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_total
% 5.01/5.29 thf(fact_6304_exp__ge__zero,axiom,
% 5.01/5.29 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ge_zero
% 5.01/5.29 thf(fact_6305_not__exp__le__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ~ ( ord_less_eq_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % not_exp_le_zero
% 5.01/5.29 thf(fact_6306_bit__take__bit__iff,axiom,
% 5.01/5.29 ! [M: nat,A: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N )
% 5.01/5.29 = ( ( ord_less_nat @ N @ M )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_take_bit_iff
% 5.01/5.29 thf(fact_6307_bit__take__bit__iff,axiom,
% 5.01/5.29 ! [M: nat,A: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N )
% 5.01/5.29 = ( ( ord_less_nat @ N @ M )
% 5.01/5.29 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_take_bit_iff
% 5.01/5.29 thf(fact_6308_sgn__not__eq__imp,axiom,
% 5.01/5.29 ! [B: real,A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ B )
% 5.01/5.29 != ( sgn_sgn_real @ A ) )
% 5.01/5.29 => ( ( ( sgn_sgn_real @ A )
% 5.01/5.29 != zero_zero_real )
% 5.01/5.29 => ( ( ( sgn_sgn_real @ B )
% 5.01/5.29 != zero_zero_real )
% 5.01/5.29 => ( ( sgn_sgn_real @ A )
% 5.01/5.29 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_not_eq_imp
% 5.01/5.29 thf(fact_6309_sgn__not__eq__imp,axiom,
% 5.01/5.29 ! [B: int,A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ B )
% 5.01/5.29 != ( sgn_sgn_int @ A ) )
% 5.01/5.29 => ( ( ( sgn_sgn_int @ A )
% 5.01/5.29 != zero_zero_int )
% 5.01/5.29 => ( ( ( sgn_sgn_int @ B )
% 5.01/5.29 != zero_zero_int )
% 5.01/5.29 => ( ( sgn_sgn_int @ A )
% 5.01/5.29 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_not_eq_imp
% 5.01/5.29 thf(fact_6310_sgn__not__eq__imp,axiom,
% 5.01/5.29 ! [B: code_integer,A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ B )
% 5.01/5.29 != ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 => ( ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 != zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( ( sgn_sgn_Code_integer @ B )
% 5.01/5.29 != zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_not_eq_imp
% 5.01/5.29 thf(fact_6311_sgn__not__eq__imp,axiom,
% 5.01/5.29 ! [B: rat,A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ B )
% 5.01/5.29 != ( sgn_sgn_rat @ A ) )
% 5.01/5.29 => ( ( ( sgn_sgn_rat @ A )
% 5.01/5.29 != zero_zero_rat )
% 5.01/5.29 => ( ( ( sgn_sgn_rat @ B )
% 5.01/5.29 != zero_zero_rat )
% 5.01/5.29 => ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_not_eq_imp
% 5.01/5.29 thf(fact_6312_bit__of__bool__iff,axiom,
% 5.01/5.29 ! [B: $o,N: nat] :
% 5.01/5.29 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N )
% 5.01/5.29 = ( B
% 5.01/5.29 & ( N = zero_zero_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_bool_iff
% 5.01/5.29 thf(fact_6313_bit__of__bool__iff,axiom,
% 5.01/5.29 ! [B: $o,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N )
% 5.01/5.29 = ( B
% 5.01/5.29 & ( N = zero_zero_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_bool_iff
% 5.01/5.29 thf(fact_6314_bit__of__bool__iff,axiom,
% 5.01/5.29 ! [B: $o,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N )
% 5.01/5.29 = ( B
% 5.01/5.29 & ( N = zero_zero_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_of_bool_iff
% 5.01/5.29 thf(fact_6315_sgn__minus__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.29 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_minus_1
% 5.01/5.29 thf(fact_6316_sgn__minus__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_minus_1
% 5.01/5.29 thf(fact_6317_sgn__minus__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_minus_1
% 5.01/5.29 thf(fact_6318_sgn__minus__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_minus_1
% 5.01/5.29 thf(fact_6319_sgn__minus__1,axiom,
% 5.01/5.29 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.29 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_minus_1
% 5.01/5.29 thf(fact_6320_AND__lower,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.29 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_lower
% 5.01/5.29 thf(fact_6321_AND__upper1,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper1
% 5.01/5.29 thf(fact_6322_AND__upper2,axiom,
% 5.01/5.29 ! [Y: int,X2: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper2
% 5.01/5.29 thf(fact_6323_AND__upper1_H,axiom,
% 5.01/5.29 ! [Y: int,Z: int,Ya: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( ord_less_eq_int @ Y @ Z )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper1'
% 5.01/5.29 thf(fact_6324_AND__upper2_H,axiom,
% 5.01/5.29 ! [Y: int,Z: int,X2: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( ord_less_eq_int @ Y @ Z )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper2'
% 5.01/5.29 thf(fact_6325_mult__sgn__abs,axiom,
% 5.01/5.29 ! [X2: code_integer] :
% 5.01/5.29 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ X2 ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % mult_sgn_abs
% 5.01/5.29 thf(fact_6326_mult__sgn__abs,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( times_times_real @ ( sgn_sgn_real @ X2 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % mult_sgn_abs
% 5.01/5.29 thf(fact_6327_mult__sgn__abs,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( times_times_rat @ ( sgn_sgn_rat @ X2 ) @ ( abs_abs_rat @ X2 ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % mult_sgn_abs
% 5.01/5.29 thf(fact_6328_mult__sgn__abs,axiom,
% 5.01/5.29 ! [X2: int] :
% 5.01/5.29 ( ( times_times_int @ ( sgn_sgn_int @ X2 ) @ ( abs_abs_int @ X2 ) )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % mult_sgn_abs
% 5.01/5.29 thf(fact_6329_sgn__mult__abs,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_abs
% 5.01/5.29 thf(fact_6330_sgn__mult__abs,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_abs
% 5.01/5.29 thf(fact_6331_sgn__mult__abs,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_abs
% 5.01/5.29 thf(fact_6332_sgn__mult__abs,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_abs
% 5.01/5.29 thf(fact_6333_sgn__mult__abs,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mult_abs
% 5.01/5.29 thf(fact_6334_abs__mult__sgn,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % abs_mult_sgn
% 5.01/5.29 thf(fact_6335_abs__mult__sgn,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % abs_mult_sgn
% 5.01/5.29 thf(fact_6336_abs__mult__sgn,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % abs_mult_sgn
% 5.01/5.29 thf(fact_6337_abs__mult__sgn,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % abs_mult_sgn
% 5.01/5.29 thf(fact_6338_abs__mult__sgn,axiom,
% 5.01/5.29 ! [A: complex] :
% 5.01/5.29 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 5.01/5.29 = A ) ).
% 5.01/5.29
% 5.01/5.29 % abs_mult_sgn
% 5.01/5.29 thf(fact_6339_linordered__idom__class_Oabs__sgn,axiom,
% 5.01/5.29 ( abs_abs_Code_integer
% 5.01/5.29 = ( ^ [K2: code_integer] : ( times_3573771949741848930nteger @ K2 @ ( sgn_sgn_Code_integer @ K2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % linordered_idom_class.abs_sgn
% 5.01/5.29 thf(fact_6340_linordered__idom__class_Oabs__sgn,axiom,
% 5.01/5.29 ( abs_abs_real
% 5.01/5.29 = ( ^ [K2: real] : ( times_times_real @ K2 @ ( sgn_sgn_real @ K2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % linordered_idom_class.abs_sgn
% 5.01/5.29 thf(fact_6341_linordered__idom__class_Oabs__sgn,axiom,
% 5.01/5.29 ( abs_abs_rat
% 5.01/5.29 = ( ^ [K2: rat] : ( times_times_rat @ K2 @ ( sgn_sgn_rat @ K2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % linordered_idom_class.abs_sgn
% 5.01/5.29 thf(fact_6342_linordered__idom__class_Oabs__sgn,axiom,
% 5.01/5.29 ( abs_abs_int
% 5.01/5.29 = ( ^ [K2: int] : ( times_times_int @ K2 @ ( sgn_sgn_int @ K2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % linordered_idom_class.abs_sgn
% 5.01/5.29 thf(fact_6343_int__sgnE,axiom,
% 5.01/5.29 ! [K: int] :
% 5.01/5.29 ~ ! [N3: nat,L3: int] :
% 5.01/5.29 ( K
% 5.01/5.29 != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % int_sgnE
% 5.01/5.29 thf(fact_6344_same__sgn__abs__add,axiom,
% 5.01/5.29 ! [B: code_integer,A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ B )
% 5.01/5.29 = ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.01/5.29 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_abs_add
% 5.01/5.29 thf(fact_6345_same__sgn__abs__add,axiom,
% 5.01/5.29 ! [B: real,A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ B )
% 5.01/5.29 = ( sgn_sgn_real @ A ) )
% 5.01/5.29 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 5.01/5.29 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_abs_add
% 5.01/5.29 thf(fact_6346_same__sgn__abs__add,axiom,
% 5.01/5.29 ! [B: rat,A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ B )
% 5.01/5.29 = ( sgn_sgn_rat @ A ) )
% 5.01/5.29 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 5.01/5.29 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_abs_add
% 5.01/5.29 thf(fact_6347_same__sgn__abs__add,axiom,
% 5.01/5.29 ! [B: int,A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ B )
% 5.01/5.29 = ( sgn_sgn_int @ A ) )
% 5.01/5.29 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 5.01/5.29 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % same_sgn_abs_add
% 5.01/5.29 thf(fact_6348_exp__add__commuting,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ( times_times_real @ X2 @ Y )
% 5.01/5.29 = ( times_times_real @ Y @ X2 ) )
% 5.01/5.29 => ( ( exp_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.29 = ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_add_commuting
% 5.01/5.29 thf(fact_6349_exp__add__commuting,axiom,
% 5.01/5.29 ! [X2: complex,Y: complex] :
% 5.01/5.29 ( ( ( times_times_complex @ X2 @ Y )
% 5.01/5.29 = ( times_times_complex @ Y @ X2 ) )
% 5.01/5.29 => ( ( exp_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.29 = ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_add_commuting
% 5.01/5.29 thf(fact_6350_mult__exp__exp,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) )
% 5.01/5.29 = ( exp_real @ ( plus_plus_real @ X2 @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mult_exp_exp
% 5.01/5.29 thf(fact_6351_mult__exp__exp,axiom,
% 5.01/5.29 ! [X2: complex,Y: complex] :
% 5.01/5.29 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) )
% 5.01/5.29 = ( exp_complex @ ( plus_plus_complex @ X2 @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mult_exp_exp
% 5.01/5.29 thf(fact_6352_exp__diff,axiom,
% 5.01/5.29 ! [X2: complex,Y: complex] :
% 5.01/5.29 ( ( exp_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.29 = ( divide1717551699836669952omplex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_diff
% 5.01/5.29 thf(fact_6353_exp__diff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( exp_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.29 = ( divide_divide_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_diff
% 5.01/5.29 thf(fact_6354_div__eq__sgn__abs,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 = ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( divide_divide_int @ K @ L )
% 5.01/5.29 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % div_eq_sgn_abs
% 5.01/5.29 thf(fact_6355_take__bit__eq__mask,axiom,
% 5.01/5.29 ( bit_se2923211474154528505it_int
% 5.01/5.29 = ( ^ [N4: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_se2000444600071755411sk_int @ N4 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_eq_mask
% 5.01/5.29 thf(fact_6356_take__bit__eq__mask,axiom,
% 5.01/5.29 ( bit_se2925701944663578781it_nat
% 5.01/5.29 = ( ^ [N4: nat,A4: nat] : ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se2002935070580805687sk_nat @ N4 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_eq_mask
% 5.01/5.29 thf(fact_6357_signed__take__bit__eq__if__positive,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.01/5.29 = ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_eq_if_positive
% 5.01/5.29 thf(fact_6358_and__exp__eq__0__iff__not__bit,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_exp_eq_0_iff_not_bit
% 5.01/5.29 thf(fact_6359_and__exp__eq__0__iff__not__bit,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = zero_zero_nat )
% 5.01/5.29 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_exp_eq_0_iff_not_bit
% 5.01/5.29 thf(fact_6360_pow_Osimps_I1_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( pow @ X2 @ one )
% 5.01/5.29 = X2 ) ).
% 5.01/5.29
% 5.01/5.29 % pow.simps(1)
% 5.01/5.29 thf(fact_6361_exp__gt__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_gt_one
% 5.01/5.29 thf(fact_6362_sgn__1__pos,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = one_one_Code_integer )
% 5.01/5.29 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_pos
% 5.01/5.29 thf(fact_6363_sgn__1__pos,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ A )
% 5.01/5.29 = one_one_real )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_pos
% 5.01/5.29 thf(fact_6364_sgn__1__pos,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = one_one_rat )
% 5.01/5.29 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_pos
% 5.01/5.29 thf(fact_6365_sgn__1__pos,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ A )
% 5.01/5.29 = one_one_int )
% 5.01/5.29 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_pos
% 5.01/5.29 thf(fact_6366_exp__ge__add__one__self,axiom,
% 5.01/5.29 ! [X2: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ge_add_one_self
% 5.01/5.29 thf(fact_6367_abs__sgn__eq,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ( A = zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = zero_z3403309356797280102nteger ) )
% 5.01/5.29 & ( ( A != zero_z3403309356797280102nteger )
% 5.01/5.29 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.01/5.29 = one_one_Code_integer ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq
% 5.01/5.29 thf(fact_6368_abs__sgn__eq,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ( A = zero_zero_real )
% 5.01/5.29 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = zero_zero_real ) )
% 5.01/5.29 & ( ( A != zero_zero_real )
% 5.01/5.29 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.29 = one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq
% 5.01/5.29 thf(fact_6369_abs__sgn__eq,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ( A = zero_zero_rat )
% 5.01/5.29 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = zero_zero_rat ) )
% 5.01/5.29 & ( ( A != zero_zero_rat )
% 5.01/5.29 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.29 = one_one_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq
% 5.01/5.29 thf(fact_6370_abs__sgn__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ( A = zero_zero_int )
% 5.01/5.29 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = zero_zero_int ) )
% 5.01/5.29 & ( ( A != zero_zero_int )
% 5.01/5.29 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.01/5.29 = one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % abs_sgn_eq
% 5.01/5.29 thf(fact_6371_AND__upper2_H_H,axiom,
% 5.01/5.29 ! [Y: int,Z: int,X2: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( ord_less_int @ Y @ Z )
% 5.01/5.29 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper2''
% 5.01/5.29 thf(fact_6372_AND__upper1_H_H,axiom,
% 5.01/5.29 ! [Y: int,Z: int,Ya: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( ord_less_int @ Y @ Z )
% 5.01/5.29 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % AND_upper1''
% 5.01/5.29 thf(fact_6373_and__less__eq,axiom,
% 5.01/5.29 ! [L: int,K: int] :
% 5.01/5.29 ( ( ord_less_int @ L @ zero_zero_int )
% 5.01/5.29 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_less_eq
% 5.01/5.29 thf(fact_6374_exp__minus__inverse,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % exp_minus_inverse
% 5.01/5.29 thf(fact_6375_exp__minus__inverse,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % exp_minus_inverse
% 5.01/5.29 thf(fact_6376_bit__not__int__iff_H,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_not_int_iff'
% 5.01/5.29 thf(fact_6377_exp__of__nat2__mult,axiom,
% 5.01/5.29 ! [X2: real,N: nat] :
% 5.01/5.29 ( ( exp_real @ ( times_times_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.29 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_of_nat2_mult
% 5.01/5.29 thf(fact_6378_exp__of__nat2__mult,axiom,
% 5.01/5.29 ! [X2: complex,N: nat] :
% 5.01/5.29 ( ( exp_complex @ ( times_times_complex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.01/5.29 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_of_nat2_mult
% 5.01/5.29 thf(fact_6379_exp__of__nat__mult,axiom,
% 5.01/5.29 ! [N: nat,X2: real] :
% 5.01/5.29 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) )
% 5.01/5.29 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_of_nat_mult
% 5.01/5.29 thf(fact_6380_exp__of__nat__mult,axiom,
% 5.01/5.29 ! [N: nat,X2: complex] :
% 5.01/5.29 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X2 ) )
% 5.01/5.29 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_of_nat_mult
% 5.01/5.29 thf(fact_6381_sgn__mod,axiom,
% 5.01/5.29 ! [L: int,K: int] :
% 5.01/5.29 ( ( L != zero_zero_int )
% 5.01/5.29 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.01/5.29 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.01/5.29 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_mod
% 5.01/5.29 thf(fact_6382_flip__bit__eq__if,axiom,
% 5.01/5.29 ( bit_se2159334234014336723it_int
% 5.01/5.29 = ( ^ [N4: nat,A4: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A4 @ N4 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N4 @ A4 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % flip_bit_eq_if
% 5.01/5.29 thf(fact_6383_flip__bit__eq__if,axiom,
% 5.01/5.29 ( bit_se2161824704523386999it_nat
% 5.01/5.29 = ( ^ [N4: nat,A4: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A4 @ N4 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N4 @ A4 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % flip_bit_eq_if
% 5.01/5.29 thf(fact_6384_even__and__iff,axiom,
% 5.01/5.29 ! [A: code_integer,B: code_integer] :
% 5.01/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.01/5.29 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_and_iff
% 5.01/5.29 thf(fact_6385_even__and__iff,axiom,
% 5.01/5.29 ! [A: int,B: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.01/5.29 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_and_iff
% 5.01/5.29 thf(fact_6386_even__and__iff,axiom,
% 5.01/5.29 ! [A: nat,B: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.01/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_and_iff
% 5.01/5.29 thf(fact_6387_sgn__1__neg,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ( sgn_sgn_real @ A )
% 5.01/5.29 = ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.29 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_neg
% 5.01/5.29 thf(fact_6388_sgn__1__neg,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ A )
% 5.01/5.29 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.29 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_neg
% 5.01/5.29 thf(fact_6389_sgn__1__neg,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( ( sgn_sgn_Code_integer @ A )
% 5.01/5.29 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.29 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_neg
% 5.01/5.29 thf(fact_6390_sgn__1__neg,axiom,
% 5.01/5.29 ! [A: rat] :
% 5.01/5.29 ( ( ( sgn_sgn_rat @ A )
% 5.01/5.29 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.29 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_1_neg
% 5.01/5.29 thf(fact_6391_sgn__if,axiom,
% 5.01/5.29 ( sgn_sgn_real
% 5.01/5.29 = ( ^ [X3: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_if
% 5.01/5.29 thf(fact_6392_sgn__if,axiom,
% 5.01/5.29 ( sgn_sgn_int
% 5.01/5.29 = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_if
% 5.01/5.29 thf(fact_6393_sgn__if,axiom,
% 5.01/5.29 ( sgn_sgn_Code_integer
% 5.01/5.29 = ( ^ [X3: code_integer] : ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X3 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_if
% 5.01/5.29 thf(fact_6394_sgn__if,axiom,
% 5.01/5.29 ( sgn_sgn_rat
% 5.01/5.29 = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_if
% 5.01/5.29 thf(fact_6395_exp__ge__add__one__self__aux,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ge_add_one_self_aux
% 5.01/5.29 thf(fact_6396_lemma__exp__total,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.01/5.29 => ? [X4: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.01/5.29 & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.01/5.29 & ( ( exp_real @ X4 )
% 5.01/5.29 = Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % lemma_exp_total
% 5.01/5.29 thf(fact_6397_even__and__iff__int,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.01/5.29 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.01/5.29 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_and_iff_int
% 5.01/5.29 thf(fact_6398_ln__ge__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ln_ge_iff
% 5.01/5.29 thf(fact_6399_zsgn__def,axiom,
% 5.01/5.29 ( sgn_sgn_int
% 5.01/5.29 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % zsgn_def
% 5.01/5.29 thf(fact_6400_ln__x__over__x__mono,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ln_x_over_x_mono
% 5.01/5.29 thf(fact_6401_norm__sgn,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( X2 = zero_zero_real )
% 5.01/5.29 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X2 ) )
% 5.01/5.29 = zero_zero_real ) )
% 5.01/5.29 & ( ( X2 != zero_zero_real )
% 5.01/5.29 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X2 ) )
% 5.01/5.29 = one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % norm_sgn
% 5.01/5.29 thf(fact_6402_norm__sgn,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( ( X2 = zero_zero_complex )
% 5.01/5.29 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X2 ) )
% 5.01/5.29 = zero_zero_real ) )
% 5.01/5.29 & ( ( X2 != zero_zero_complex )
% 5.01/5.29 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X2 ) )
% 5.01/5.29 = one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % norm_sgn
% 5.01/5.29 thf(fact_6403_div__sgn__abs__cancel,axiom,
% 5.01/5.29 ! [V: int,K: int,L: int] :
% 5.01/5.29 ( ( V != zero_zero_int )
% 5.01/5.29 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 5.01/5.29 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % div_sgn_abs_cancel
% 5.01/5.29 thf(fact_6404_bit__imp__take__bit__positive,axiom,
% 5.01/5.29 ! [N: nat,M: nat,K: int] :
% 5.01/5.29 ( ( ord_less_nat @ N @ M )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.01/5.29 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_imp_take_bit_positive
% 5.01/5.29 thf(fact_6405_div__dvd__sgn__abs,axiom,
% 5.01/5.29 ! [L: int,K: int] :
% 5.01/5.29 ( ( dvd_dvd_int @ L @ K )
% 5.01/5.29 => ( ( divide_divide_int @ K @ L )
% 5.01/5.29 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % div_dvd_sgn_abs
% 5.01/5.29 thf(fact_6406_bit__concat__bit__iff,axiom,
% 5.01/5.29 ! [M: nat,K: int,L: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.01/5.29 = ( ( ( ord_less_nat @ N @ M )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.01/5.29 | ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_concat_bit_iff
% 5.01/5.29 thf(fact_6407_signed__take__bit__eq__concat__bit,axiom,
% 5.01/5.29 ( bit_ri631733984087533419it_int
% 5.01/5.29 = ( ^ [N4: nat,K2: int] : ( bit_concat_bit @ N4 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N4 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % signed_take_bit_eq_concat_bit
% 5.01/5.29 thf(fact_6408_exp__eq__0__imp__not__bit,axiom,
% 5.01/5.29 ! [N: nat,A: int] :
% 5.01/5.29 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.29 = zero_zero_int )
% 5.01/5.29 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_eq_0_imp_not_bit
% 5.01/5.29 thf(fact_6409_exp__eq__0__imp__not__bit,axiom,
% 5.01/5.29 ! [N: nat,A: nat] :
% 5.01/5.29 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.29 = zero_zero_nat )
% 5.01/5.29 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_eq_0_imp_not_bit
% 5.01/5.29 thf(fact_6410_bit__Suc,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_Suc
% 5.01/5.29 thf(fact_6411_bit__Suc,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.01/5.29 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_Suc
% 5.01/5.29 thf(fact_6412_one__and__eq,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.01/5.29 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_and_eq
% 5.01/5.29 thf(fact_6413_one__and__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.01/5.29 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_and_eq
% 5.01/5.29 thf(fact_6414_one__and__eq,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.01/5.29 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_and_eq
% 5.01/5.29 thf(fact_6415_and__one__eq,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.01/5.29 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_one_eq
% 5.01/5.29 thf(fact_6416_and__one__eq,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.01/5.29 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_one_eq
% 5.01/5.29 thf(fact_6417_and__one__eq,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.01/5.29 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_one_eq
% 5.01/5.29 thf(fact_6418_stable__imp__bit__iff__odd,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.01/5.29 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_bit_iff_odd
% 5.01/5.29 thf(fact_6419_stable__imp__bit__iff__odd,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_bit_iff_odd
% 5.01/5.29 thf(fact_6420_stable__imp__bit__iff__odd,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = A )
% 5.01/5.29 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % stable_imp_bit_iff_odd
% 5.01/5.29 thf(fact_6421_bit__iff__idd__imp__stable,axiom,
% 5.01/5.29 ! [A: code_integer] :
% 5.01/5.29 ( ! [N3: nat] :
% 5.01/5.29 ( ( bit_se9216721137139052372nteger @ A @ N3 )
% 5.01/5.29 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.29 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.29 = A ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_idd_imp_stable
% 5.01/5.29 thf(fact_6422_bit__iff__idd__imp__stable,axiom,
% 5.01/5.29 ! [A: int] :
% 5.01/5.29 ( ! [N3: nat] :
% 5.01/5.29 ( ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.01/5.29 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.29 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.29 = A ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_idd_imp_stable
% 5.01/5.29 thf(fact_6423_bit__iff__idd__imp__stable,axiom,
% 5.01/5.29 ! [A: nat] :
% 5.01/5.29 ( ! [N3: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.01/5.29 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.29 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = A ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_idd_imp_stable
% 5.01/5.29 thf(fact_6424_exp__le,axiom,
% 5.01/5.29 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_le
% 5.01/5.29 thf(fact_6425_int__bit__bound,axiom,
% 5.01/5.29 ! [K: int] :
% 5.01/5.29 ~ ! [N3: nat] :
% 5.01/5.29 ( ! [M2: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.01/5.29 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.01/5.29 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.01/5.29 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % int_bit_bound
% 5.01/5.29 thf(fact_6426_exp__divide__power__eq,axiom,
% 5.01/5.29 ! [N: nat,X2: real] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.01/5.29 = ( exp_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_divide_power_eq
% 5.01/5.29 thf(fact_6427_exp__divide__power__eq,axiom,
% 5.01/5.29 ! [N: nat,X2: complex] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.01/5.29 = ( exp_complex @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_divide_power_eq
% 5.01/5.29 thf(fact_6428_tanh__altdef,axiom,
% 5.01/5.29 ( tanh_real
% 5.01/5.29 = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % tanh_altdef
% 5.01/5.29 thf(fact_6429_tanh__altdef,axiom,
% 5.01/5.29 ( tanh_complex
% 5.01/5.29 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % tanh_altdef
% 5.01/5.29 thf(fact_6430_bit__iff__odd,axiom,
% 5.01/5.29 ( bit_se9216721137139052372nteger
% 5.01/5.29 = ( ^ [A4: code_integer,N4: nat] :
% 5.01/5.29 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A4 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_odd
% 5.01/5.29 thf(fact_6431_bit__iff__odd,axiom,
% 5.01/5.29 ( bit_se1146084159140164899it_int
% 5.01/5.29 = ( ^ [A4: int,N4: nat] :
% 5.01/5.29 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_odd
% 5.01/5.29 thf(fact_6432_bit__iff__odd,axiom,
% 5.01/5.29 ( bit_se1148574629649215175it_nat
% 5.01/5.29 = ( ^ [A4: nat,N4: nat] :
% 5.01/5.29 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_iff_odd
% 5.01/5.29 thf(fact_6433_exp__half__le2,axiom,
% 5.01/5.29 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_half_le2
% 5.01/5.29 thf(fact_6434_exp__double,axiom,
% 5.01/5.29 ! [Z: complex] :
% 5.01/5.29 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.01/5.29 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_double
% 5.01/5.29 thf(fact_6435_exp__double,axiom,
% 5.01/5.29 ! [Z: real] :
% 5.01/5.29 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.01/5.29 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_double
% 5.01/5.29 thf(fact_6436_bit__int__def,axiom,
% 5.01/5.29 ( bit_se1146084159140164899it_int
% 5.01/5.29 = ( ^ [K2: int,N4: nat] :
% 5.01/5.29 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_int_def
% 5.01/5.29 thf(fact_6437_eucl__rel__int__remainderI,axiom,
% 5.01/5.29 ! [R: int,L: int,K: int,Q2: int] :
% 5.01/5.29 ( ( ( sgn_sgn_int @ R )
% 5.01/5.29 = ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 5.01/5.29 => ( ( K
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R ) )
% 5.01/5.29 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % eucl_rel_int_remainderI
% 5.01/5.29 thf(fact_6438_even__bit__succ__iff,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.01/5.29 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_bit_succ_iff
% 5.01/5.29 thf(fact_6439_even__bit__succ__iff,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_bit_succ_iff
% 5.01/5.29 thf(fact_6440_even__bit__succ__iff,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.01/5.29 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_bit_succ_iff
% 5.01/5.29 thf(fact_6441_odd__bit__iff__bit__pred,axiom,
% 5.01/5.29 ! [A: code_integer,N: nat] :
% 5.01/5.29 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.01/5.29 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % odd_bit_iff_bit_pred
% 5.01/5.29 thf(fact_6442_odd__bit__iff__bit__pred,axiom,
% 5.01/5.29 ! [A: int,N: nat] :
% 5.01/5.29 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.29 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % odd_bit_iff_bit_pred
% 5.01/5.29 thf(fact_6443_odd__bit__iff__bit__pred,axiom,
% 5.01/5.29 ! [A: nat,N: nat] :
% 5.01/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.29 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.29 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.01/5.29 | ( N = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % odd_bit_iff_bit_pred
% 5.01/5.29 thf(fact_6444_eucl__rel__int_Ocases,axiom,
% 5.01/5.29 ! [A12: int,A23: int,A32: product_prod_int_int] :
% 5.01/5.29 ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 5.01/5.29 => ( ( ( A23 = zero_zero_int )
% 5.01/5.29 => ( A32
% 5.01/5.29 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.01/5.29 => ( ! [Q3: int] :
% 5.01/5.29 ( ( A32
% 5.01/5.29 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.01/5.29 => ( ( A23 != zero_zero_int )
% 5.01/5.29 => ( A12
% 5.01/5.29 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.01/5.29 => ~ ! [R4: int,Q3: int] :
% 5.01/5.29 ( ( A32
% 5.01/5.29 = ( product_Pair_int_int @ Q3 @ R4 ) )
% 5.01/5.29 => ( ( ( sgn_sgn_int @ R4 )
% 5.01/5.29 = ( sgn_sgn_int @ A23 ) )
% 5.01/5.29 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 5.01/5.29 => ( A12
% 5.01/5.29 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % eucl_rel_int.cases
% 5.01/5.29 thf(fact_6445_eucl__rel__int_Osimps,axiom,
% 5.01/5.29 ( eucl_rel_int
% 5.01/5.29 = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 5.01/5.29 ( ? [K2: int] :
% 5.01/5.29 ( ( A1 = K2 )
% 5.01/5.29 & ( A22 = zero_zero_int )
% 5.01/5.29 & ( A33
% 5.01/5.29 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.01/5.29 | ? [L2: int,K2: int,Q4: int] :
% 5.01/5.29 ( ( A1 = K2 )
% 5.01/5.29 & ( A22 = L2 )
% 5.01/5.29 & ( A33
% 5.01/5.29 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.01/5.29 & ( L2 != zero_zero_int )
% 5.01/5.29 & ( K2
% 5.01/5.29 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.01/5.29 | ? [R5: int,L2: int,K2: int,Q4: int] :
% 5.01/5.29 ( ( A1 = K2 )
% 5.01/5.29 & ( A22 = L2 )
% 5.01/5.29 & ( A33
% 5.01/5.29 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.01/5.29 & ( ( sgn_sgn_int @ R5 )
% 5.01/5.29 = ( sgn_sgn_int @ L2 ) )
% 5.01/5.29 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.01/5.29 & ( K2
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % eucl_rel_int.simps
% 5.01/5.29 thf(fact_6446_exp__bound__half,axiom,
% 5.01/5.29 ! [Z: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_bound_half
% 5.01/5.29 thf(fact_6447_exp__bound__half,axiom,
% 5.01/5.29 ! [Z: complex] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_bound_half
% 5.01/5.29 thf(fact_6448_div__noneq__sgn__abs,axiom,
% 5.01/5.29 ! [L: int,K: int] :
% 5.01/5.29 ( ( L != zero_zero_int )
% 5.01/5.29 => ( ( ( sgn_sgn_int @ K )
% 5.01/5.29 != ( sgn_sgn_int @ L ) )
% 5.01/5.29 => ( ( divide_divide_int @ K @ L )
% 5.01/5.29 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.01/5.29 @ ( zero_n2684676970156552555ol_int
% 5.01/5.29 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % div_noneq_sgn_abs
% 5.01/5.29 thf(fact_6449_bit__sum__mult__2__cases,axiom,
% 5.01/5.29 ! [A: code_integer,B: code_integer,N: nat] :
% 5.01/5.29 ( ! [J2: nat] :
% 5.01/5.29 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.01/5.29 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.01/5.29 = ( ( ( N = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.29 & ( ( N != zero_zero_nat )
% 5.01/5.29 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_sum_mult_2_cases
% 5.01/5.29 thf(fact_6450_bit__sum__mult__2__cases,axiom,
% 5.01/5.29 ! [A: int,B: int,N: nat] :
% 5.01/5.29 ( ! [J2: nat] :
% 5.01/5.29 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.01/5.29 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.01/5.29 = ( ( ( N = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.29 & ( ( N != zero_zero_nat )
% 5.01/5.29 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_sum_mult_2_cases
% 5.01/5.29 thf(fact_6451_bit__sum__mult__2__cases,axiom,
% 5.01/5.29 ! [A: nat,B: nat,N: nat] :
% 5.01/5.29 ( ! [J2: nat] :
% 5.01/5.29 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.01/5.29 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.01/5.29 = ( ( ( N = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.01/5.29 & ( ( N != zero_zero_nat )
% 5.01/5.29 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_sum_mult_2_cases
% 5.01/5.29 thf(fact_6452_bit__rec,axiom,
% 5.01/5.29 ( bit_se9216721137139052372nteger
% 5.01/5.29 = ( ^ [A4: code_integer,N4: nat] :
% 5.01/5.29 ( ( ( N4 = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) )
% 5.01/5.29 & ( ( N4 != zero_zero_nat )
% 5.01/5.29 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_rec
% 5.01/5.29 thf(fact_6453_bit__rec,axiom,
% 5.01/5.29 ( bit_se1146084159140164899it_int
% 5.01/5.29 = ( ^ [A4: int,N4: nat] :
% 5.01/5.29 ( ( ( N4 = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) )
% 5.01/5.29 & ( ( N4 != zero_zero_nat )
% 5.01/5.29 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_rec
% 5.01/5.29 thf(fact_6454_bit__rec,axiom,
% 5.01/5.29 ( bit_se1148574629649215175it_nat
% 5.01/5.29 = ( ^ [A4: nat,N4: nat] :
% 5.01/5.29 ( ( ( N4 = zero_zero_nat )
% 5.01/5.29 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) )
% 5.01/5.29 & ( ( N4 != zero_zero_nat )
% 5.01/5.29 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_rec
% 5.01/5.29 thf(fact_6455_exp__bound,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.29 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_bound
% 5.01/5.29 thf(fact_6456_and__int__rec,axiom,
% 5.01/5.29 ( bit_se725231765392027082nd_int
% 5.01/5.29 = ( ^ [K2: int,L2: int] :
% 5.01/5.29 ( plus_plus_int
% 5.01/5.29 @ ( zero_n2684676970156552555ol_int
% 5.01/5.29 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.01/5.29 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.01/5.29 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_int_rec
% 5.01/5.29 thf(fact_6457_set__bit__eq,axiom,
% 5.01/5.29 ( bit_se7879613467334960850it_int
% 5.01/5.29 = ( ^ [N4: nat,K2: int] :
% 5.01/5.29 ( plus_plus_int @ K2
% 5.01/5.29 @ ( times_times_int
% 5.01/5.29 @ ( zero_n2684676970156552555ol_int
% 5.01/5.29 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N4 ) )
% 5.01/5.29 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % set_bit_eq
% 5.01/5.29 thf(fact_6458_unset__bit__eq,axiom,
% 5.01/5.29 ( bit_se4203085406695923979it_int
% 5.01/5.29 = ( ^ [N4: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % unset_bit_eq
% 5.01/5.29 thf(fact_6459_real__exp__bound__lemma,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_exp_bound_lemma
% 5.01/5.29 thf(fact_6460_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.01/5.29 ! [N: nat,X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ge_one_plus_x_over_n_power_n
% 5.01/5.29 thf(fact_6461_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.01/5.29 ! [X2: real,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_ge_one_minus_x_over_n_power_n
% 5.01/5.29 thf(fact_6462_take__bit__Suc__from__most,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.01/5.29 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_Suc_from_most
% 5.01/5.29 thf(fact_6463_exp__bound__lemma,axiom,
% 5.01/5.29 ! [Z: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_bound_lemma
% 5.01/5.29 thf(fact_6464_exp__bound__lemma,axiom,
% 5.01/5.29 ! [Z: complex] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_bound_lemma
% 5.01/5.29 thf(fact_6465_exp__lower__Taylor__quadratic,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % exp_lower_Taylor_quadratic
% 5.01/5.29 thf(fact_6466_log__base__10__eq1,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.29 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_base_10_eq1
% 5.01/5.29 thf(fact_6467_modulo__int__def,axiom,
% 5.01/5.29 ( modulo_modulo_int
% 5.01/5.29 = ( ^ [K2: int,L2: int] :
% 5.01/5.29 ( if_int @ ( L2 = zero_zero_int ) @ K2
% 5.01/5.29 @ ( if_int
% 5.01/5.29 @ ( ( sgn_sgn_int @ K2 )
% 5.01/5.29 = ( sgn_sgn_int @ L2 ) )
% 5.01/5.29 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.01/5.29 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.01/5.29 @ ( minus_minus_int
% 5.01/5.29 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.01/5.29 @ ( zero_n2684676970156552555ol_int
% 5.01/5.29 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 5.01/5.29 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % modulo_int_def
% 5.01/5.29 thf(fact_6468_divide__int__def,axiom,
% 5.01/5.29 ( divide_divide_int
% 5.01/5.29 = ( ^ [K2: int,L2: int] :
% 5.01/5.29 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.01/5.29 @ ( if_int
% 5.01/5.29 @ ( ( sgn_sgn_int @ K2 )
% 5.01/5.29 = ( sgn_sgn_int @ L2 ) )
% 5.01/5.29 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.01/5.29 @ ( uminus_uminus_int
% 5.01/5.29 @ ( semiri1314217659103216013at_int
% 5.01/5.29 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.01/5.29 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.29 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % divide_int_def
% 5.01/5.29 thf(fact_6469_arctan__half,axiom,
% 5.01/5.29 ( arctan
% 5.01/5.29 = ( ^ [X3: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X3 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_half
% 5.01/5.29 thf(fact_6470_log__base__10__eq2,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.29 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_base_10_eq2
% 5.01/5.29 thf(fact_6471_machin,axiom,
% 5.01/5.29 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.29 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % machin
% 5.01/5.29 thf(fact_6472_real__sqrt__eq__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ( sqrt @ X2 )
% 5.01/5.29 = ( sqrt @ Y ) )
% 5.01/5.29 = ( X2 = Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_eq_iff
% 5.01/5.29 thf(fact_6473_zero__le__sgn__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_sgn_iff
% 5.01/5.29 thf(fact_6474_sgn__le__0__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X2 ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_le_0_iff
% 5.01/5.29 thf(fact_6475_real__sqrt__zero,axiom,
% 5.01/5.29 ( ( sqrt @ zero_zero_real )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_zero
% 5.01/5.29 thf(fact_6476_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( sqrt @ X2 )
% 5.01/5.29 = zero_zero_real )
% 5.01/5.29 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_eq_zero_cancel_iff
% 5.01/5.29 thf(fact_6477_real__sqrt__less__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_less_iff
% 5.01/5.29 thf(fact_6478_real__sqrt__le__iff,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_le_iff
% 5.01/5.29 thf(fact_6479_real__sqrt__eq__1__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( sqrt @ X2 )
% 5.01/5.29 = one_one_real )
% 5.01/5.29 = ( X2 = one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_eq_1_iff
% 5.01/5.29 thf(fact_6480_real__sqrt__one,axiom,
% 5.01/5.29 ( ( sqrt @ one_one_real )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_one
% 5.01/5.29 thf(fact_6481_nat__int,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.29 = N ) ).
% 5.01/5.29
% 5.01/5.29 % nat_int
% 5.01/5.29 thf(fact_6482_nat__numeral,axiom,
% 5.01/5.29 ! [K: num] :
% 5.01/5.29 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.01/5.29 = ( numeral_numeral_nat @ K ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_numeral
% 5.01/5.29 thf(fact_6483_real__sqrt__lt__0__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_lt_0_iff
% 5.01/5.29 thf(fact_6484_real__sqrt__gt__0__iff,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_gt_0_iff
% 5.01/5.29 thf(fact_6485_real__sqrt__ge__0__iff,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_0_iff
% 5.01/5.29 thf(fact_6486_real__sqrt__le__0__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_le_0_iff
% 5.01/5.29 thf(fact_6487_real__sqrt__gt__1__iff,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_gt_1_iff
% 5.01/5.29 thf(fact_6488_real__sqrt__lt__1__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_lt_1_iff
% 5.01/5.29 thf(fact_6489_real__sqrt__le__1__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_le_1_iff
% 5.01/5.29 thf(fact_6490_real__sqrt__ge__1__iff,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.01/5.29 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_1_iff
% 5.01/5.29 thf(fact_6491_log__one,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( log @ A @ one_one_real )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % log_one
% 5.01/5.29 thf(fact_6492_real__sqrt__abs2,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sqrt @ ( times_times_real @ X2 @ X2 ) )
% 5.01/5.29 = ( abs_abs_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_abs2
% 5.01/5.29 thf(fact_6493_real__sqrt__mult__self,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.01/5.29 = ( abs_abs_real @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_mult_self
% 5.01/5.29 thf(fact_6494_real__sqrt__four,axiom,
% 5.01/5.29 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.29 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_four
% 5.01/5.29 thf(fact_6495_nat__1,axiom,
% 5.01/5.29 ( ( nat2 @ one_one_int )
% 5.01/5.29 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_1
% 5.01/5.29 thf(fact_6496_nat__0__iff,axiom,
% 5.01/5.29 ! [I: int] :
% 5.01/5.29 ( ( ( nat2 @ I )
% 5.01/5.29 = zero_zero_nat )
% 5.01/5.29 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_0_iff
% 5.01/5.29 thf(fact_6497_nat__le__0,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.01/5.29 => ( ( nat2 @ Z )
% 5.01/5.29 = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_le_0
% 5.01/5.29 thf(fact_6498_zless__nat__conj,axiom,
% 5.01/5.29 ! [W: int,Z: int] :
% 5.01/5.29 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.29 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % zless_nat_conj
% 5.01/5.29 thf(fact_6499_nat__neg__numeral,axiom,
% 5.01/5.29 ! [K: num] :
% 5.01/5.29 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % nat_neg_numeral
% 5.01/5.29 thf(fact_6500_log__eq__one,axiom,
% 5.01/5.29 ! [A: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( log @ A @ A )
% 5.01/5.29 = one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_eq_one
% 5.01/5.29 thf(fact_6501_log__less__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( ord_less_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) )
% 5.01/5.29 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_less_cancel_iff
% 5.01/5.29 thf(fact_6502_log__less__one__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_real @ X2 @ A ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_less_one_cancel_iff
% 5.01/5.29 thf(fact_6503_one__less__log__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ A @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_log_cancel_iff
% 5.01/5.29 thf(fact_6504_log__less__zero__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_less_zero_cancel_iff
% 5.01/5.29 thf(fact_6505_zero__less__log__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_log_cancel_iff
% 5.01/5.29 thf(fact_6506_nat__zminus__int,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % nat_zminus_int
% 5.01/5.29 thf(fact_6507_int__nat__eq,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.01/5.29 = Z ) )
% 5.01/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.01/5.29 = zero_zero_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % int_nat_eq
% 5.01/5.29 thf(fact_6508_zero__less__nat__eq,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_nat_eq
% 5.01/5.29 thf(fact_6509_zero__le__log__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_log_cancel_iff
% 5.01/5.29 thf(fact_6510_log__le__zero__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_le_zero_cancel_iff
% 5.01/5.29 thf(fact_6511_one__le__log__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ A @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_log_cancel_iff
% 5.01/5.29 thf(fact_6512_log__le__one__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ A ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_le_one_cancel_iff
% 5.01/5.29 thf(fact_6513_log__le__cancel__iff,axiom,
% 5.01/5.29 ! [A: real,X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_le_cancel_iff
% 5.01/5.29 thf(fact_6514_diff__nat__numeral,axiom,
% 5.01/5.29 ! [V: num,V3: num] :
% 5.01/5.29 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.01/5.29 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % diff_nat_numeral
% 5.01/5.29 thf(fact_6515_and__nat__numerals_I1_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_numerals(1)
% 5.01/5.29 thf(fact_6516_and__nat__numerals_I3_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.29 = zero_zero_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_numerals(3)
% 5.01/5.29 thf(fact_6517_numeral__power__eq__nat__cancel__iff,axiom,
% 5.01/5.29 ! [X2: num,N: nat,Y: int] :
% 5.01/5.29 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.01/5.29 = ( nat2 @ Y ) )
% 5.01/5.29 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.29 = Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_power_eq_nat_cancel_iff
% 5.01/5.29 thf(fact_6518_nat__eq__numeral__power__cancel__iff,axiom,
% 5.01/5.29 ! [Y: int,X2: num,N: nat] :
% 5.01/5.29 ( ( ( nat2 @ Y )
% 5.01/5.29 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.01/5.29 = ( Y
% 5.01/5.29 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_eq_numeral_power_cancel_iff
% 5.01/5.29 thf(fact_6519_nat__abs__dvd__iff,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.01/5.29 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_abs_dvd_iff
% 5.01/5.29 thf(fact_6520_dvd__nat__abs__iff,axiom,
% 5.01/5.29 ! [N: nat,K: int] :
% 5.01/5.29 ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.01/5.29 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.01/5.29
% 5.01/5.29 % dvd_nat_abs_iff
% 5.01/5.29 thf(fact_6521_one__less__nat__eq,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_nat_eq
% 5.01/5.29 thf(fact_6522_real__sqrt__abs,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.29 = ( abs_abs_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_abs
% 5.01/5.29 thf(fact_6523_log__pow__cancel,axiom,
% 5.01/5.29 ! [A: real,B: nat] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.01/5.29 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_pow_cancel
% 5.01/5.29 thf(fact_6524_and__nat__numerals_I4_J,axiom,
% 5.01/5.29 ! [X2: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.29 = one_one_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_numerals(4)
% 5.01/5.29 thf(fact_6525_and__nat__numerals_I2_J,axiom,
% 5.01/5.29 ! [Y: num] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.29 = one_one_nat ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_numerals(2)
% 5.01/5.29 thf(fact_6526_real__sqrt__pow2,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_pow2
% 5.01/5.29 thf(fact_6527_real__sqrt__pow2__iff,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = X2 )
% 5.01/5.29 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_pow2_iff
% 5.01/5.29 thf(fact_6528_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.01/5.29 ! [X2: real,Y: real,Xa: real,Ya: real] :
% 5.01/5.29 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_mult_squared_eq
% 5.01/5.29 thf(fact_6529_nat__numeral__diff__1,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.01/5.29 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_numeral_diff_1
% 5.01/5.29 thf(fact_6530_nat__less__numeral__power__cancel__iff,axiom,
% 5.01/5.29 ! [A: int,X2: num,N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.01/5.29 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_less_numeral_power_cancel_iff
% 5.01/5.29 thf(fact_6531_numeral__power__less__nat__cancel__iff,axiom,
% 5.01/5.29 ! [X2: num,N: nat,A: int] :
% 5.01/5.29 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.01/5.29 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_power_less_nat_cancel_iff
% 5.01/5.29 thf(fact_6532_numeral__power__le__nat__cancel__iff,axiom,
% 5.01/5.29 ! [X2: num,N: nat,A: int] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.01/5.29 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_power_le_nat_cancel_iff
% 5.01/5.29 thf(fact_6533_nat__le__numeral__power__cancel__iff,axiom,
% 5.01/5.29 ! [A: int,X2: num,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.01/5.29 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_le_numeral_power_cancel_iff
% 5.01/5.29 thf(fact_6534_and__Suc__0__eq,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.29 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_Suc_0_eq
% 5.01/5.29 thf(fact_6535_Suc__0__and__eq,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.29 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Suc_0_and_eq
% 5.01/5.29 thf(fact_6536_and__nat__def,axiom,
% 5.01/5.29 ( bit_se727722235901077358nd_nat
% 5.01/5.29 = ( ^ [M3: nat,N4: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_def
% 5.01/5.29 thf(fact_6537_real__sqrt__less__mono,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.29 => ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_less_mono
% 5.01/5.29 thf(fact_6538_real__sqrt__le__mono,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_le_mono
% 5.01/5.29 thf(fact_6539_real__sqrt__divide,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( sqrt @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.29 = ( divide_divide_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_divide
% 5.01/5.29 thf(fact_6540_real__sqrt__mult,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( sqrt @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.29 = ( times_times_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_mult
% 5.01/5.29 thf(fact_6541_real__sqrt__power,axiom,
% 5.01/5.29 ! [X2: real,K: nat] :
% 5.01/5.29 ( ( sqrt @ ( power_power_real @ X2 @ K ) )
% 5.01/5.29 = ( power_power_real @ ( sqrt @ X2 ) @ K ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_power
% 5.01/5.29 thf(fact_6542_real__sqrt__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sqrt @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sqrt @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_minus
% 5.01/5.29 thf(fact_6543_pi__neq__zero,axiom,
% 5.01/5.29 pi != zero_zero_real ).
% 5.01/5.29
% 5.01/5.29 % pi_neq_zero
% 5.01/5.29 thf(fact_6544_bit__nat__iff,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.01/5.29 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_nat_iff
% 5.01/5.29 thf(fact_6545_bit__Suc__0__iff,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.29 = ( N = zero_zero_nat ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_Suc_0_iff
% 5.01/5.29 thf(fact_6546_not__bit__Suc__0__Suc,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % not_bit_Suc_0_Suc
% 5.01/5.29 thf(fact_6547_real__sqrt__gt__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_gt_zero
% 5.01/5.29 thf(fact_6548_real__sqrt__eq__zero__cancel,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ( sqrt @ X2 )
% 5.01/5.29 = zero_zero_real )
% 5.01/5.29 => ( X2 = zero_zero_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_eq_zero_cancel
% 5.01/5.29 thf(fact_6549_real__sqrt__ge__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_zero
% 5.01/5.29 thf(fact_6550_real__sqrt__ge__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.29 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_one
% 5.01/5.29 thf(fact_6551_nat__zero__as__int,axiom,
% 5.01/5.29 ( zero_zero_nat
% 5.01/5.29 = ( nat2 @ zero_zero_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_zero_as_int
% 5.01/5.29 thf(fact_6552_nat__numeral__as__int,axiom,
% 5.01/5.29 ( numeral_numeral_nat
% 5.01/5.29 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_numeral_as_int
% 5.01/5.29 thf(fact_6553_real__sgn__eq,axiom,
% 5.01/5.29 ( sgn_sgn_real
% 5.01/5.29 = ( ^ [X3: real] : ( divide_divide_real @ X3 @ ( abs_abs_real @ X3 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sgn_eq
% 5.01/5.29 thf(fact_6554_nat__mono,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.29 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mono
% 5.01/5.29 thf(fact_6555_ex__nat,axiom,
% 5.01/5.29 ( ( ^ [P2: nat > $o] :
% 5.01/5.29 ? [X6: nat] : ( P2 @ X6 ) )
% 5.01/5.29 = ( ^ [P3: nat > $o] :
% 5.01/5.29 ? [X3: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.01/5.29 & ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ex_nat
% 5.01/5.29 thf(fact_6556_all__nat,axiom,
% 5.01/5.29 ( ( ^ [P2: nat > $o] :
% 5.01/5.29 ! [X6: nat] : ( P2 @ X6 ) )
% 5.01/5.29 = ( ^ [P3: nat > $o] :
% 5.01/5.29 ! [X3: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.01/5.29 => ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % all_nat
% 5.01/5.29 thf(fact_6557_eq__nat__nat__iff,axiom,
% 5.01/5.29 ! [Z: int,Z6: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.01/5.29 => ( ( ( nat2 @ Z )
% 5.01/5.29 = ( nat2 @ Z6 ) )
% 5.01/5.29 = ( Z = Z6 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % eq_nat_nat_iff
% 5.01/5.29 thf(fact_6558_nat__one__as__int,axiom,
% 5.01/5.29 ( one_one_nat
% 5.01/5.29 = ( nat2 @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_one_as_int
% 5.01/5.29 thf(fact_6559_log__def,axiom,
% 5.01/5.29 ( log
% 5.01/5.29 = ( ^ [A4: real,X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ A4 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_def
% 5.01/5.29 thf(fact_6560_pi__gt__zero,axiom,
% 5.01/5.29 ord_less_real @ zero_zero_real @ pi ).
% 5.01/5.29
% 5.01/5.29 % pi_gt_zero
% 5.01/5.29 thf(fact_6561_pi__not__less__zero,axiom,
% 5.01/5.29 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % pi_not_less_zero
% 5.01/5.29 thf(fact_6562_pi__ge__zero,axiom,
% 5.01/5.29 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.01/5.29
% 5.01/5.29 % pi_ge_zero
% 5.01/5.29 thf(fact_6563_unset__bit__nat__def,axiom,
% 5.01/5.29 ( bit_se4205575877204974255it_nat
% 5.01/5.29 = ( ^ [M3: nat,N4: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % unset_bit_nat_def
% 5.01/5.29 thf(fact_6564_nat__mask__eq,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.29 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mask_eq
% 5.01/5.29 thf(fact_6565_not__bit__Suc__0__numeral,axiom,
% 5.01/5.29 ! [N: num] :
% 5.01/5.29 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % not_bit_Suc_0_numeral
% 5.01/5.29 thf(fact_6566_real__div__sqrt,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.01/5.29 = ( sqrt @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_div_sqrt
% 5.01/5.29 thf(fact_6567_sqrt__add__le__add__sqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_add_le_add_sqrt
% 5.01/5.29 thf(fact_6568_le__real__sqrt__sumsq,axiom,
% 5.01/5.29 ! [X2: real,Y: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % le_real_sqrt_sumsq
% 5.01/5.29 thf(fact_6569_nat__mono__iff,axiom,
% 5.01/5.29 ! [Z: int,W: int] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mono_iff
% 5.01/5.29 thf(fact_6570_zless__nat__eq__int__zless,axiom,
% 5.01/5.29 ! [M: nat,Z: int] :
% 5.01/5.29 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.01/5.29
% 5.01/5.29 % zless_nat_eq_int_zless
% 5.01/5.29 thf(fact_6571_nat__le__iff,axiom,
% 5.01/5.29 ! [X2: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.01/5.29 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_le_iff
% 5.01/5.29 thf(fact_6572_nat__0__le,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.01/5.29 = Z ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_0_le
% 5.01/5.29 thf(fact_6573_int__eq__iff,axiom,
% 5.01/5.29 ! [M: nat,Z: int] :
% 5.01/5.29 ( ( ( semiri1314217659103216013at_int @ M )
% 5.01/5.29 = Z )
% 5.01/5.29 = ( ( M
% 5.01/5.29 = ( nat2 @ Z ) )
% 5.01/5.29 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % int_eq_iff
% 5.01/5.29 thf(fact_6574_nat__int__add,axiom,
% 5.01/5.29 ! [A: nat,B: nat] :
% 5.01/5.29 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.01/5.29 = ( plus_plus_nat @ A @ B ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_int_add
% 5.01/5.29 thf(fact_6575_int__minus,axiom,
% 5.01/5.29 ! [N: nat,M: nat] :
% 5.01/5.29 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % int_minus
% 5.01/5.29 thf(fact_6576_nat__abs__mult__distrib,axiom,
% 5.01/5.29 ! [W: int,Z: int] :
% 5.01/5.29 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.01/5.29 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_abs_mult_distrib
% 5.01/5.29 thf(fact_6577_log__ln,axiom,
% 5.01/5.29 ( ln_ln_real
% 5.01/5.29 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_ln
% 5.01/5.29 thf(fact_6578_sqrt2__less__2,axiom,
% 5.01/5.29 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt2_less_2
% 5.01/5.29 thf(fact_6579_sgn__real__def,axiom,
% 5.01/5.29 ( sgn_sgn_real
% 5.01/5.29 = ( ^ [A4: real] : ( if_real @ ( A4 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A4 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_real_def
% 5.01/5.29 thf(fact_6580_log__base__change,axiom,
% 5.01/5.29 ! [A: real,B: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( log @ B @ X2 )
% 5.01/5.29 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_base_change
% 5.01/5.29 thf(fact_6581_less__log__of__power,axiom,
% 5.01/5.29 ! [B: real,N: nat,M: real] :
% 5.01/5.29 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.29 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % less_log_of_power
% 5.01/5.29 thf(fact_6582_log__of__power__eq,axiom,
% 5.01/5.29 ! [M: nat,B: real,N: nat] :
% 5.01/5.29 ( ( ( semiri5074537144036343181t_real @ M )
% 5.01/5.29 = ( power_power_real @ B @ N ) )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.29 => ( ( semiri5074537144036343181t_real @ N )
% 5.01/5.29 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_of_power_eq
% 5.01/5.29 thf(fact_6583_nat__less__eq__zless,axiom,
% 5.01/5.29 ! [W: int,Z: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_less_eq_zless
% 5.01/5.29 thf(fact_6584_nat__le__eq__zle,axiom,
% 5.01/5.29 ! [W: int,Z: int] :
% 5.01/5.29 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.01/5.29 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.01/5.29 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.01/5.29 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_le_eq_zle
% 5.01/5.29 thf(fact_6585_nat__eq__iff2,axiom,
% 5.01/5.29 ! [M: nat,W: int] :
% 5.01/5.29 ( ( M
% 5.01/5.29 = ( nat2 @ W ) )
% 5.01/5.29 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( W
% 5.01/5.29 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.01/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( M = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_eq_iff2
% 5.01/5.29 thf(fact_6586_nat__eq__iff,axiom,
% 5.01/5.29 ! [W: int,M: nat] :
% 5.01/5.29 ( ( ( nat2 @ W )
% 5.01/5.29 = M )
% 5.01/5.29 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( W
% 5.01/5.29 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.01/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( M = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_eq_iff
% 5.01/5.29 thf(fact_6587_split__nat,axiom,
% 5.01/5.29 ! [P: nat > $o,I: int] :
% 5.01/5.29 ( ( P @ ( nat2 @ I ) )
% 5.01/5.29 = ( ! [N4: nat] :
% 5.01/5.29 ( ( I
% 5.01/5.29 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.01/5.29 => ( P @ N4 ) )
% 5.01/5.29 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.01/5.29 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % split_nat
% 5.01/5.29 thf(fact_6588_le__nat__iff,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.01/5.29 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % le_nat_iff
% 5.01/5.29 thf(fact_6589_nat__add__distrib,axiom,
% 5.01/5.29 ! [Z: int,Z6: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.01/5.29 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.01/5.29 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_add_distrib
% 5.01/5.29 thf(fact_6590_nat__mult__distrib,axiom,
% 5.01/5.29 ! [Z: int,Z6: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.01/5.29 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mult_distrib
% 5.01/5.29 thf(fact_6591_Suc__as__int,axiom,
% 5.01/5.29 ( suc
% 5.01/5.29 = ( ^ [A4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ one_one_int ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Suc_as_int
% 5.01/5.29 thf(fact_6592_nat__diff__distrib,axiom,
% 5.01/5.29 ! [Z6: int,Z: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.01/5.29 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.01/5.29 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.01/5.29 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_diff_distrib
% 5.01/5.29 thf(fact_6593_nat__diff__distrib_H,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( nat2 @ ( minus_minus_int @ X2 @ Y ) )
% 5.01/5.29 = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_diff_distrib'
% 5.01/5.29 thf(fact_6594_nat__abs__triangle__ineq,axiom,
% 5.01/5.29 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_abs_triangle_ineq
% 5.01/5.29 thf(fact_6595_nat__div__distrib_H,axiom,
% 5.01/5.29 ! [Y: int,X2: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 5.01/5.29 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_div_distrib'
% 5.01/5.29 thf(fact_6596_nat__div__distrib,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.29 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 5.01/5.29 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_div_distrib
% 5.01/5.29 thf(fact_6597_nat__power__eq,axiom,
% 5.01/5.29 ! [Z: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.01/5.29 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_power_eq
% 5.01/5.29 thf(fact_6598_nat__mod__distrib,axiom,
% 5.01/5.29 ! [X2: int,Y: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.29 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y ) )
% 5.01/5.29 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mod_distrib
% 5.01/5.29 thf(fact_6599_pi__less__4,axiom,
% 5.01/5.29 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_less_4
% 5.01/5.29 thf(fact_6600_pi__ge__two,axiom,
% 5.01/5.29 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.01/5.29
% 5.01/5.29 % pi_ge_two
% 5.01/5.29 thf(fact_6601_div__abs__eq__div__nat,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % div_abs_eq_div_nat
% 5.01/5.29 thf(fact_6602_pi__half__neq__two,axiom,
% 5.01/5.29 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.29 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_neq_two
% 5.01/5.29 thf(fact_6603_mod__abs__eq__div__nat,axiom,
% 5.01/5.29 ! [K: int,L: int] :
% 5.01/5.29 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % mod_abs_eq_div_nat
% 5.01/5.29 thf(fact_6604_take__bit__nat__eq,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.01/5.29 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % take_bit_nat_eq
% 5.01/5.29 thf(fact_6605_nat__take__bit__eq,axiom,
% 5.01/5.29 ! [K: int,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.01/5.29 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_take_bit_eq
% 5.01/5.29 thf(fact_6606_arctan__inverse,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( X2 != zero_zero_real )
% 5.01/5.29 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.01/5.29 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_inverse
% 5.01/5.29 thf(fact_6607_real__less__rsqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.01/5.29 => ( ord_less_real @ X2 @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_less_rsqrt
% 5.01/5.29 thf(fact_6608_sqrt__le__D,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_le_D
% 5.01/5.29 thf(fact_6609_real__le__rsqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_le_rsqrt
% 5.01/5.29 thf(fact_6610_nat__2,axiom,
% 5.01/5.29 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.29 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_2
% 5.01/5.29 thf(fact_6611_log__mult,axiom,
% 5.01/5.29 ! [A: real,X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( log @ A @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.29 = ( plus_plus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_mult
% 5.01/5.29 thf(fact_6612_sgn__power__injE,axiom,
% 5.01/5.29 ! [A: real,N: nat,X2: real,B: real] :
% 5.01/5.29 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.01/5.29 = X2 )
% 5.01/5.29 => ( ( X2
% 5.01/5.29 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.29 => ( A = B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sgn_power_injE
% 5.01/5.29 thf(fact_6613_log__divide,axiom,
% 5.01/5.29 ! [A: real,X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( log @ A @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.29 = ( minus_minus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_divide
% 5.01/5.29 thf(fact_6614_le__log__of__power,axiom,
% 5.01/5.29 ! [B: real,N: nat,M: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.29 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % le_log_of_power
% 5.01/5.29 thf(fact_6615_log__base__pow,axiom,
% 5.01/5.29 ! [A: real,N: nat,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( log @ ( power_power_real @ A @ N ) @ X2 )
% 5.01/5.29 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_base_pow
% 5.01/5.29 thf(fact_6616_log__nat__power,axiom,
% 5.01/5.29 ! [X2: real,B: real,N: nat] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( log @ B @ ( power_power_real @ X2 @ N ) )
% 5.01/5.29 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_nat_power
% 5.01/5.29 thf(fact_6617_Suc__nat__eq__nat__zadd1,axiom,
% 5.01/5.29 ! [Z: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( ( suc @ ( nat2 @ Z ) )
% 5.01/5.29 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % Suc_nat_eq_nat_zadd1
% 5.01/5.29 thf(fact_6618_nat__less__iff,axiom,
% 5.01/5.29 ! [W: int,M: nat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.01/5.29 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.01/5.29 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_less_iff
% 5.01/5.29 thf(fact_6619_nat__mult__distrib__neg,axiom,
% 5.01/5.29 ! [Z: int,Z6: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.01/5.29 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.01/5.29 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_mult_distrib_neg
% 5.01/5.29 thf(fact_6620_nat__abs__int__diff,axiom,
% 5.01/5.29 ! [A: nat,B: nat] :
% 5.01/5.29 ( ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.29 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.01/5.29 = ( minus_minus_nat @ B @ A ) ) )
% 5.01/5.29 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.01/5.29 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.01/5.29 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_abs_int_diff
% 5.01/5.29 thf(fact_6621_pi__half__neq__zero,axiom,
% 5.01/5.29 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.29 != zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_neq_zero
% 5.01/5.29 thf(fact_6622_pi__half__less__two,axiom,
% 5.01/5.29 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_less_two
% 5.01/5.29 thf(fact_6623_pi__half__le__two,axiom,
% 5.01/5.29 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_le_two
% 5.01/5.29 thf(fact_6624_real__le__lsqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_le_lsqrt
% 5.01/5.29 thf(fact_6625_real__sqrt__unique,axiom,
% 5.01/5.29 ! [Y: real,X2: real] :
% 5.01/5.29 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.29 = X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( sqrt @ X2 )
% 5.01/5.29 = Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_unique
% 5.01/5.29 thf(fact_6626_lemma__real__divide__sqrt__less,axiom,
% 5.01/5.29 ! [U: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ U )
% 5.01/5.29 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.01/5.29
% 5.01/5.29 % lemma_real_divide_sqrt_less
% 5.01/5.29 thf(fact_6627_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.29 = X2 )
% 5.01/5.29 => ( Y = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_eq_cancel
% 5.01/5.29 thf(fact_6628_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.29 = Y )
% 5.01/5.29 => ( X2 = zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_eq_cancel2
% 5.01/5.29 thf(fact_6629_real__sqrt__sum__squares__ge1,axiom,
% 5.01/5.29 ! [X2: real,Y: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_ge1
% 5.01/5.29 thf(fact_6630_real__sqrt__sum__squares__ge2,axiom,
% 5.01/5.29 ! [Y: real,X2: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_ge2
% 5.01/5.29 thf(fact_6631_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.01/5.29 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_triangle_ineq
% 5.01/5.29 thf(fact_6632_sqrt__ge__absD,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y ) )
% 5.01/5.29 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_ge_absD
% 5.01/5.29 thf(fact_6633_bit__nat__def,axiom,
% 5.01/5.29 ( bit_se1148574629649215175it_nat
% 5.01/5.29 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.29 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % bit_nat_def
% 5.01/5.29 thf(fact_6634_log2__of__power__eq,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( M
% 5.01/5.29 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 => ( ( semiri5074537144036343181t_real @ N )
% 5.01/5.29 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log2_of_power_eq
% 5.01/5.29 thf(fact_6635_log__of__power__less,axiom,
% 5.01/5.29 ! [M: nat,B: real,N: nat] :
% 5.01/5.29 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.29 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_of_power_less
% 5.01/5.29 thf(fact_6636_log__eq__div__ln__mult__log,axiom,
% 5.01/5.29 ! [A: real,B: real,X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.29 => ( ( A != one_one_real )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.29 => ( ( B != one_one_real )
% 5.01/5.29 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( log @ A @ X2 )
% 5.01/5.29 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_eq_div_ln_mult_log
% 5.01/5.29 thf(fact_6637_nat__dvd__iff,axiom,
% 5.01/5.29 ! [Z: int,M: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.01/5.29 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.01/5.29 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.29 => ( M = zero_zero_nat ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_dvd_iff
% 5.01/5.29 thf(fact_6638_pi__half__gt__zero,axiom,
% 5.01/5.29 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_gt_zero
% 5.01/5.29 thf(fact_6639_pi__half__ge__zero,axiom,
% 5.01/5.29 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % pi_half_ge_zero
% 5.01/5.29 thf(fact_6640_m2pi__less__pi,axiom,
% 5.01/5.29 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.01/5.29
% 5.01/5.29 % m2pi_less_pi
% 5.01/5.29 thf(fact_6641_arctan__ubound,axiom,
% 5.01/5.29 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_ubound
% 5.01/5.29 thf(fact_6642_arctan__one,axiom,
% 5.01/5.29 ( ( arctan @ one_one_real )
% 5.01/5.29 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_one
% 5.01/5.29 thf(fact_6643_real__less__lsqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ord_less_real @ ( sqrt @ X2 ) @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_less_lsqrt
% 5.01/5.29 thf(fact_6644_sqrt__sum__squares__le__sum,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_sum_squares_le_sum
% 5.01/5.29 thf(fact_6645_log__of__power__le,axiom,
% 5.01/5.29 ! [M: nat,B: real,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.01/5.29 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.29 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log_of_power_le
% 5.01/5.29 thf(fact_6646_real__sqrt__ge__abs1,axiom,
% 5.01/5.29 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_abs1
% 5.01/5.29 thf(fact_6647_real__sqrt__ge__abs2,axiom,
% 5.01/5.29 ! [Y: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_ge_abs2
% 5.01/5.29 thf(fact_6648_sqrt__sum__squares__le__sum__abs,axiom,
% 5.01/5.29 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_sum_squares_le_sum_abs
% 5.01/5.29 thf(fact_6649_ln__sqrt,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.01/5.29 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ln_sqrt
% 5.01/5.29 thf(fact_6650_sqrt__even__pow2,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.29 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_even_pow2
% 5.01/5.29 thf(fact_6651_minus__pi__half__less__zero,axiom,
% 5.01/5.29 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.01/5.29
% 5.01/5.29 % minus_pi_half_less_zero
% 5.01/5.29 thf(fact_6652_arctan__lbound,axiom,
% 5.01/5.29 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_lbound
% 5.01/5.29 thf(fact_6653_arctan__bounded,axiom,
% 5.01/5.29 ! [Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.01/5.29 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arctan_bounded
% 5.01/5.29 thf(fact_6654_and__nat__unfold,axiom,
% 5.01/5.29 ( bit_se727722235901077358nd_nat
% 5.01/5.29 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.29 ( if_nat
% 5.01/5.29 @ ( ( M3 = zero_zero_nat )
% 5.01/5.29 | ( N4 = zero_zero_nat ) )
% 5.01/5.29 @ zero_zero_nat
% 5.01/5.29 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_unfold
% 5.01/5.29 thf(fact_6655_arsinh__real__aux,axiom,
% 5.01/5.29 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arsinh_real_aux
% 5.01/5.29 thf(fact_6656_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.01/5.29 ! [X2: real,Y: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_mult_ge_zero
% 5.01/5.29 thf(fact_6657_real__sqrt__power__even,axiom,
% 5.01/5.29 ! [N: nat,X2: real] :
% 5.01/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.01/5.29 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_power_even
% 5.01/5.29 thf(fact_6658_arith__geo__mean__sqrt,axiom,
% 5.01/5.29 ! [X2: real,Y: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arith_geo_mean_sqrt
% 5.01/5.29 thf(fact_6659_less__log2__of__power,axiom,
% 5.01/5.29 ! [N: nat,M: nat] :
% 5.01/5.29 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.01/5.29 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % less_log2_of_power
% 5.01/5.29 thf(fact_6660_le__log2__of__power,axiom,
% 5.01/5.29 ! [N: nat,M: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.01/5.29 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % le_log2_of_power
% 5.01/5.29 thf(fact_6661_and__nat__rec,axiom,
% 5.01/5.29 ( bit_se727722235901077358nd_nat
% 5.01/5.29 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.29 ( plus_plus_nat
% 5.01/5.29 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.29 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.01/5.29 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.29 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % and_nat_rec
% 5.01/5.29 thf(fact_6662_even__nat__iff,axiom,
% 5.01/5.29 ! [K: int] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.29 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.01/5.29 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % even_nat_iff
% 5.01/5.29 thf(fact_6663_arsinh__real__def,axiom,
% 5.01/5.29 ( arsinh_real
% 5.01/5.29 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arsinh_real_def
% 5.01/5.29 thf(fact_6664_log2__of__power__less,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.29 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log2_of_power_less
% 5.01/5.29 thf(fact_6665_cos__x__y__le__one,axiom,
% 5.01/5.29 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % cos_x_y_le_one
% 5.01/5.29 thf(fact_6666_real__sqrt__sum__squares__less,axiom,
% 5.01/5.29 ! [X2: real,U: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.29 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.29 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % real_sqrt_sum_squares_less
% 5.01/5.29 thf(fact_6667_arcosh__real__def,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.29 => ( ( arcosh_real @ X2 )
% 5.01/5.29 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % arcosh_real_def
% 5.01/5.29 thf(fact_6668_sqrt__sum__squares__half__less,axiom,
% 5.01/5.29 ! [X2: real,U: real,Y: real] :
% 5.01/5.29 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.29 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sqrt_sum_squares_half_less
% 5.01/5.29 thf(fact_6669_log2__of__power__le,axiom,
% 5.01/5.29 ! [M: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.29 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % log2_of_power_le
% 5.01/5.29 thf(fact_6670_machin__Euler,axiom,
% 5.01/5.29 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.01/5.29 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % machin_Euler
% 5.01/5.29 thf(fact_6671_sin__cos__npi,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_cos_npi
% 5.01/5.29 thf(fact_6672_ceiling__log__nat__eq__powr__iff,axiom,
% 5.01/5.29 ! [B: nat,K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.29 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.01/5.29 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.01/5.29 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_log_nat_eq_powr_iff
% 5.01/5.29 thf(fact_6673_cos__pi__eq__zero,axiom,
% 5.01/5.29 ! [M: nat] :
% 5.01/5.29 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % cos_pi_eq_zero
% 5.01/5.29 thf(fact_6674_ceiling__log__nat__eq__if,axiom,
% 5.01/5.29 ! [B: nat,N: nat,K: nat] :
% 5.01/5.29 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.01/5.29 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.01/5.29 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.01/5.29 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_log_nat_eq_if
% 5.01/5.29 thf(fact_6675_ceiling__log2__div2,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.29 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_log2_div2
% 5.01/5.29 thf(fact_6676_floor__log__nat__eq__powr__iff,axiom,
% 5.01/5.29 ! [B: nat,K: nat,N: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.01/5.29 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.29 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.29 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.01/5.29 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_log_nat_eq_powr_iff
% 5.01/5.29 thf(fact_6677_sin__zero,axiom,
% 5.01/5.29 ( ( sin_complex @ zero_zero_complex )
% 5.01/5.29 = zero_zero_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sin_zero
% 5.01/5.29 thf(fact_6678_sin__zero,axiom,
% 5.01/5.29 ( ( sin_real @ zero_zero_real )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_zero
% 5.01/5.29 thf(fact_6679_cos__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( cos_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.29 = ( cos_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_minus
% 5.01/5.29 thf(fact_6680_cos__minus,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( cos_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.29 = ( cos_complex @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_minus
% 5.01/5.29 thf(fact_6681_sin__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sin_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_minus
% 5.01/5.29 thf(fact_6682_sin__minus,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( sin_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.29 = ( uminus1482373934393186551omplex @ ( sin_complex @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_minus
% 5.01/5.29 thf(fact_6683_cos__zero,axiom,
% 5.01/5.29 ( ( cos_complex @ zero_zero_complex )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % cos_zero
% 5.01/5.29 thf(fact_6684_cos__zero,axiom,
% 5.01/5.29 ( ( cos_real @ zero_zero_real )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % cos_zero
% 5.01/5.29 thf(fact_6685_floor__zero,axiom,
% 5.01/5.29 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % floor_zero
% 5.01/5.29 thf(fact_6686_floor__zero,axiom,
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % floor_zero
% 5.01/5.29 thf(fact_6687_floor__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.01/5.29 = ( numeral_numeral_int @ V ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_numeral
% 5.01/5.29 thf(fact_6688_floor__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.01/5.29 = ( numeral_numeral_int @ V ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_numeral
% 5.01/5.29 thf(fact_6689_ceiling__zero,axiom,
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_zero
% 5.01/5.29 thf(fact_6690_ceiling__zero,axiom,
% 5.01/5.29 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 5.01/5.29 = zero_zero_int ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_zero
% 5.01/5.29 thf(fact_6691_floor__one,axiom,
% 5.01/5.29 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % floor_one
% 5.01/5.29 thf(fact_6692_floor__one,axiom,
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % floor_one
% 5.01/5.29 thf(fact_6693_ceiling__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.01/5.29 = ( numeral_numeral_int @ V ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_numeral
% 5.01/5.29 thf(fact_6694_ceiling__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.01/5.29 = ( numeral_numeral_int @ V ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_numeral
% 5.01/5.29 thf(fact_6695_ceiling__one,axiom,
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_one
% 5.01/5.29 thf(fact_6696_ceiling__one,axiom,
% 5.01/5.29 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.01/5.29 = one_one_int ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_one
% 5.01/5.29 thf(fact_6697_sin__pi,axiom,
% 5.01/5.29 ( ( sin_real @ pi )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_pi
% 5.01/5.29 thf(fact_6698_floor__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_of_nat
% 5.01/5.29 thf(fact_6699_floor__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_of_nat
% 5.01/5.29 thf(fact_6700_ceiling__of__nat,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.29 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_of_nat
% 5.01/5.29 thf(fact_6701_sin__pi__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sin_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.01/5.29 = ( sin_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_pi_minus
% 5.01/5.29 thf(fact_6702_cos__pi,axiom,
% 5.01/5.29 ( ( cos_real @ pi )
% 5.01/5.29 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_pi
% 5.01/5.29 thf(fact_6703_cos__periodic__pi2,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( cos_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_periodic_pi2
% 5.01/5.29 thf(fact_6704_cos__periodic__pi,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( cos_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_periodic_pi
% 5.01/5.29 thf(fact_6705_sin__periodic__pi2,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sin_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_periodic_pi2
% 5.01/5.29 thf(fact_6706_sin__periodic__pi,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sin_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_periodic_pi
% 5.01/5.29 thf(fact_6707_cos__pi__minus,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( cos_real @ ( minus_minus_real @ pi @ X2 ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_pi_minus
% 5.01/5.29 thf(fact_6708_cos__minus__pi,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( cos_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % cos_minus_pi
% 5.01/5.29 thf(fact_6709_sin__minus__pi,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( sin_real @ ( minus_minus_real @ X2 @ pi ) )
% 5.01/5.29 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % sin_minus_pi
% 5.01/5.29 thf(fact_6710_zero__le__floor,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_floor
% 5.01/5.29 thf(fact_6711_zero__le__floor,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_floor
% 5.01/5.29 thf(fact_6712_sin__cos__squared__add3,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ X2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ X2 ) ) )
% 5.01/5.29 = one_one_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_cos_squared_add3
% 5.01/5.29 thf(fact_6713_sin__cos__squared__add3,axiom,
% 5.01/5.29 ! [X2: complex] :
% 5.01/5.29 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ X2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ X2 ) ) )
% 5.01/5.29 = one_one_complex ) ).
% 5.01/5.29
% 5.01/5.29 % sin_cos_squared_add3
% 5.01/5.29 thf(fact_6714_floor__less__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_zero
% 5.01/5.29 thf(fact_6715_floor__less__zero,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_zero
% 5.01/5.29 thf(fact_6716_numeral__le__floor,axiom,
% 5.01/5.29 ! [V: num,X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_le_floor
% 5.01/5.29 thf(fact_6717_numeral__le__floor,axiom,
% 5.01/5.29 ! [V: num,X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_le_floor
% 5.01/5.29 thf(fact_6718_zero__less__floor,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_floor
% 5.01/5.29 thf(fact_6719_zero__less__floor,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_floor
% 5.01/5.29 thf(fact_6720_floor__le__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_zero
% 5.01/5.29 thf(fact_6721_floor__le__zero,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_zero
% 5.01/5.29 thf(fact_6722_ceiling__le__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_zero
% 5.01/5.29 thf(fact_6723_ceiling__le__zero,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_zero
% 5.01/5.29 thf(fact_6724_floor__less__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_numeral
% 5.01/5.29 thf(fact_6725_floor__less__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_numeral
% 5.01/5.29 thf(fact_6726_zero__less__ceiling,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_ceiling
% 5.01/5.29 thf(fact_6727_zero__less__ceiling,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_less_ceiling
% 5.01/5.29 thf(fact_6728_one__le__floor,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_floor
% 5.01/5.29 thf(fact_6729_one__le__floor,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_floor
% 5.01/5.29 thf(fact_6730_ceiling__le__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_numeral
% 5.01/5.29 thf(fact_6731_ceiling__le__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_numeral
% 5.01/5.29 thf(fact_6732_floor__less__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_one
% 5.01/5.29 thf(fact_6733_floor__less__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_less_one
% 5.01/5.29 thf(fact_6734_ceiling__less__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_one
% 5.01/5.29 thf(fact_6735_ceiling__less__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_one
% 5.01/5.29 thf(fact_6736_one__le__ceiling,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_ceiling
% 5.01/5.29 thf(fact_6737_one__le__ceiling,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_le_ceiling
% 5.01/5.29 thf(fact_6738_numeral__less__ceiling,axiom,
% 5.01/5.29 ! [V: num,X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_less_ceiling
% 5.01/5.29 thf(fact_6739_numeral__less__ceiling,axiom,
% 5.01/5.29 ! [V: num,X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_less_ceiling
% 5.01/5.29 thf(fact_6740_floor__neg__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_neg_numeral
% 5.01/5.29 thf(fact_6741_floor__neg__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_neg_numeral
% 5.01/5.29 thf(fact_6742_ceiling__le__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_one
% 5.01/5.29 thf(fact_6743_ceiling__le__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_le_one
% 5.01/5.29 thf(fact_6744_one__less__ceiling,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_ceiling
% 5.01/5.29 thf(fact_6745_one__less__ceiling,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_ceiling
% 5.01/5.29 thf(fact_6746_ceiling__add__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_add_numeral
% 5.01/5.29 thf(fact_6747_ceiling__add__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.01/5.29 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_add_numeral
% 5.01/5.29 thf(fact_6748_floor__diff__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_diff_numeral
% 5.01/5.29 thf(fact_6749_floor__diff__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_diff_numeral
% 5.01/5.29 thf(fact_6750_ceiling__neg__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_neg_numeral
% 5.01/5.29 thf(fact_6751_ceiling__neg__numeral,axiom,
% 5.01/5.29 ! [V: num] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_neg_numeral
% 5.01/5.29 thf(fact_6752_ceiling__add__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.01/5.29 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_add_one
% 5.01/5.29 thf(fact_6753_ceiling__add__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.01/5.29 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_add_one
% 5.01/5.29 thf(fact_6754_floor__diff__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_diff_one
% 5.01/5.29 thf(fact_6755_floor__diff__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_diff_one
% 5.01/5.29 thf(fact_6756_ceiling__diff__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_diff_numeral
% 5.01/5.29 thf(fact_6757_ceiling__diff__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_diff_numeral
% 5.01/5.29 thf(fact_6758_ceiling__diff__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_diff_one
% 5.01/5.29 thf(fact_6759_ceiling__diff__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.01/5.29 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_diff_one
% 5.01/5.29 thf(fact_6760_floor__numeral__power,axiom,
% 5.01/5.29 ! [X2: num,N: nat] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.01/5.29 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_numeral_power
% 5.01/5.29 thf(fact_6761_floor__numeral__power,axiom,
% 5.01/5.29 ! [X2: num,N: nat] :
% 5.01/5.29 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.01/5.29 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_numeral_power
% 5.01/5.29 thf(fact_6762_ceiling__numeral__power,axiom,
% 5.01/5.29 ! [X2: num,N: nat] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.01/5.29 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_numeral_power
% 5.01/5.29 thf(fact_6763_ceiling__numeral__power,axiom,
% 5.01/5.29 ! [X2: num,N: nat] :
% 5.01/5.29 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.01/5.29 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_numeral_power
% 5.01/5.29 thf(fact_6764_sin__npi,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_npi
% 5.01/5.29 thf(fact_6765_sin__npi2,axiom,
% 5.01/5.29 ! [N: nat] :
% 5.01/5.29 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.29 = zero_zero_real ) ).
% 5.01/5.29
% 5.01/5.29 % sin_npi2
% 5.01/5.29 thf(fact_6766_floor__divide__eq__div__numeral,axiom,
% 5.01/5.29 ! [A: num,B: num] :
% 5.01/5.29 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.01/5.29 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_divide_eq_div_numeral
% 5.01/5.29 thf(fact_6767_nat__ceiling__le__eq,axiom,
% 5.01/5.29 ! [X2: real,A: nat] :
% 5.01/5.29 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % nat_ceiling_le_eq
% 5.01/5.29 thf(fact_6768_ceiling__less__zero,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_zero
% 5.01/5.29 thf(fact_6769_ceiling__less__zero,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_zero
% 5.01/5.29 thf(fact_6770_zero__le__ceiling,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.29 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_ceiling
% 5.01/5.29 thf(fact_6771_zero__le__ceiling,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % zero_le_ceiling
% 5.01/5.29 thf(fact_6772_ceiling__divide__eq__div__numeral,axiom,
% 5.01/5.29 ! [A: num,B: num] :
% 5.01/5.29 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.01/5.29 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_divide_eq_div_numeral
% 5.01/5.29 thf(fact_6773_numeral__less__floor,axiom,
% 5.01/5.29 ! [V: num,X2: real] :
% 5.01/5.29 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_less_floor
% 5.01/5.29 thf(fact_6774_numeral__less__floor,axiom,
% 5.01/5.29 ! [V: num,X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % numeral_less_floor
% 5.01/5.29 thf(fact_6775_floor__le__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_numeral
% 5.01/5.29 thf(fact_6776_floor__le__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_numeral
% 5.01/5.29 thf(fact_6777_one__less__floor,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_floor
% 5.01/5.29 thf(fact_6778_one__less__floor,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.29 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.01/5.29
% 5.01/5.29 % one_less_floor
% 5.01/5.29 thf(fact_6779_floor__le__one,axiom,
% 5.01/5.29 ! [X2: real] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_one
% 5.01/5.29 thf(fact_6780_floor__le__one,axiom,
% 5.01/5.29 ! [X2: rat] :
% 5.01/5.29 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.01/5.29 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % floor_le_one
% 5.01/5.29 thf(fact_6781_ceiling__less__numeral,axiom,
% 5.01/5.29 ! [X2: real,V: num] :
% 5.01/5.29 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_numeral
% 5.01/5.29 thf(fact_6782_ceiling__less__numeral,axiom,
% 5.01/5.29 ! [X2: rat,V: num] :
% 5.01/5.29 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.01/5.29 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.01/5.29
% 5.01/5.29 % ceiling_less_numeral
% 5.01/5.30 thf(fact_6783_numeral__le__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_le_ceiling
% 5.01/5.30 thf(fact_6784_numeral__le__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_le_ceiling
% 5.01/5.30 thf(fact_6785_neg__numeral__le__floor,axiom,
% 5.01/5.30 ! [V: num,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_le_floor
% 5.01/5.30 thf(fact_6786_neg__numeral__le__floor,axiom,
% 5.01/5.30 ! [V: num,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_le_floor
% 5.01/5.30 thf(fact_6787_floor__less__neg__numeral,axiom,
% 5.01/5.30 ! [X2: real,V: num] :
% 5.01/5.30 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_neg_numeral
% 5.01/5.30 thf(fact_6788_floor__less__neg__numeral,axiom,
% 5.01/5.30 ! [X2: rat,V: num] :
% 5.01/5.30 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_neg_numeral
% 5.01/5.30 thf(fact_6789_ceiling__le__neg__numeral,axiom,
% 5.01/5.30 ! [X2: real,V: num] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le_neg_numeral
% 5.01/5.30 thf(fact_6790_ceiling__le__neg__numeral,axiom,
% 5.01/5.30 ! [X2: rat,V: num] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le_neg_numeral
% 5.01/5.30 thf(fact_6791_neg__numeral__less__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: real] :
% 5.01/5.30 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_less_ceiling
% 5.01/5.30 thf(fact_6792_neg__numeral__less__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: rat] :
% 5.01/5.30 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_less_ceiling
% 5.01/5.30 thf(fact_6793_cos__pi__half,axiom,
% 5.01/5.30 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_pi_half
% 5.01/5.30 thf(fact_6794_sin__two__pi,axiom,
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_two_pi
% 5.01/5.30 thf(fact_6795_sin__pi__half,axiom,
% 5.01/5.30 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_pi_half
% 5.01/5.30 thf(fact_6796_cos__two__pi,axiom,
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_two_pi
% 5.01/5.30 thf(fact_6797_cos__periodic,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.30 = ( cos_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_periodic
% 5.01/5.30 thf(fact_6798_sin__periodic,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.30 = ( sin_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_periodic
% 5.01/5.30 thf(fact_6799_cos__2pi__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.01/5.30 = ( cos_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_2pi_minus
% 5.01/5.30 thf(fact_6800_cos__npi,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.01/5.30 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_npi
% 5.01/5.30 thf(fact_6801_cos__npi2,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.30 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_npi2
% 5.01/5.30 thf(fact_6802_floor__one__divide__eq__div__numeral,axiom,
% 5.01/5.30 ! [B: num] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.01/5.30 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_one_divide_eq_div_numeral
% 5.01/5.30 thf(fact_6803_floor__minus__divide__eq__div__numeral,axiom,
% 5.01/5.30 ! [A: num,B: num] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.01/5.30 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_minus_divide_eq_div_numeral
% 5.01/5.30 thf(fact_6804_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.01/5.30 ! [A: num,B: num] :
% 5.01/5.30 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_minus_divide_eq_div_numeral
% 5.01/5.30 thf(fact_6805_sin__cos__squared__add2,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_squared_add2
% 5.01/5.30 thf(fact_6806_sin__cos__squared__add2,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_squared_add2
% 5.01/5.30 thf(fact_6807_sin__cos__squared__add,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_squared_add
% 5.01/5.30 thf(fact_6808_sin__cos__squared__add,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_squared_add
% 5.01/5.30 thf(fact_6809_sin__2npi,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_2npi
% 5.01/5.30 thf(fact_6810_cos__2npi,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_2npi
% 5.01/5.30 thf(fact_6811_sin__2pi__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_2pi_minus
% 5.01/5.30 thf(fact_6812_neg__numeral__less__floor,axiom,
% 5.01/5.30 ! [V: num,X2: real] :
% 5.01/5.30 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_less_floor
% 5.01/5.30 thf(fact_6813_neg__numeral__less__floor,axiom,
% 5.01/5.30 ! [V: num,X2: rat] :
% 5.01/5.30 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_less_floor
% 5.01/5.30 thf(fact_6814_floor__le__neg__numeral,axiom,
% 5.01/5.30 ! [X2: real,V: num] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_neg_numeral
% 5.01/5.30 thf(fact_6815_floor__le__neg__numeral,axiom,
% 5.01/5.30 ! [X2: rat,V: num] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_neg_numeral
% 5.01/5.30 thf(fact_6816_ceiling__less__neg__numeral,axiom,
% 5.01/5.30 ! [X2: real,V: num] :
% 5.01/5.30 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_neg_numeral
% 5.01/5.30 thf(fact_6817_ceiling__less__neg__numeral,axiom,
% 5.01/5.30 ! [X2: rat,V: num] :
% 5.01/5.30 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.01/5.30 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_neg_numeral
% 5.01/5.30 thf(fact_6818_neg__numeral__le__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_le_ceiling
% 5.01/5.30 thf(fact_6819_neg__numeral__le__ceiling,axiom,
% 5.01/5.30 ! [V: num,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_le_ceiling
% 5.01/5.30 thf(fact_6820_cos__3over2__pi,axiom,
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_3over2_pi
% 5.01/5.30 thf(fact_6821_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.01/5.30 ! [B: num] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.01/5.30 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_minus_one_divide_eq_div_numeral
% 5.01/5.30 thf(fact_6822_sin__3over2__pi,axiom,
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.01/5.30 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_3over2_pi
% 5.01/5.30 thf(fact_6823_floor__le__ceiling,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_ceiling
% 5.01/5.30 thf(fact_6824_floor__le__ceiling,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_ceiling
% 5.01/5.30 thf(fact_6825_polar__Ex,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ? [R4: real,A3: real] :
% 5.01/5.30 ( ( X2
% 5.01/5.30 = ( times_times_real @ R4 @ ( cos_real @ A3 ) ) )
% 5.01/5.30 & ( Y
% 5.01/5.30 = ( times_times_real @ R4 @ ( sin_real @ A3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % polar_Ex
% 5.01/5.30 thf(fact_6826_ceiling__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( archim6058952711729229775r_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_minus
% 5.01/5.30 thf(fact_6827_ceiling__minus,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_minus
% 5.01/5.30 thf(fact_6828_floor__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_minus
% 5.01/5.30 thf(fact_6829_floor__minus,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_minus
% 5.01/5.30 thf(fact_6830_ceiling__def,axiom,
% 5.01/5.30 ( archim7802044766580827645g_real
% 5.01/5.30 = ( ^ [X3: real] : ( uminus_uminus_int @ ( archim6058952711729229775r_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_def
% 5.01/5.30 thf(fact_6831_ceiling__def,axiom,
% 5.01/5.30 ( archim2889992004027027881ng_rat
% 5.01/5.30 = ( ^ [X3: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X3 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_def
% 5.01/5.30 thf(fact_6832_sin__diff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( sin_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_diff
% 5.01/5.30 thf(fact_6833_sin__diff,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( sin_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_complex @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_diff
% 5.01/5.30 thf(fact_6834_sin__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( sin_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_add
% 5.01/5.30 thf(fact_6835_sin__add,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( sin_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_add
% 5.01/5.30 thf(fact_6836_cos__one__sin__zero,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 = one_one_complex )
% 5.01/5.30 => ( ( sin_complex @ X2 )
% 5.01/5.30 = zero_zero_complex ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_one_sin_zero
% 5.01/5.30 thf(fact_6837_cos__one__sin__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_one_sin_zero
% 5.01/5.30 thf(fact_6838_cos__diff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( cos_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_diff
% 5.01/5.30 thf(fact_6839_cos__diff,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_diff
% 5.01/5.30 thf(fact_6840_cos__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( cos_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_add
% 5.01/5.30 thf(fact_6841_cos__add,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_add
% 5.01/5.30 thf(fact_6842_sin__zero__norm__cos__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X2 ) )
% 5.01/5.30 = one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_norm_cos_one
% 5.01/5.30 thf(fact_6843_sin__zero__norm__cos__one,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( ( sin_complex @ X2 )
% 5.01/5.30 = zero_zero_complex )
% 5.01/5.30 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X2 ) )
% 5.01/5.30 = one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_norm_cos_one
% 5.01/5.30 thf(fact_6844_ceiling__diff__floor__le__1,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) @ one_one_int ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_diff_floor_le_1
% 5.01/5.30 thf(fact_6845_ceiling__diff__floor__le__1,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) @ one_one_int ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_diff_floor_le_1
% 5.01/5.30 thf(fact_6846_sin__zero__abs__cos__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 => ( ( abs_abs_real @ ( cos_real @ X2 ) )
% 5.01/5.30 = one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_abs_cos_one
% 5.01/5.30 thf(fact_6847_sin__double,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X2 ) ) @ ( cos_complex @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_double
% 5.01/5.30 thf(fact_6848_sin__double,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X2 ) ) @ ( cos_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_double
% 5.01/5.30 thf(fact_6849_sincos__principal__value,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [Y3: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.01/5.30 & ( ord_less_eq_real @ Y3 @ pi )
% 5.01/5.30 & ( ( sin_real @ Y3 )
% 5.01/5.30 = ( sin_real @ X2 ) )
% 5.01/5.30 & ( ( cos_real @ Y3 )
% 5.01/5.30 = ( cos_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sincos_principal_value
% 5.01/5.30 thf(fact_6850_floor__mono,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_mono
% 5.01/5.30 thf(fact_6851_floor__mono,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_mono
% 5.01/5.30 thf(fact_6852_floor__less__cancel,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) )
% 5.01/5.30 => ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_cancel
% 5.01/5.30 thf(fact_6853_floor__less__cancel,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] :
% 5.01/5.30 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 5.01/5.30 => ( ord_less_rat @ X2 @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_cancel
% 5.01/5.30 thf(fact_6854_ceiling__mono,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_mono
% 5.01/5.30 thf(fact_6855_ceiling__mono,axiom,
% 5.01/5.30 ! [Y: rat,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_mono
% 5.01/5.30 thf(fact_6856_sin__x__le__x,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_x_le_x
% 5.01/5.30 thf(fact_6857_ceiling__less__cancel,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] :
% 5.01/5.30 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 5.01/5.30 => ( ord_less_rat @ X2 @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_cancel
% 5.01/5.30 thf(fact_6858_ceiling__less__cancel,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y ) )
% 5.01/5.30 => ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_cancel
% 5.01/5.30 thf(fact_6859_sin__le__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( sin_real @ X2 ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_le_one
% 5.01/5.30 thf(fact_6860_cos__le__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( cos_real @ X2 ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_le_one
% 5.01/5.30 thf(fact_6861_abs__sin__x__le__abs__x,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ ( abs_abs_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % abs_sin_x_le_abs_x
% 5.01/5.30 thf(fact_6862_cos__arctan__not__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( arctan @ X2 ) )
% 5.01/5.30 != zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arctan_not_zero
% 5.01/5.30 thf(fact_6863_sin__cos__le1,axiom,
% 5.01/5.30 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_le1
% 5.01/5.30 thf(fact_6864_sin__squared__eq,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.30 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_squared_eq
% 5.01/5.30 thf(fact_6865_sin__squared__eq,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.30 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_squared_eq
% 5.01/5.30 thf(fact_6866_cos__squared__eq,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.30 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_squared_eq
% 5.01/5.30 thf(fact_6867_cos__squared__eq,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.30 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_squared_eq
% 5.01/5.30 thf(fact_6868_le__floor__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_floor_add
% 5.01/5.30 thf(fact_6869_le__floor__add,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_floor_add
% 5.01/5.30 thf(fact_6870_of__nat__ceiling,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_eq_real @ R @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_ceiling
% 5.01/5.30 thf(fact_6871_of__nat__ceiling,axiom,
% 5.01/5.30 ! [R: rat] : ( ord_less_eq_rat @ R @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_ceiling
% 5.01/5.30 thf(fact_6872_sin__gt__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ pi )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_gt_zero
% 5.01/5.30 thf(fact_6873_sin__x__ge__neg__x,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ ( sin_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_x_ge_neg_x
% 5.01/5.30 thf(fact_6874_sin__ge__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_ge_zero
% 5.01/5.30 thf(fact_6875_real__nat__ceiling__ge,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_nat_ceiling_ge
% 5.01/5.30 thf(fact_6876_sin__ge__minus__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_ge_minus_one
% 5.01/5.30 thf(fact_6877_ceiling__add__le,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_add_le
% 5.01/5.30 thf(fact_6878_ceiling__add__le,axiom,
% 5.01/5.30 ! [X2: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_add_le
% 5.01/5.30 thf(fact_6879_cos__inj__pi,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ pi )
% 5.01/5.30 => ( ( ( cos_real @ X2 )
% 5.01/5.30 = ( cos_real @ Y ) )
% 5.01/5.30 => ( X2 = Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_inj_pi
% 5.01/5.30 thf(fact_6880_cos__mono__le__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ pi )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ Y @ X2 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_mono_le_eq
% 5.01/5.30 thf(fact_6881_cos__monotone__0__pi__le,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ord_less_eq_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_monotone_0_pi_le
% 5.01/5.30 thf(fact_6882_cos__ge__minus__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_ge_minus_one
% 5.01/5.30 thf(fact_6883_abs__sin__le__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % abs_sin_le_one
% 5.01/5.30 thf(fact_6884_abs__cos__le__one,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X2 ) ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % abs_cos_le_one
% 5.01/5.30 thf(fact_6885_sin__times__sin,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_times_sin
% 5.01/5.30 thf(fact_6886_sin__times__sin,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.01/5.30 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_times_sin
% 5.01/5.30 thf(fact_6887_sin__times__cos,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_times_cos
% 5.01/5.30 thf(fact_6888_sin__times__cos,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.01/5.30 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_times_cos
% 5.01/5.30 thf(fact_6889_cos__times__sin,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_times_sin
% 5.01/5.30 thf(fact_6890_cos__times__sin,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.01/5.30 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_times_sin
% 5.01/5.30 thf(fact_6891_sin__plus__sin,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.01/5.30 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_plus_sin
% 5.01/5.30 thf(fact_6892_sin__plus__sin,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_plus_sin
% 5.01/5.30 thf(fact_6893_sin__diff__sin,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.01/5.30 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_diff_sin
% 5.01/5.30 thf(fact_6894_sin__diff__sin,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_diff_sin
% 5.01/5.30 thf(fact_6895_cos__diff__cos,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.01/5.30 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_diff_cos
% 5.01/5.30 thf(fact_6896_cos__diff__cos,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_diff_cos
% 5.01/5.30 thf(fact_6897_cos__double,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double
% 5.01/5.30 thf(fact_6898_cos__double,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double
% 5.01/5.30 thf(fact_6899_cos__double__sin,axiom,
% 5.01/5.30 ! [W: complex] :
% 5.01/5.30 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.01/5.30 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double_sin
% 5.01/5.30 thf(fact_6900_cos__double__sin,axiom,
% 5.01/5.30 ! [W: real] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.01/5.30 = ( minus_minus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( sin_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double_sin
% 5.01/5.30 thf(fact_6901_of__nat__floor,axiom,
% 5.01/5.30 ! [R: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.01/5.30 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R ) ) ) @ R ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_floor
% 5.01/5.30 thf(fact_6902_of__nat__floor,axiom,
% 5.01/5.30 ! [R: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 5.01/5.30 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R ) ) ) @ R ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_floor
% 5.01/5.30 thf(fact_6903_one__add__floor,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.01/5.30 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % one_add_floor
% 5.01/5.30 thf(fact_6904_one__add__floor,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.01/5.30 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % one_add_floor
% 5.01/5.30 thf(fact_6905_le__mult__nat__floor,axiom,
% 5.01/5.30 ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_mult_nat_floor
% 5.01/5.30 thf(fact_6906_le__mult__nat__floor,axiom,
% 5.01/5.30 ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_mult_nat_floor
% 5.01/5.30 thf(fact_6907_floor__divide__of__nat__eq,axiom,
% 5.01/5.30 ! [M: nat,N: nat] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.30 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_of_nat_eq
% 5.01/5.30 thf(fact_6908_floor__divide__of__nat__eq,axiom,
% 5.01/5.30 ! [M: nat,N: nat] :
% 5.01/5.30 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.01/5.30 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_of_nat_eq
% 5.01/5.30 thf(fact_6909_nat__floor__neg,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = zero_zero_nat ) ) ).
% 5.01/5.30
% 5.01/5.30 % nat_floor_neg
% 5.01/5.30 thf(fact_6910_cos__two__neq__zero,axiom,
% 5.01/5.30 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.30 != zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_two_neq_zero
% 5.01/5.30 thf(fact_6911_floor__eq3,axiom,
% 5.01/5.30 ! [N: nat,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.01/5.30 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq3
% 5.01/5.30 thf(fact_6912_le__nat__floor,axiom,
% 5.01/5.30 ! [X2: nat,A: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A )
% 5.01/5.30 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_nat_floor
% 5.01/5.30 thf(fact_6913_cos__mono__less__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ pi )
% 5.01/5.30 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) )
% 5.01/5.30 = ( ord_less_real @ Y @ X2 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_mono_less_eq
% 5.01/5.30 thf(fact_6914_cos__monotone__0__pi,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_monotone_0_pi
% 5.01/5.30 thf(fact_6915_sin__eq__0__pi,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ pi )
% 5.01/5.30 => ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_eq_0_pi
% 5.01/5.30 thf(fact_6916_sin__zero__pi__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ pi )
% 5.01/5.30 => ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( X2 = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_pi_iff
% 5.01/5.30 thf(fact_6917_cos__monotone__minus__pi__0_H,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_monotone_minus_pi_0'
% 5.01/5.30 thf(fact_6918_sincos__total__pi,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ? [T3: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.30 & ( ord_less_eq_real @ T3 @ pi )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( cos_real @ T3 ) )
% 5.01/5.30 & ( Y
% 5.01/5.30 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sincos_total_pi
% 5.01/5.30 thf(fact_6919_sin__cos__sqrt,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.01/5.30 => ( ( sin_real @ X2 )
% 5.01/5.30 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_sqrt
% 5.01/5.30 thf(fact_6920_sin__expansion__lemma,axiom,
% 5.01/5.30 ! [X2: real,M: nat] :
% 5.01/5.30 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_expansion_lemma
% 5.01/5.30 thf(fact_6921_le__mult__floor,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_mult_floor
% 5.01/5.30 thf(fact_6922_le__mult__floor,axiom,
% 5.01/5.30 ! [A: rat,B: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.30 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_mult_floor
% 5.01/5.30 thf(fact_6923_cos__expansion__lemma,axiom,
% 5.01/5.30 ! [X2: real,M: nat] :
% 5.01/5.30 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_expansion_lemma
% 5.01/5.30 thf(fact_6924_sin__gt__zero__02,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_gt_zero_02
% 5.01/5.30 thf(fact_6925_mult__ceiling__le,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_ceiling_le
% 5.01/5.30 thf(fact_6926_mult__ceiling__le,axiom,
% 5.01/5.30 ! [A: rat,B: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.30 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_ceiling_le
% 5.01/5.30 thf(fact_6927_floor__eq4,axiom,
% 5.01/5.30 ! [N: nat,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.01/5.30 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq4
% 5.01/5.30 thf(fact_6928_cos__two__less__zero,axiom,
% 5.01/5.30 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.01/5.30
% 5.01/5.30 % cos_two_less_zero
% 5.01/5.30 thf(fact_6929_cos__two__le__zero,axiom,
% 5.01/5.30 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.01/5.30
% 5.01/5.30 % cos_two_le_zero
% 5.01/5.30 thf(fact_6930_cos__is__zero,axiom,
% 5.01/5.30 ? [X4: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.01/5.30 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.30 & ( ( cos_real @ X4 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 & ! [Y4: real] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.01/5.30 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.30 & ( ( cos_real @ Y4 )
% 5.01/5.30 = zero_zero_real ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_is_zero
% 5.01/5.30 thf(fact_6931_cos__monotone__minus__pi__0,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_monotone_minus_pi_0
% 5.01/5.30 thf(fact_6932_cos__total,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ? [X4: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.01/5.30 & ( ord_less_eq_real @ X4 @ pi )
% 5.01/5.30 & ( ( cos_real @ X4 )
% 5.01/5.30 = Y )
% 5.01/5.30 & ! [Y4: real] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.01/5.30 & ( ord_less_eq_real @ Y4 @ pi )
% 5.01/5.30 & ( ( cos_real @ Y4 )
% 5.01/5.30 = Y ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_total
% 5.01/5.30 thf(fact_6933_sincos__total__pi__half,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ? [T3: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.30 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( cos_real @ T3 ) )
% 5.01/5.30 & ( Y
% 5.01/5.30 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sincos_total_pi_half
% 5.01/5.30 thf(fact_6934_sincos__total__2pi__le,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ? [T3: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.30 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( cos_real @ T3 ) )
% 5.01/5.30 & ( Y
% 5.01/5.30 = ( sin_real @ T3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sincos_total_2pi_le
% 5.01/5.30 thf(fact_6935_sincos__total__2pi,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ~ ! [T3: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.30 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 => ( ( X2
% 5.01/5.30 = ( cos_real @ T3 ) )
% 5.01/5.30 => ( Y
% 5.01/5.30 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sincos_total_2pi
% 5.01/5.30 thf(fact_6936_sin__pi__divide__n__ge__0,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( N != zero_zero_nat )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_pi_divide_n_ge_0
% 5.01/5.30 thf(fact_6937_sin__45,axiom,
% 5.01/5.30 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_45
% 5.01/5.30 thf(fact_6938_cos__45,axiom,
% 5.01/5.30 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_45
% 5.01/5.30 thf(fact_6939_cos__times__cos,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_times_cos
% 5.01/5.30 thf(fact_6940_cos__times__cos,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.01/5.30 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_times_cos
% 5.01/5.30 thf(fact_6941_cos__plus__cos,axiom,
% 5.01/5.30 ! [W: complex,Z: complex] :
% 5.01/5.30 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.01/5.30 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_plus_cos
% 5.01/5.30 thf(fact_6942_cos__plus__cos,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_plus_cos
% 5.01/5.30 thf(fact_6943_sin__gt__zero2,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_gt_zero2
% 5.01/5.30 thf(fact_6944_sin__lt__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ pi @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_lt_zero
% 5.01/5.30 thf(fact_6945_cos__double__less__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.30 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double_less_one
% 5.01/5.30 thf(fact_6946_sin__30,axiom,
% 5.01/5.30 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_30
% 5.01/5.30 thf(fact_6947_cos__gt__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_gt_zero
% 5.01/5.30 thf(fact_6948_sin__monotone__2pi__le,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_monotone_2pi_le
% 5.01/5.30 thf(fact_6949_sin__mono__le__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_mono_le_eq
% 5.01/5.30 thf(fact_6950_sin__inj__pi,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ( sin_real @ X2 )
% 5.01/5.30 = ( sin_real @ Y ) )
% 5.01/5.30 => ( X2 = Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_inj_pi
% 5.01/5.30 thf(fact_6951_cos__60,axiom,
% 5.01/5.30 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_60
% 5.01/5.30 thf(fact_6952_sin__60,axiom,
% 5.01/5.30 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_60
% 5.01/5.30 thf(fact_6953_cos__30,axiom,
% 5.01/5.30 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_30
% 5.01/5.30 thf(fact_6954_cos__double__cos,axiom,
% 5.01/5.30 ! [W: complex] :
% 5.01/5.30 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.01/5.30 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double_cos
% 5.01/5.30 thf(fact_6955_cos__double__cos,axiom,
% 5.01/5.30 ! [W: real] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.01/5.30 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_double_cos
% 5.01/5.30 thf(fact_6956_cos__treble__cos,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_treble_cos
% 5.01/5.30 thf(fact_6957_cos__treble__cos,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_treble_cos
% 5.01/5.30 thf(fact_6958_sin__le__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ pi @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_le_zero
% 5.01/5.30 thf(fact_6959_sin__less__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_less_zero
% 5.01/5.30 thf(fact_6960_sin__monotone__2pi,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_monotone_2pi
% 5.01/5.30 thf(fact_6961_sin__mono__less__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) )
% 5.01/5.30 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_mono_less_eq
% 5.01/5.30 thf(fact_6962_sin__total,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ? [X4: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.01/5.30 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( sin_real @ X4 )
% 5.01/5.30 = Y )
% 5.01/5.30 & ! [Y4: real] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.01/5.30 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( sin_real @ Y4 )
% 5.01/5.30 = Y ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_total
% 5.01/5.30 thf(fact_6963_cos__gt__zero__pi,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_gt_zero_pi
% 5.01/5.30 thf(fact_6964_cos__ge__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_ge_zero
% 5.01/5.30 thf(fact_6965_cos__one__2pi,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 = ( ? [X3: nat] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.01/5.30 | ? [X3: nat] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_one_2pi
% 5.01/5.30 thf(fact_6966_sin__pi__divide__n__gt__0,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_pi_divide_n_gt_0
% 5.01/5.30 thf(fact_6967_sin__arctan,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( sin_real @ ( arctan @ X2 ) )
% 5.01/5.30 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_arctan
% 5.01/5.30 thf(fact_6968_cos__arctan,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cos_real @ ( arctan @ X2 ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arctan
% 5.01/5.30 thf(fact_6969_floor__log2__div2,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.30 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_log2_div2
% 5.01/5.30 thf(fact_6970_floor__log__nat__eq__if,axiom,
% 5.01/5.30 ! [B: nat,N: nat,K: nat] :
% 5.01/5.30 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.01/5.30 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.01/5.30 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.01/5.30 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_log_nat_eq_if
% 5.01/5.30 thf(fact_6971_sin__zero__lemma,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 => ? [N3: nat] :
% 5.01/5.30 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_lemma
% 5.01/5.30 thf(fact_6972_sin__zero__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( ? [N4: nat] :
% 5.01/5.30 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.30 | ? [N4: nat] :
% 5.01/5.30 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_iff
% 5.01/5.30 thf(fact_6973_cos__zero__lemma,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ( cos_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 => ? [N3: nat] :
% 5.01/5.30 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_zero_lemma
% 5.01/5.30 thf(fact_6974_cos__zero__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( ? [N4: nat] :
% 5.01/5.30 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.30 | ? [N4: nat] :
% 5.01/5.30 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_zero_iff
% 5.01/5.30 thf(fact_6975_tan__double,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_double
% 5.01/5.30 thf(fact_6976_tan__double,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.30 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X2 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_double
% 5.01/5.30 thf(fact_6977_sin__tan,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( sin_real @ X2 )
% 5.01/5.30 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_tan
% 5.01/5.30 thf(fact_6978_cos__tan,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( cos_real @ X2 )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_tan
% 5.01/5.30 thf(fact_6979_complex__unimodular__polar,axiom,
% 5.01/5.30 ! [Z: complex] :
% 5.01/5.30 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 => ~ ! [T3: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.30 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 => ( Z
% 5.01/5.30 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_unimodular_polar
% 5.01/5.30 thf(fact_6980_ceiling__log__eq__powr__iff,axiom,
% 5.01/5.30 ! [X2: real,B: real,K: nat] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X2 ) )
% 5.01/5.30 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.01/5.30 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.01/5.30 & ( ord_less_eq_real @ X2 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_log_eq_powr_iff
% 5.01/5.30 thf(fact_6981_powr__eq__0__iff,axiom,
% 5.01/5.30 ! [W: real,Z: real] :
% 5.01/5.30 ( ( ( powr_real @ W @ Z )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( W = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_eq_0_iff
% 5.01/5.30 thf(fact_6982_powr__0,axiom,
% 5.01/5.30 ! [Z: real] :
% 5.01/5.30 ( ( powr_real @ zero_zero_real @ Z )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % powr_0
% 5.01/5.30 thf(fact_6983_powr__one__eq__one,axiom,
% 5.01/5.30 ! [A: real] :
% 5.01/5.30 ( ( powr_real @ one_one_real @ A )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % powr_one_eq_one
% 5.01/5.30 thf(fact_6984_tan__zero,axiom,
% 5.01/5.30 ( ( tan_complex @ zero_zero_complex )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % tan_zero
% 5.01/5.30 thf(fact_6985_tan__zero,axiom,
% 5.01/5.30 ( ( tan_real @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % tan_zero
% 5.01/5.30 thf(fact_6986_tan__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( tan_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( tan_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_minus
% 5.01/5.30 thf(fact_6987_tan__minus,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( tan_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( tan_complex @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_minus
% 5.01/5.30 thf(fact_6988_powr__zero__eq__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( X2 = zero_zero_real )
% 5.01/5.30 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) )
% 5.01/5.30 & ( ( X2 != zero_zero_real )
% 5.01/5.30 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.01/5.30 = one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_zero_eq_one
% 5.01/5.30 thf(fact_6989_powr__gt__zero,axiom,
% 5.01/5.30 ! [X2: real,A: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X2 @ A ) )
% 5.01/5.30 = ( X2 != zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_gt_zero
% 5.01/5.30 thf(fact_6990_powr__nonneg__iff,axiom,
% 5.01/5.30 ! [A: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( powr_real @ A @ X2 ) @ zero_zero_real )
% 5.01/5.30 = ( A = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_nonneg_iff
% 5.01/5.30 thf(fact_6991_powr__less__cancel__iff,axiom,
% 5.01/5.30 ! [X2: real,A: real,B: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.01/5.30 = ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_cancel_iff
% 5.01/5.30 thf(fact_6992_tan__pi,axiom,
% 5.01/5.30 ( ( tan_real @ pi )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % tan_pi
% 5.01/5.30 thf(fact_6993_tan__periodic__pi,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( tan_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.01/5.30 = ( tan_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_periodic_pi
% 5.01/5.30 thf(fact_6994_powr__eq__one__iff,axiom,
% 5.01/5.30 ! [A: real,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ A )
% 5.01/5.30 => ( ( ( powr_real @ A @ X2 )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 = ( X2 = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_eq_one_iff
% 5.01/5.30 thf(fact_6995_powr__one__gt__zero__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( powr_real @ X2 @ one_one_real )
% 5.01/5.30 = X2 )
% 5.01/5.30 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_one_gt_zero_iff
% 5.01/5.30 thf(fact_6996_powr__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ one_one_real )
% 5.01/5.30 = X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_one
% 5.01/5.30 thf(fact_6997_powr__le__cancel__iff,axiom,
% 5.01/5.30 ! [X2: real,A: real,B: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.01/5.30 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_le_cancel_iff
% 5.01/5.30 thf(fact_6998_numeral__powr__numeral__real,axiom,
% 5.01/5.30 ! [M: num,N: num] :
% 5.01/5.30 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_powr_numeral_real
% 5.01/5.30 thf(fact_6999_powr__log__cancel,axiom,
% 5.01/5.30 ! [A: real,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( A != one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ A @ ( log @ A @ X2 ) )
% 5.01/5.30 = X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_log_cancel
% 5.01/5.30 thf(fact_7000_log__powr__cancel,axiom,
% 5.01/5.30 ! [A: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( A != one_one_real )
% 5.01/5.30 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_powr_cancel
% 5.01/5.30 thf(fact_7001_tan__npi,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % tan_npi
% 5.01/5.30 thf(fact_7002_tan__periodic__n,axiom,
% 5.01/5.30 ! [X2: real,N: num] :
% 5.01/5.30 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.01/5.30 = ( tan_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_periodic_n
% 5.01/5.30 thf(fact_7003_tan__periodic__nat,axiom,
% 5.01/5.30 ! [X2: real,N: nat] :
% 5.01/5.30 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.01/5.30 = ( tan_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_periodic_nat
% 5.01/5.30 thf(fact_7004_norm__cos__sin,axiom,
% 5.01/5.30 ! [T: real] :
% 5.01/5.30 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % norm_cos_sin
% 5.01/5.30 thf(fact_7005_powr__numeral,axiom,
% 5.01/5.30 ! [X2: real,N: num] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_numeral
% 5.01/5.30 thf(fact_7006_tan__periodic,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.30 = ( tan_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_periodic
% 5.01/5.30 thf(fact_7007_square__powr__half,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = ( abs_abs_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % square_powr_half
% 5.01/5.30 thf(fact_7008_powr__powr,axiom,
% 5.01/5.30 ! [X2: real,A: real,B: real] :
% 5.01/5.30 ( ( powr_real @ ( powr_real @ X2 @ A ) @ B )
% 5.01/5.30 = ( powr_real @ X2 @ ( times_times_real @ A @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_powr
% 5.01/5.30 thf(fact_7009_zero__complex_Ocode,axiom,
% 5.01/5.30 ( zero_zero_complex
% 5.01/5.30 = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % zero_complex.code
% 5.01/5.30 thf(fact_7010_Complex__eq__0,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ( complex2 @ A @ B )
% 5.01/5.30 = zero_zero_complex )
% 5.01/5.30 = ( ( A = zero_zero_real )
% 5.01/5.30 & ( B = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_eq_0
% 5.01/5.30 thf(fact_7011_complex__minus,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( uminus1482373934393186551omplex @ ( complex2 @ A @ B ) )
% 5.01/5.30 = ( complex2 @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_minus
% 5.01/5.30 thf(fact_7012_complex__diff,axiom,
% 5.01/5.30 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.30 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.01/5.30 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_diff
% 5.01/5.30 thf(fact_7013_powr__non__neg,axiom,
% 5.01/5.30 ! [A: real,X2: real] :
% 5.01/5.30 ~ ( ord_less_real @ ( powr_real @ A @ X2 ) @ zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % powr_non_neg
% 5.01/5.30 thf(fact_7014_powr__less__mono2__neg,axiom,
% 5.01/5.30 ! [A: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_mono2_neg
% 5.01/5.30 thf(fact_7015_powr__ge__pzero,axiom,
% 5.01/5.30 ! [X2: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X2 @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_ge_pzero
% 5.01/5.30 thf(fact_7016_powr__mono2,axiom,
% 5.01/5.30 ! [A: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mono2
% 5.01/5.30 thf(fact_7017_powr__less__cancel,axiom,
% 5.01/5.30 ! [X2: real,A: real,B: real] :
% 5.01/5.30 ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.01/5.30 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_cancel
% 5.01/5.30 thf(fact_7018_powr__less__mono,axiom,
% 5.01/5.30 ! [A: real,B: real,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ A @ B )
% 5.01/5.30 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_mono
% 5.01/5.30 thf(fact_7019_powr__mono,axiom,
% 5.01/5.30 ! [A: real,B: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.30 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mono
% 5.01/5.30 thf(fact_7020_Complex__eq__1,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ( complex2 @ A @ B )
% 5.01/5.30 = one_one_complex )
% 5.01/5.30 = ( ( A = one_one_real )
% 5.01/5.30 & ( B = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_eq_1
% 5.01/5.30 thf(fact_7021_one__complex_Ocode,axiom,
% 5.01/5.30 ( one_one_complex
% 5.01/5.30 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % one_complex.code
% 5.01/5.30 thf(fact_7022_Complex__eq__numeral,axiom,
% 5.01/5.30 ! [A: real,B: real,W: num] :
% 5.01/5.30 ( ( ( complex2 @ A @ B )
% 5.01/5.30 = ( numera6690914467698888265omplex @ W ) )
% 5.01/5.30 = ( ( A
% 5.01/5.30 = ( numeral_numeral_real @ W ) )
% 5.01/5.30 & ( B = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_eq_numeral
% 5.01/5.30 thf(fact_7023_complex__add,axiom,
% 5.01/5.30 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.30 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.01/5.30 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_add
% 5.01/5.30 thf(fact_7024_powr__mono2_H,axiom,
% 5.01/5.30 ! [A: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mono2'
% 5.01/5.30 thf(fact_7025_powr__less__mono2,axiom,
% 5.01/5.30 ! [A: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_mono2
% 5.01/5.30 thf(fact_7026_powr__inj,axiom,
% 5.01/5.30 ! [A: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( A != one_one_real )
% 5.01/5.30 => ( ( ( powr_real @ A @ X2 )
% 5.01/5.30 = ( powr_real @ A @ Y ) )
% 5.01/5.30 = ( X2 = Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_inj
% 5.01/5.30 thf(fact_7027_gr__one__powr,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % gr_one_powr
% 5.01/5.30 thf(fact_7028_ge__one__powr__ge__zero,axiom,
% 5.01/5.30 ! [X2: real,A: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ge_one_powr_ge_zero
% 5.01/5.30 thf(fact_7029_powr__mono__both,axiom,
% 5.01/5.30 ! [A: real,B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ A @ B )
% 5.01/5.30 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mono_both
% 5.01/5.30 thf(fact_7030_powr__le1,axiom,
% 5.01/5.30 ! [A: real,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ one_one_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_le1
% 5.01/5.30 thf(fact_7031_powr__divide,axiom,
% 5.01/5.30 ! [X2: real,Y: real,A: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( powr_real @ ( divide_divide_real @ X2 @ Y ) @ A )
% 5.01/5.30 = ( divide_divide_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_divide
% 5.01/5.30 thf(fact_7032_powr__mult,axiom,
% 5.01/5.30 ! [X2: real,Y: real,A: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( powr_real @ ( times_times_real @ X2 @ Y ) @ A )
% 5.01/5.30 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mult
% 5.01/5.30 thf(fact_7033_divide__powr__uminus,axiom,
% 5.01/5.30 ! [A: real,B: real,C: real] :
% 5.01/5.30 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.01/5.30 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % divide_powr_uminus
% 5.01/5.30 thf(fact_7034_ln__powr,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( X2 != zero_zero_real )
% 5.01/5.30 => ( ( ln_ln_real @ ( powr_real @ X2 @ Y ) )
% 5.01/5.30 = ( times_times_real @ Y @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ln_powr
% 5.01/5.30 thf(fact_7035_log__base__powr,axiom,
% 5.01/5.30 ! [A: real,B: real,X2: real] :
% 5.01/5.30 ( ( A != zero_zero_real )
% 5.01/5.30 => ( ( log @ ( powr_real @ A @ B ) @ X2 )
% 5.01/5.30 = ( divide_divide_real @ ( log @ A @ X2 ) @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_base_powr
% 5.01/5.30 thf(fact_7036_log__powr,axiom,
% 5.01/5.30 ! [X2: real,B: real,Y: real] :
% 5.01/5.30 ( ( X2 != zero_zero_real )
% 5.01/5.30 => ( ( log @ B @ ( powr_real @ X2 @ Y ) )
% 5.01/5.30 = ( times_times_real @ Y @ ( log @ B @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_powr
% 5.01/5.30 thf(fact_7037_Complex__eq__neg__1,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ( complex2 @ A @ B )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.01/5.30 = ( ( A
% 5.01/5.30 = ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.30 & ( B = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_eq_neg_1
% 5.01/5.30 thf(fact_7038_Complex__eq__neg__numeral,axiom,
% 5.01/5.30 ! [A: real,B: real,W: num] :
% 5.01/5.30 ( ( ( complex2 @ A @ B )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.30 = ( ( A
% 5.01/5.30 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.30 & ( B = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_eq_neg_numeral
% 5.01/5.30 thf(fact_7039_powr__add,axiom,
% 5.01/5.30 ! [X2: real,A: real,B: real] :
% 5.01/5.30 ( ( powr_real @ X2 @ ( plus_plus_real @ A @ B ) )
% 5.01/5.30 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_add
% 5.01/5.30 thf(fact_7040_powr__diff,axiom,
% 5.01/5.30 ! [W: real,Z1: real,Z22: real] :
% 5.01/5.30 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.01/5.30 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_diff
% 5.01/5.30 thf(fact_7041_complex__mult,axiom,
% 5.01/5.30 ! [A: real,B: real,C: real,D: real] :
% 5.01/5.30 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.01/5.30 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_mult
% 5.01/5.30 thf(fact_7042_tan__def,axiom,
% 5.01/5.30 ( tan_complex
% 5.01/5.30 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X3 ) @ ( cos_complex @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_def
% 5.01/5.30 thf(fact_7043_tan__def,axiom,
% 5.01/5.30 ( tan_real
% 5.01/5.30 = ( ^ [X3: real] : ( divide_divide_real @ ( sin_real @ X3 ) @ ( cos_real @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_def
% 5.01/5.30 thf(fact_7044_powr__realpow,axiom,
% 5.01/5.30 ! [X2: real,N: nat] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.30 = ( power_power_real @ X2 @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_realpow
% 5.01/5.30 thf(fact_7045_powr__less__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X2 )
% 5.01/5.30 = ( ord_less_real @ Y @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_less_iff
% 5.01/5.30 thf(fact_7046_less__powr__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( powr_real @ B @ Y ) )
% 5.01/5.30 = ( ord_less_real @ ( log @ B @ X2 ) @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_powr_iff
% 5.01/5.30 thf(fact_7047_log__less__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ ( log @ B @ X2 ) @ Y )
% 5.01/5.30 = ( ord_less_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_less_iff
% 5.01/5.30 thf(fact_7048_less__log__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ Y @ ( log @ B @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_log_iff
% 5.01/5.30 thf(fact_7049_powr__minus__divide,axiom,
% 5.01/5.30 ! [X2: real,A: real] :
% 5.01/5.30 ( ( powr_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_minus_divide
% 5.01/5.30 thf(fact_7050_powr__neg__one,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_neg_one
% 5.01/5.30 thf(fact_7051_powr__mult__base,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y ) )
% 5.01/5.30 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_mult_base
% 5.01/5.30 thf(fact_7052_le__log__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_log_iff
% 5.01/5.30 thf(fact_7053_log__le__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_le_iff
% 5.01/5.30 thf(fact_7054_le__powr__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_powr_iff
% 5.01/5.30 thf(fact_7055_powr__le__iff,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X2 )
% 5.01/5.30 = ( ord_less_eq_real @ Y @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_le_iff
% 5.01/5.30 thf(fact_7056_ln__powr__bound,axiom,
% 5.01/5.30 ! [X2: real,A: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A ) @ A ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ln_powr_bound
% 5.01/5.30 thf(fact_7057_ln__powr__bound2,axiom,
% 5.01/5.30 ! [X2: real,A: real] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.30 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ln_powr_bound2
% 5.01/5.30 thf(fact_7058_tan__45,axiom,
% 5.01/5.30 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % tan_45
% 5.01/5.30 thf(fact_7059_log__add__eq__powr,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ( B != one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( plus_plus_real @ ( log @ B @ X2 ) @ Y )
% 5.01/5.30 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_add_eq_powr
% 5.01/5.30 thf(fact_7060_add__log__eq__powr,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ( B != one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( plus_plus_real @ Y @ ( log @ B @ X2 ) )
% 5.01/5.30 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % add_log_eq_powr
% 5.01/5.30 thf(fact_7061_minus__log__eq__powr,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ( B != one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( minus_minus_real @ Y @ ( log @ B @ X2 ) )
% 5.01/5.30 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % minus_log_eq_powr
% 5.01/5.30 thf(fact_7062_tan__60,axiom,
% 5.01/5.30 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.01/5.30 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_60
% 5.01/5.30 thf(fact_7063_powr__def,axiom,
% 5.01/5.30 ( powr_real
% 5.01/5.30 = ( ^ [X3: real,A4: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A4 @ ( ln_ln_real @ X3 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_def
% 5.01/5.30 thf(fact_7064_tan__gt__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_gt_zero
% 5.01/5.30 thf(fact_7065_lemma__tan__total,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.01/5.30 => ? [X4: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.01/5.30 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ord_less_real @ Y @ ( tan_real @ X4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % lemma_tan_total
% 5.01/5.30 thf(fact_7066_tan__total,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ? [X4: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.01/5.30 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( tan_real @ X4 )
% 5.01/5.30 = Y )
% 5.01/5.30 & ! [Y4: real] :
% 5.01/5.30 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.01/5.30 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( tan_real @ Y4 )
% 5.01/5.30 = Y ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_total
% 5.01/5.30 thf(fact_7067_tan__monotone,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_monotone
% 5.01/5.30 thf(fact_7068_tan__monotone_H,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.30 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_monotone'
% 5.01/5.30 thf(fact_7069_tan__mono__lt__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.01/5.30 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_mono_lt_eq
% 5.01/5.30 thf(fact_7070_lemma__tan__total1,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ? [X4: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.01/5.30 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( tan_real @ X4 )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % lemma_tan_total1
% 5.01/5.30 thf(fact_7071_tan__minus__45,axiom,
% 5.01/5.30 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.30 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_minus_45
% 5.01/5.30 thf(fact_7072_tan__inverse,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.01/5.30 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_inverse
% 5.01/5.30 thf(fact_7073_log__minus__eq__powr,axiom,
% 5.01/5.30 ! [B: real,X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.30 => ( ( B != one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( minus_minus_real @ ( log @ B @ X2 ) @ Y )
% 5.01/5.30 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % log_minus_eq_powr
% 5.01/5.30 thf(fact_7074_complex__norm,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y ) )
% 5.01/5.30 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_norm
% 5.01/5.30 thf(fact_7075_add__tan__eq,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ Y )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % add_tan_eq
% 5.01/5.30 thf(fact_7076_add__tan__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ Y )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.01/5.30 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % add_tan_eq
% 5.01/5.30 thf(fact_7077_powr__half__sqrt,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = ( sqrt @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_half_sqrt
% 5.01/5.30 thf(fact_7078_powr__neg__numeral,axiom,
% 5.01/5.30 ! [X2: real,N: num] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_neg_numeral
% 5.01/5.30 thf(fact_7079_tan__total__pos,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ? [X4: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.01/5.30 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( tan_real @ X4 )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_total_pos
% 5.01/5.30 thf(fact_7080_tan__pos__pi2__le,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_pos_pi2_le
% 5.01/5.30 thf(fact_7081_tan__less__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_less_zero
% 5.01/5.30 thf(fact_7082_tan__mono__le,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_mono_le
% 5.01/5.30 thf(fact_7083_tan__mono__le__eq,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_mono_le_eq
% 5.01/5.30 thf(fact_7084_tan__bound__pi2,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_bound_pi2
% 5.01/5.30 thf(fact_7085_tan__30,axiom,
% 5.01/5.30 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_30
% 5.01/5.30 thf(fact_7086_arctan__unique,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ( tan_real @ X2 )
% 5.01/5.30 = Y )
% 5.01/5.30 => ( ( arctan @ Y )
% 5.01/5.30 = X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arctan_unique
% 5.01/5.30 thf(fact_7087_arctan__tan,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.01/5.30 = X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arctan_tan
% 5.01/5.30 thf(fact_7088_arctan,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.01/5.30 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( tan_real @ ( arctan @ Y ) )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % arctan
% 5.01/5.30 thf(fact_7089_lemma__tan__add1,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ Y )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % lemma_tan_add1
% 5.01/5.30 thf(fact_7090_lemma__tan__add1,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ Y )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) )
% 5.01/5.30 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % lemma_tan_add1
% 5.01/5.30 thf(fact_7091_tan__diff,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ Y )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( tan_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_diff
% 5.01/5.30 thf(fact_7092_tan__diff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ Y )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( tan_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_diff
% 5.01/5.30 thf(fact_7093_tan__add,axiom,
% 5.01/5.30 ! [X2: complex,Y: complex] :
% 5.01/5.30 ( ( ( cos_complex @ X2 )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ Y )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.30 != zero_zero_complex )
% 5.01/5.30 => ( ( tan_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_add
% 5.01/5.30 thf(fact_7094_tan__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ Y )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( ( cos_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 != zero_zero_real )
% 5.01/5.30 => ( ( tan_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_add
% 5.01/5.30 thf(fact_7095_tan__total__pi4,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ? [Z3: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 5.01/5.30 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 & ( ( tan_real @ Z3 )
% 5.01/5.30 = X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_total_pi4
% 5.01/5.30 thf(fact_7096_tan__half,axiom,
% 5.01/5.30 ( tan_complex
% 5.01/5.30 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_complex ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_half
% 5.01/5.30 thf(fact_7097_tan__half,axiom,
% 5.01/5.30 ( tan_real
% 5.01/5.30 = ( ^ [X3: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X3 ) ) @ one_one_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_half
% 5.01/5.30 thf(fact_7098_arcosh__def,axiom,
% 5.01/5.30 ( arcosh_real
% 5.01/5.30 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcosh_def
% 5.01/5.30 thf(fact_7099_cos__arcsin,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.01/5.30 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arcsin
% 5.01/5.30 thf(fact_7100_sin__arccos__abs,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( sin_real @ ( arccos @ Y ) )
% 5.01/5.30 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_arccos_abs
% 5.01/5.30 thf(fact_7101_sin__arccos,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.01/5.30 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_arccos
% 5.01/5.30 thf(fact_7102_arsinh__def,axiom,
% 5.01/5.30 ( arsinh_real
% 5.01/5.30 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arsinh_def
% 5.01/5.30 thf(fact_7103_arcsin__0,axiom,
% 5.01/5.30 ( ( arcsin @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_0
% 5.01/5.30 thf(fact_7104_of__real__eq__0__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_0_iff
% 5.01/5.30 thf(fact_7105_of__real__eq__0__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.01/5.30 = zero_zero_complex )
% 5.01/5.30 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_0_iff
% 5.01/5.30 thf(fact_7106_of__real__0,axiom,
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_0
% 5.01/5.30 thf(fact_7107_of__real__0,axiom,
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_0
% 5.01/5.30 thf(fact_7108_of__real__1,axiom,
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_1
% 5.01/5.30 thf(fact_7109_of__real__1,axiom,
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_1
% 5.01/5.30 thf(fact_7110_of__real__eq__1__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 = ( X2 = one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_1_iff
% 5.01/5.30 thf(fact_7111_of__real__eq__1__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.01/5.30 = one_one_complex )
% 5.01/5.30 = ( X2 = one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_1_iff
% 5.01/5.30 thf(fact_7112_of__real__numeral,axiom,
% 5.01/5.30 ! [W: num] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.30 = ( numeral_numeral_real @ W ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_numeral
% 5.01/5.30 thf(fact_7113_of__real__numeral,axiom,
% 5.01/5.30 ! [W: num] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.01/5.30 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_numeral
% 5.01/5.30 thf(fact_7114_of__real__mult,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.30 = ( times_times_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_mult
% 5.01/5.30 thf(fact_7115_of__real__mult,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.30 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_mult
% 5.01/5.30 thf(fact_7116_of__real__divide,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_divide
% 5.01/5.30 thf(fact_7117_of__real__divide,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_divide
% 5.01/5.30 thf(fact_7118_of__real__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_add
% 5.01/5.30 thf(fact_7119_of__real__add,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.30 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_add
% 5.01/5.30 thf(fact_7120_of__real__power,axiom,
% 5.01/5.30 ! [X2: real,N: nat] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X2 @ N ) )
% 5.01/5.30 = ( power_power_real @ ( real_V1803761363581548252l_real @ X2 ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_power
% 5.01/5.30 thf(fact_7121_of__real__power,axiom,
% 5.01/5.30 ! [X2: real,N: nat] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X2 @ N ) )
% 5.01/5.30 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X2 ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_power
% 5.01/5.30 thf(fact_7122_of__real__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_minus
% 5.01/5.30 thf(fact_7123_of__real__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_minus
% 5.01/5.30 thf(fact_7124_minus__of__real__eq__of__real__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ X2 ) )
% 5.01/5.30 = ( real_V1803761363581548252l_real @ Y ) )
% 5.01/5.30 = ( ( uminus_uminus_real @ X2 )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % minus_of_real_eq_of_real_iff
% 5.01/5.30 thf(fact_7125_minus__of__real__eq__of__real__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ X2 ) )
% 5.01/5.30 = ( real_V4546457046886955230omplex @ Y ) )
% 5.01/5.30 = ( ( uminus_uminus_real @ X2 )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % minus_of_real_eq_of_real_iff
% 5.01/5.30 thf(fact_7126_of__real__eq__minus__of__real__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.01/5.30 = ( uminus_uminus_real @ ( real_V1803761363581548252l_real @ Y ) ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( uminus_uminus_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_minus_of_real_iff
% 5.01/5.30 thf(fact_7127_of__real__eq__minus__of__real__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( real_V4546457046886955230omplex @ Y ) ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( uminus_uminus_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_eq_minus_of_real_iff
% 5.01/5.30 thf(fact_7128_of__real__diff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_diff
% 5.01/5.30 thf(fact_7129_of__real__diff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.30 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_diff
% 5.01/5.30 thf(fact_7130_of__real__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.30 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_of_nat_eq
% 5.01/5.30 thf(fact_7131_of__real__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.30 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_of_nat_eq
% 5.01/5.30 thf(fact_7132_arccos__1,axiom,
% 5.01/5.30 ( ( arccos @ one_one_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_1
% 5.01/5.30 thf(fact_7133_sin__of__real__pi,axiom,
% 5.01/5.30 ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_of_real_pi
% 5.01/5.30 thf(fact_7134_sin__of__real__pi,axiom,
% 5.01/5.30 ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % sin_of_real_pi
% 5.01/5.30 thf(fact_7135_arccos__minus__1,axiom,
% 5.01/5.30 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.30 = pi ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_minus_1
% 5.01/5.30 thf(fact_7136_of__real__neg__numeral,axiom,
% 5.01/5.30 ! [W: num] :
% 5.01/5.30 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_neg_numeral
% 5.01/5.30 thf(fact_7137_of__real__neg__numeral,axiom,
% 5.01/5.30 ! [W: num] :
% 5.01/5.30 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_real_neg_numeral
% 5.01/5.30 thf(fact_7138_cos__of__real__pi,axiom,
% 5.01/5.30 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.01/5.30 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_of_real_pi
% 5.01/5.30 thf(fact_7139_cos__of__real__pi,axiom,
% 5.01/5.30 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_of_real_pi
% 5.01/5.30 thf(fact_7140_cos__arccos,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( cos_real @ ( arccos @ Y ) )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arccos
% 5.01/5.30 thf(fact_7141_sin__arcsin,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_arcsin
% 5.01/5.30 thf(fact_7142_norm__of__real__add1,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ one_one_real ) )
% 5.01/5.30 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_add1
% 5.01/5.30 thf(fact_7143_norm__of__real__add1,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ one_one_complex ) )
% 5.01/5.30 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_add1
% 5.01/5.30 thf(fact_7144_norm__of__real__addn,axiom,
% 5.01/5.30 ! [X2: real,B: num] :
% 5.01/5.30 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( numeral_numeral_real @ B ) ) )
% 5.01/5.30 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_addn
% 5.01/5.30 thf(fact_7145_norm__of__real__addn,axiom,
% 5.01/5.30 ! [X2: real,B: num] :
% 5.01/5.30 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.01/5.30 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_addn
% 5.01/5.30 thf(fact_7146_arccos__0,axiom,
% 5.01/5.30 ( ( arccos @ zero_zero_real )
% 5.01/5.30 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_0
% 5.01/5.30 thf(fact_7147_arcsin__1,axiom,
% 5.01/5.30 ( ( arcsin @ one_one_real )
% 5.01/5.30 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_1
% 5.01/5.30 thf(fact_7148_cos__of__real__pi__half,axiom,
% 5.01/5.30 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_of_real_pi_half
% 5.01/5.30 thf(fact_7149_cos__of__real__pi__half,axiom,
% 5.01/5.30 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % cos_of_real_pi_half
% 5.01/5.30 thf(fact_7150_sin__of__real__pi__half,axiom,
% 5.01/5.30 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_of_real_pi_half
% 5.01/5.30 thf(fact_7151_sin__of__real__pi__half,axiom,
% 5.01/5.30 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % sin_of_real_pi_half
% 5.01/5.30 thf(fact_7152_arcsin__minus__1,axiom,
% 5.01/5.30 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_minus_1
% 5.01/5.30 thf(fact_7153_complex__of__real__def,axiom,
% 5.01/5.30 ( real_V4546457046886955230omplex
% 5.01/5.30 = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_of_real_def
% 5.01/5.30 thf(fact_7154_complex__of__real__code,axiom,
% 5.01/5.30 ( real_V4546457046886955230omplex
% 5.01/5.30 = ( ^ [X3: real] : ( complex2 @ X3 @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_of_real_code
% 5.01/5.30 thf(fact_7155_complex__eq__cancel__iff2,axiom,
% 5.01/5.30 ! [X2: real,Y: real,Xa: real] :
% 5.01/5.30 ( ( ( complex2 @ X2 @ Y )
% 5.01/5.30 = ( real_V4546457046886955230omplex @ Xa ) )
% 5.01/5.30 = ( ( X2 = Xa )
% 5.01/5.30 & ( Y = zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_eq_cancel_iff2
% 5.01/5.30 thf(fact_7156_Complex__mult__complex__of__real,axiom,
% 5.01/5.30 ! [X2: real,Y: real,R: real] :
% 5.01/5.30 ( ( times_times_complex @ ( complex2 @ X2 @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.01/5.30 = ( complex2 @ ( times_times_real @ X2 @ R ) @ ( times_times_real @ Y @ R ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_mult_complex_of_real
% 5.01/5.30 thf(fact_7157_complex__of__real__mult__Complex,axiom,
% 5.01/5.30 ! [R: real,X2: real,Y: real] :
% 5.01/5.30 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X2 @ Y ) )
% 5.01/5.30 = ( complex2 @ ( times_times_real @ R @ X2 ) @ ( times_times_real @ R @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_of_real_mult_Complex
% 5.01/5.30 thf(fact_7158_nonzero__of__real__divide,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( Y != zero_zero_real )
% 5.01/5.30 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % nonzero_of_real_divide
% 5.01/5.30 thf(fact_7159_nonzero__of__real__divide,axiom,
% 5.01/5.30 ! [Y: real,X2: real] :
% 5.01/5.30 ( ( Y != zero_zero_real )
% 5.01/5.30 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.30 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % nonzero_of_real_divide
% 5.01/5.30 thf(fact_7160_Complex__add__complex__of__real,axiom,
% 5.01/5.30 ! [X2: real,Y: real,R: real] :
% 5.01/5.30 ( ( plus_plus_complex @ ( complex2 @ X2 @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.01/5.30 = ( complex2 @ ( plus_plus_real @ X2 @ R ) @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % Complex_add_complex_of_real
% 5.01/5.30 thf(fact_7161_complex__of__real__add__Complex,axiom,
% 5.01/5.30 ! [R: real,X2: real,Y: real] :
% 5.01/5.30 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X2 @ Y ) )
% 5.01/5.30 = ( complex2 @ ( plus_plus_real @ R @ X2 ) @ Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % complex_of_real_add_Complex
% 5.01/5.30 thf(fact_7162_arccos__le__arccos,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_le_arccos
% 5.01/5.30 thf(fact_7163_arccos__eq__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.01/5.30 => ( ( ( arccos @ X2 )
% 5.01/5.30 = ( arccos @ Y ) )
% 5.01/5.30 = ( X2 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_eq_iff
% 5.01/5.30 thf(fact_7164_arccos__le__mono,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( arccos @ X2 ) @ ( arccos @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ Y @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_le_mono
% 5.01/5.30 thf(fact_7165_arcsin__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( arcsin @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( arcsin @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_minus
% 5.01/5.30 thf(fact_7166_arcsin__le__arcsin,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_le_arcsin
% 5.01/5.30 thf(fact_7167_arcsin__eq__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( ( arcsin @ X2 )
% 5.01/5.30 = ( arcsin @ Y ) )
% 5.01/5.30 = ( X2 = Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_eq_iff
% 5.01/5.30 thf(fact_7168_arcsin__le__mono,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_le_mono
% 5.01/5.30 thf(fact_7169_norm__less__p1,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X2 ) ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_less_p1
% 5.01/5.30 thf(fact_7170_norm__less__p1,axiom,
% 5.01/5.30 ! [X2: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X2 ) ) @ one_one_complex ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_less_p1
% 5.01/5.30 thf(fact_7171_arccos__lbound,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_lbound
% 5.01/5.30 thf(fact_7172_arccos__less__arccos,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_less_arccos
% 5.01/5.30 thf(fact_7173_arccos__less__mono,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y ) )
% 5.01/5.30 = ( ord_less_real @ Y @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_less_mono
% 5.01/5.30 thf(fact_7174_arccos__ubound,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_ubound
% 5.01/5.30 thf(fact_7175_arccos__cos,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.30 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.01/5.30 = X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_cos
% 5.01/5.30 thf(fact_7176_arcsin__less__arcsin,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_less_arcsin
% 5.01/5.30 thf(fact_7177_arcsin__less__mono,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) )
% 5.01/5.30 = ( ord_less_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_less_mono
% 5.01/5.30 thf(fact_7178_cos__arccos__abs,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.01/5.30 => ( ( cos_real @ ( arccos @ Y ) )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arccos_abs
% 5.01/5.30 thf(fact_7179_norm__of__real__diff,axiom,
% 5.01/5.30 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_diff
% 5.01/5.30 thf(fact_7180_norm__of__real__diff,axiom,
% 5.01/5.30 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % norm_of_real_diff
% 5.01/5.30 thf(fact_7181_arccos__cos__eq__abs,axiom,
% 5.01/5.30 ! [Theta: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.01/5.30 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.01/5.30 = ( abs_abs_real @ Theta ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_cos_eq_abs
% 5.01/5.30 thf(fact_7182_arccos__lt__bounded,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.01/5.30 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_lt_bounded
% 5.01/5.30 thf(fact_7183_arccos__bounded,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.01/5.30 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_bounded
% 5.01/5.30 thf(fact_7184_sin__arccos__nonzero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.01/5.30 != zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_arccos_nonzero
% 5.01/5.30 thf(fact_7185_arccos__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_minus
% 5.01/5.30 thf(fact_7186_arccos__cos2,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.01/5.30 => ( ( arccos @ ( cos_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_cos2
% 5.01/5.30 thf(fact_7187_cos__arcsin__nonzero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.01/5.30 != zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_arcsin_nonzero
% 5.01/5.30 thf(fact_7188_arccos,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.01/5.30 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.01/5.30 & ( ( cos_real @ ( arccos @ Y ) )
% 5.01/5.30 = Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos
% 5.01/5.30 thf(fact_7189_arccos__minus__abs,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.30 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_minus_abs
% 5.01/5.30 thf(fact_7190_sin__cos__eq,axiom,
% 5.01/5.30 ( sin_real
% 5.01/5.30 = ( ^ [X3: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_eq
% 5.01/5.30 thf(fact_7191_sin__cos__eq,axiom,
% 5.01/5.30 ( sin_complex
% 5.01/5.30 = ( ^ [X3: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_cos_eq
% 5.01/5.30 thf(fact_7192_cos__sin__eq,axiom,
% 5.01/5.30 ( cos_real
% 5.01/5.30 = ( ^ [X3: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_sin_eq
% 5.01/5.30 thf(fact_7193_cos__sin__eq,axiom,
% 5.01/5.30 ( cos_complex
% 5.01/5.30 = ( ^ [X3: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_sin_eq
% 5.01/5.30 thf(fact_7194_minus__sin__cos__eq,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( uminus_uminus_real @ ( sin_real @ X2 ) )
% 5.01/5.30 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % minus_sin_cos_eq
% 5.01/5.30 thf(fact_7195_minus__sin__cos__eq,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X2 ) )
% 5.01/5.30 = ( cos_complex @ ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % minus_sin_cos_eq
% 5.01/5.30 thf(fact_7196_arccos__le__pi2,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_le_pi2
% 5.01/5.30 thf(fact_7197_arcsin__lt__bounded,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.01/5.30 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_lt_bounded
% 5.01/5.30 thf(fact_7198_arcsin__bounded,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.01/5.30 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_bounded
% 5.01/5.30 thf(fact_7199_arcsin__ubound,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_ubound
% 5.01/5.30 thf(fact_7200_arcsin__lbound,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_lbound
% 5.01/5.30 thf(fact_7201_arcsin__sin,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.01/5.30 = X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_sin
% 5.01/5.30 thf(fact_7202_le__arcsin__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_arcsin_iff
% 5.01/5.30 thf(fact_7203_arcsin__le__iff,axiom,
% 5.01/5.30 ! [X2: real,Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_le_iff
% 5.01/5.30 thf(fact_7204_arcsin__pi,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.01/5.30 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.01/5.30 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.01/5.30 = Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin_pi
% 5.01/5.30 thf(fact_7205_arcsin,axiom,
% 5.01/5.30 ! [Y: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.01/5.30 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.01/5.30 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.01/5.30 = Y ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arcsin
% 5.01/5.30 thf(fact_7206_cos__npi__int,axiom,
% 5.01/5.30 ! [N: int] :
% 5.01/5.30 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.30 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.01/5.30 = one_one_real ) )
% 5.01/5.30 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.30 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.01/5.30 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_npi_int
% 5.01/5.30 thf(fact_7207_cot__less__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.30 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_less_zero
% 5.01/5.30 thf(fact_7208_cot__periodic,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.30 = ( cot_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_periodic
% 5.01/5.30 thf(fact_7209_powr__int,axiom,
% 5.01/5.30 ! [X2: real,I: int] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.01/5.30 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.01/5.30 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.01/5.30 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_int
% 5.01/5.30 thf(fact_7210_sin__zero__iff__int,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( ? [I4: int] :
% 5.01/5.30 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_iff_int
% 5.01/5.30 thf(fact_7211_of__int__floor__cancel,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = X2 )
% 5.01/5.30 = ( ? [N4: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_floor_cancel
% 5.01/5.30 thf(fact_7212_of__int__floor__cancel,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = X2 )
% 5.01/5.30 = ( ? [N4: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_floor_cancel
% 5.01/5.30 thf(fact_7213_of__int__ceiling__cancel,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = X2 )
% 5.01/5.30 = ( ? [N4: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_cancel
% 5.01/5.30 thf(fact_7214_of__int__ceiling__cancel,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = X2 )
% 5.01/5.30 = ( ? [N4: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_cancel
% 5.01/5.30 thf(fact_7215_cot__zero,axiom,
% 5.01/5.30 ( ( cot_complex @ zero_zero_complex )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % cot_zero
% 5.01/5.30 thf(fact_7216_cot__zero,axiom,
% 5.01/5.30 ( ( cot_real @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cot_zero
% 5.01/5.30 thf(fact_7217_cot__minus,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( cot_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( cot_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_minus
% 5.01/5.30 thf(fact_7218_cot__minus,axiom,
% 5.01/5.30 ! [X2: complex] :
% 5.01/5.30 ( ( cot_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( cot_complex @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_minus
% 5.01/5.30 thf(fact_7219_of__int__eq__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ Z )
% 5.01/5.30 = zero_zero_int )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_0_iff
% 5.01/5.30 thf(fact_7220_of__int__eq__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ Z )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_0_iff
% 5.01/5.30 thf(fact_7221_of__int__eq__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.01/5.30 = zero_zero_complex )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_0_iff
% 5.01/5.30 thf(fact_7222_of__int__eq__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ Z )
% 5.01/5.30 = zero_zero_rat )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_0_iff
% 5.01/5.30 thf(fact_7223_of__int__0__eq__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( zero_zero_int
% 5.01/5.30 = ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_eq_iff
% 5.01/5.30 thf(fact_7224_of__int__0__eq__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( zero_zero_real
% 5.01/5.30 = ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_eq_iff
% 5.01/5.30 thf(fact_7225_of__int__0__eq__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( zero_zero_complex
% 5.01/5.30 = ( ring_17405671764205052669omplex @ Z ) )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_eq_iff
% 5.01/5.30 thf(fact_7226_of__int__0__eq__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( zero_zero_rat
% 5.01/5.30 = ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( Z = zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_eq_iff
% 5.01/5.30 thf(fact_7227_of__int__0,axiom,
% 5.01/5.30 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.01/5.30 = zero_zero_int ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0
% 5.01/5.30 thf(fact_7228_of__int__0,axiom,
% 5.01/5.30 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0
% 5.01/5.30 thf(fact_7229_of__int__0,axiom,
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0
% 5.01/5.30 thf(fact_7230_of__int__0,axiom,
% 5.01/5.30 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.01/5.30 = zero_zero_rat ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0
% 5.01/5.30 thf(fact_7231_of__int__le__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_iff
% 5.01/5.30 thf(fact_7232_of__int__le__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_iff
% 5.01/5.30 thf(fact_7233_of__int__le__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_iff
% 5.01/5.30 thf(fact_7234_of__int__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.01/5.30 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral
% 5.01/5.30 thf(fact_7235_of__int__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.01/5.30 = ( numeral_numeral_real @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral
% 5.01/5.30 thf(fact_7236_of__int__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.01/5.30 = ( numeral_numeral_rat @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral
% 5.01/5.30 thf(fact_7237_of__int__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.01/5.30 = ( numeral_numeral_int @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral
% 5.01/5.30 thf(fact_7238_of__int__eq__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.01/5.30 = ( numera6690914467698888265omplex @ N ) )
% 5.01/5.30 = ( Z
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_iff
% 5.01/5.30 thf(fact_7239_of__int__eq__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ Z )
% 5.01/5.30 = ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( Z
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_iff
% 5.01/5.30 thf(fact_7240_of__int__eq__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ Z )
% 5.01/5.30 = ( numeral_numeral_rat @ N ) )
% 5.01/5.30 = ( Z
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_iff
% 5.01/5.30 thf(fact_7241_of__int__eq__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ Z )
% 5.01/5.30 = ( numeral_numeral_int @ N ) )
% 5.01/5.30 = ( Z
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_iff
% 5.01/5.30 thf(fact_7242_of__int__less__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_iff
% 5.01/5.30 thf(fact_7243_of__int__less__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_iff
% 5.01/5.30 thf(fact_7244_of__int__less__iff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_int @ W @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_iff
% 5.01/5.30 thf(fact_7245_of__int__eq__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ Z )
% 5.01/5.30 = one_one_int )
% 5.01/5.30 = ( Z = one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_1_iff
% 5.01/5.30 thf(fact_7246_of__int__eq__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ Z )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 = ( Z = one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_1_iff
% 5.01/5.30 thf(fact_7247_of__int__eq__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.01/5.30 = one_one_complex )
% 5.01/5.30 = ( Z = one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_1_iff
% 5.01/5.30 thf(fact_7248_of__int__eq__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ Z )
% 5.01/5.30 = one_one_rat )
% 5.01/5.30 = ( Z = one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_1_iff
% 5.01/5.30 thf(fact_7249_of__int__1,axiom,
% 5.01/5.30 ( ( ring_1_of_int_int @ one_one_int )
% 5.01/5.30 = one_one_int ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1
% 5.01/5.30 thf(fact_7250_of__int__1,axiom,
% 5.01/5.30 ( ( ring_1_of_int_real @ one_one_int )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1
% 5.01/5.30 thf(fact_7251_of__int__1,axiom,
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1
% 5.01/5.30 thf(fact_7252_of__int__1,axiom,
% 5.01/5.30 ( ( ring_1_of_int_rat @ one_one_int )
% 5.01/5.30 = one_one_rat ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1
% 5.01/5.30 thf(fact_7253_of__int__mult,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.01/5.30 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_mult
% 5.01/5.30 thf(fact_7254_of__int__mult,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.01/5.30 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_mult
% 5.01/5.30 thf(fact_7255_of__int__mult,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.01/5.30 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_mult
% 5.01/5.30 thf(fact_7256_of__int__mult,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 5.01/5.30 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_mult
% 5.01/5.30 thf(fact_7257_of__int__add,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.01/5.30 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_add
% 5.01/5.30 thf(fact_7258_of__int__add,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.01/5.30 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_add
% 5.01/5.30 thf(fact_7259_of__int__add,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.01/5.30 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_add
% 5.01/5.30 thf(fact_7260_of__int__add,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.01/5.30 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_add
% 5.01/5.30 thf(fact_7261_of__int__minus,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_minus
% 5.01/5.30 thf(fact_7262_of__int__minus,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_minus
% 5.01/5.30 thf(fact_7263_of__int__minus,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_minus
% 5.01/5.30 thf(fact_7264_of__int__minus,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 5.01/5.30 = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_minus
% 5.01/5.30 thf(fact_7265_of__int__minus,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 5.01/5.30 = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_minus
% 5.01/5.30 thf(fact_7266_of__int__diff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.01/5.30 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_diff
% 5.01/5.30 thf(fact_7267_of__int__diff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.01/5.30 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_diff
% 5.01/5.30 thf(fact_7268_of__int__diff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.01/5.30 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_diff
% 5.01/5.30 thf(fact_7269_of__int__diff,axiom,
% 5.01/5.30 ! [W: int,Z: int] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 5.01/5.30 = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_diff
% 5.01/5.30 thf(fact_7270_of__int__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.30 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat_eq
% 5.01/5.30 thf(fact_7271_of__int__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.30 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat_eq
% 5.01/5.30 thf(fact_7272_of__int__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.30 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat_eq
% 5.01/5.30 thf(fact_7273_of__int__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.30 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat_eq
% 5.01/5.30 thf(fact_7274_of__int__of__nat__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_18347121197199848620nteger @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.30 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat_eq
% 5.01/5.30 thf(fact_7275_of__int__power,axiom,
% 5.01/5.30 ! [Z: int,N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.01/5.30 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power
% 5.01/5.30 thf(fact_7276_of__int__power,axiom,
% 5.01/5.30 ! [Z: int,N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.01/5.30 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power
% 5.01/5.30 thf(fact_7277_of__int__power,axiom,
% 5.01/5.30 ! [Z: int,N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.01/5.30 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power
% 5.01/5.30 thf(fact_7278_of__int__power,axiom,
% 5.01/5.30 ! [Z: int,N: nat] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.01/5.30 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power
% 5.01/5.30 thf(fact_7279_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.01/5.30 = ( ring_1_of_int_rat @ X2 ) )
% 5.01/5.30 = ( ( power_power_int @ B @ W )
% 5.01/5.30 = X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7280_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.01/5.30 = ( ring_1_of_int_real @ X2 ) )
% 5.01/5.30 = ( ( power_power_int @ B @ W )
% 5.01/5.30 = X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7281_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.01/5.30 = ( ring_1_of_int_int @ X2 ) )
% 5.01/5.30 = ( ( power_power_int @ B @ W )
% 5.01/5.30 = X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7282_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.01/5.30 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.01/5.30 = ( ( power_power_int @ B @ W )
% 5.01/5.30 = X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7283_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ X2 )
% 5.01/5.30 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7284_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ X2 )
% 5.01/5.30 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7285_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ X2 )
% 5.01/5.30 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7286_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.01/5.30 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.01/5.30 = ( X2
% 5.01/5.30 = ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7287_cot__pi,axiom,
% 5.01/5.30 ( ( cot_real @ pi )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cot_pi
% 5.01/5.30 thf(fact_7288_floor__uminus__of__int,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_uminus_of_int
% 5.01/5.30 thf(fact_7289_floor__uminus__of__int,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_uminus_of_int
% 5.01/5.30 thf(fact_7290_ceiling__add__of__int,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.01/5.30 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_add_of_int
% 5.01/5.30 thf(fact_7291_ceiling__add__of__int,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.01/5.30 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_add_of_int
% 5.01/5.30 thf(fact_7292_floor__diff__of__int,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.01/5.30 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_diff_of_int
% 5.01/5.30 thf(fact_7293_floor__diff__of__int,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.01/5.30 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_diff_of_int
% 5.01/5.30 thf(fact_7294_ceiling__diff__of__int,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.01/5.30 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_diff_of_int
% 5.01/5.30 thf(fact_7295_ceiling__diff__of__int,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.01/5.30 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_diff_of_int
% 5.01/5.30 thf(fact_7296_of__nat__nat__take__bit__eq,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.30 = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat_take_bit_eq
% 5.01/5.30 thf(fact_7297_of__nat__nat__take__bit__eq,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.30 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat_take_bit_eq
% 5.01/5.30 thf(fact_7298_of__nat__nat__take__bit__eq,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.30 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat_take_bit_eq
% 5.01/5.30 thf(fact_7299_of__nat__nat__take__bit__eq,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.30 = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat_take_bit_eq
% 5.01/5.30 thf(fact_7300_of__nat__nat__take__bit__eq,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( semiri4939895301339042750nteger @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.01/5.30 = ( ring_18347121197199848620nteger @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat_take_bit_eq
% 5.01/5.30 thf(fact_7301_of__int__le__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_0_iff
% 5.01/5.30 thf(fact_7302_of__int__le__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_0_iff
% 5.01/5.30 thf(fact_7303_of__int__le__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_0_iff
% 5.01/5.30 thf(fact_7304_of__int__0__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_le_iff
% 5.01/5.30 thf(fact_7305_of__int__0__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_le_iff
% 5.01/5.30 thf(fact_7306_of__int__0__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_le_iff
% 5.01/5.30 thf(fact_7307_of__int__0__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_less_iff
% 5.01/5.30 thf(fact_7308_of__int__0__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_less_iff
% 5.01/5.30 thf(fact_7309_of__int__0__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_0_less_iff
% 5.01/5.30 thf(fact_7310_of__int__less__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.01/5.30 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_0_iff
% 5.01/5.30 thf(fact_7311_of__int__less__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.01/5.30 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_0_iff
% 5.01/5.30 thf(fact_7312_of__int__less__0__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.01/5.30 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_0_iff
% 5.01/5.30 thf(fact_7313_of__int__le__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_iff
% 5.01/5.30 thf(fact_7314_of__int__le__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_iff
% 5.01/5.30 thf(fact_7315_of__int__le__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_iff
% 5.01/5.30 thf(fact_7316_of__int__numeral__le__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_le_iff
% 5.01/5.30 thf(fact_7317_of__int__numeral__le__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_le_iff
% 5.01/5.30 thf(fact_7318_of__int__numeral__le__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_le_iff
% 5.01/5.30 thf(fact_7319_of__int__less__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_iff
% 5.01/5.30 thf(fact_7320_of__int__less__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.01/5.30 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_iff
% 5.01/5.30 thf(fact_7321_of__int__less__numeral__iff,axiom,
% 5.01/5.30 ! [Z: int,N: num] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.30 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_iff
% 5.01/5.30 thf(fact_7322_of__int__numeral__less__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_less_iff
% 5.01/5.30 thf(fact_7323_of__int__numeral__less__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_less_iff
% 5.01/5.30 thf(fact_7324_of__int__numeral__less__iff,axiom,
% 5.01/5.30 ! [N: num,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_numeral_less_iff
% 5.01/5.30 thf(fact_7325_of__int__le__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_1_iff
% 5.01/5.30 thf(fact_7326_of__int__le__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_1_iff
% 5.01/5.30 thf(fact_7327_of__int__le__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.01/5.30 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_1_iff
% 5.01/5.30 thf(fact_7328_of__int__1__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_le_iff
% 5.01/5.30 thf(fact_7329_of__int__1__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_le_iff
% 5.01/5.30 thf(fact_7330_of__int__1__le__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_le_iff
% 5.01/5.30 thf(fact_7331_of__int__1__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_less_iff
% 5.01/5.30 thf(fact_7332_of__int__1__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_less_iff
% 5.01/5.30 thf(fact_7333_of__int__1__less__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.01/5.30 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_1_less_iff
% 5.01/5.30 thf(fact_7334_of__int__less__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.01/5.30 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_1_iff
% 5.01/5.30 thf(fact_7335_of__int__less__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.01/5.30 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_1_iff
% 5.01/5.30 thf(fact_7336_of__int__less__1__iff,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.01/5.30 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_1_iff
% 5.01/5.30 thf(fact_7337_of__int__le__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7338_of__int__le__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7339_of__int__le__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7340_of__int__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7341_of__int__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7342_of__int__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7343_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.01/5.30 = ( ring_17405671764205052669omplex @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7344_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.01/5.30 = ( ring_1_of_int_real @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7345_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.01/5.30 = ( ring_1_of_int_rat @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7346_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.30 = ( ring_1_of_int_int @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7347_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.01/5.30 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7348_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ Y )
% 5.01/5.30 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7349_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ Y )
% 5.01/5.30 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7350_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ Y )
% 5.01/5.30 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7351_of__int__less__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7352_of__int__less__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7353_of__int__less__of__int__power__cancel__iff,axiom,
% 5.01/5.30 ! [B: int,W: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_of_int_power_cancel_iff
% 5.01/5.30 thf(fact_7354_of__int__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7355_of__int__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7356_of__int__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: int,B: int,W: nat] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.01/5.30 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7357_of__nat__nat,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 5.01/5.30 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat
% 5.01/5.30 thf(fact_7358_of__nat__nat,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 5.01/5.30 = ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat
% 5.01/5.30 thf(fact_7359_of__nat__nat,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.01/5.30 = ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat
% 5.01/5.30 thf(fact_7360_of__nat__nat,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z ) )
% 5.01/5.30 = ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat
% 5.01/5.30 thf(fact_7361_of__nat__nat,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ( semiri4939895301339042750nteger @ ( nat2 @ Z ) )
% 5.01/5.30 = ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_nat
% 5.01/5.30 thf(fact_7362_sin__npi__int,axiom,
% 5.01/5.30 ! [N: int] :
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_npi_int
% 5.01/5.30 thf(fact_7363_tan__periodic__int,axiom,
% 5.01/5.30 ! [X2: real,I: int] :
% 5.01/5.30 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.01/5.30 = ( tan_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_periodic_int
% 5.01/5.30 thf(fact_7364_cot__npi,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % cot_npi
% 5.01/5.30 thf(fact_7365_numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7366_numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7367_numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7368_of__int__le__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7369_of__int__le__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7370_of__int__le__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7371_numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7372_numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7373_numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7374_of__int__less__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7375_of__int__less__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7376_of__int__less__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7377_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N )
% 5.01/5.30 = ( ring_1_of_int_real @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7378_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = ( ring_1_of_int_int @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7379_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N )
% 5.01/5.30 = ( ring_17405671764205052669omplex @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7380_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 5.01/5.30 = ( ring_18347121197199848620nteger @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7381_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,Y: int] :
% 5.01/5.30 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 5.01/5.30 = ( ring_1_of_int_rat @ Y ) )
% 5.01/5.30 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.01/5.30 = Y ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_eq_of_int_cancel_iff
% 5.01/5.30 thf(fact_7382_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_real @ Y )
% 5.01/5.30 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7383_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_int @ Y )
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7384_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.01/5.30 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7385_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.01/5.30 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7386_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [Y: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ( ring_1_of_int_rat @ Y )
% 5.01/5.30 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.01/5.30 = ( Y
% 5.01/5.30 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_eq_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7387_sin__int__2pin,axiom,
% 5.01/5.30 ! [N: int] :
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % sin_int_2pin
% 5.01/5.30 thf(fact_7388_cos__int__2pin,axiom,
% 5.01/5.30 ! [N: int] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % cos_int_2pin
% 5.01/5.30 thf(fact_7389_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7390_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7391_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7392_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.01/5.30 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_le_of_int_cancel_iff
% 5.01/5.30 thf(fact_7393_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7394_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7395_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7396_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_le_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7397_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7398_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7399_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7400_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.01/5.30 ! [X2: num,N: nat,A: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.01/5.30 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % neg_numeral_power_less_of_int_cancel_iff
% 5.01/5.30 thf(fact_7401_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7402_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7403_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7404_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.01/5.30 ! [A: int,X2: num,N: nat] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.01/5.30 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_less_neg_numeral_power_cancel_iff
% 5.01/5.30 thf(fact_7405_mult__of__int__commute,axiom,
% 5.01/5.30 ! [X2: int,Y: real] :
% 5.01/5.30 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y )
% 5.01/5.30 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_of_int_commute
% 5.01/5.30 thf(fact_7406_mult__of__int__commute,axiom,
% 5.01/5.30 ! [X2: int,Y: rat] :
% 5.01/5.30 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y )
% 5.01/5.30 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_of_int_commute
% 5.01/5.30 thf(fact_7407_mult__of__int__commute,axiom,
% 5.01/5.30 ! [X2: int,Y: int] :
% 5.01/5.30 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y )
% 5.01/5.30 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_of_int_commute
% 5.01/5.30 thf(fact_7408_mult__of__int__commute,axiom,
% 5.01/5.30 ! [X2: int,Y: complex] :
% 5.01/5.30 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X2 ) @ Y )
% 5.01/5.30 = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % mult_of_int_commute
% 5.01/5.30 thf(fact_7409_ex__le__of__int,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ex_le_of_int
% 5.01/5.30 thf(fact_7410_ex__le__of__int,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ex_le_of_int
% 5.01/5.30 thf(fact_7411_ex__less__of__int,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ex_less_of_int
% 5.01/5.30 thf(fact_7412_ex__less__of__int,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ex_less_of_int
% 5.01/5.30 thf(fact_7413_ex__of__int__less,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X2 ) ).
% 5.01/5.30
% 5.01/5.30 % ex_of_int_less
% 5.01/5.30 thf(fact_7414_ex__of__int__less,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 ) ).
% 5.01/5.30
% 5.01/5.30 % ex_of_int_less
% 5.01/5.30 thf(fact_7415_of__int__floor__le,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_floor_le
% 5.01/5.30 thf(fact_7416_of__int__floor__le,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_floor_le
% 5.01/5.30 thf(fact_7417_le__of__int__ceiling,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_of_int_ceiling
% 5.01/5.30 thf(fact_7418_le__of__int__ceiling,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_of_int_ceiling
% 5.01/5.30 thf(fact_7419_take__bit__of__int,axiom,
% 5.01/5.30 ! [N: nat,K: int] :
% 5.01/5.30 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.01/5.30 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % take_bit_of_int
% 5.01/5.30 thf(fact_7420_of__int__and__eq,axiom,
% 5.01/5.30 ! [K: int,L: int] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.01/5.30 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_and_eq
% 5.01/5.30 thf(fact_7421_cos__int__times__real,axiom,
% 5.01/5.30 ! [M: int,X2: real] :
% 5.01/5.30 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.01/5.30 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_int_times_real
% 5.01/5.30 thf(fact_7422_cos__int__times__real,axiom,
% 5.01/5.30 ! [M: int,X2: real] :
% 5.01/5.30 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.01/5.30 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_int_times_real
% 5.01/5.30 thf(fact_7423_sin__int__times__real,axiom,
% 5.01/5.30 ! [M: int,X2: real] :
% 5.01/5.30 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.01/5.30 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_int_times_real
% 5.01/5.30 thf(fact_7424_sin__int__times__real,axiom,
% 5.01/5.30 ! [M: int,X2: real] :
% 5.01/5.30 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.01/5.30 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_int_times_real
% 5.01/5.30 thf(fact_7425_of__int__mask__eq,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.30 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_mask_eq
% 5.01/5.30 thf(fact_7426_le__floor__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_floor_iff
% 5.01/5.30 thf(fact_7427_le__floor__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_floor_iff
% 5.01/5.30 thf(fact_7428_floor__less__iff,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_iff
% 5.01/5.30 thf(fact_7429_floor__less__iff,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_less_iff
% 5.01/5.30 thf(fact_7430_ceiling__le,axiom,
% 5.01/5.30 ! [X2: real,A: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le
% 5.01/5.30 thf(fact_7431_ceiling__le,axiom,
% 5.01/5.30 ! [X2: rat,A: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le
% 5.01/5.30 thf(fact_7432_ceiling__le__iff,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le_iff
% 5.01/5.30 thf(fact_7433_ceiling__le__iff,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_le_iff
% 5.01/5.30 thf(fact_7434_less__ceiling__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_ceiling_iff
% 5.01/5.30 thf(fact_7435_less__ceiling__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_ceiling_iff
% 5.01/5.30 thf(fact_7436_floor__add__int,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.01/5.30 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_add_int
% 5.01/5.30 thf(fact_7437_floor__add__int,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.01/5.30 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_add_int
% 5.01/5.30 thf(fact_7438_int__add__floor,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % int_add_floor
% 5.01/5.30 thf(fact_7439_int__add__floor,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % int_add_floor
% 5.01/5.30 thf(fact_7440_real__of__int__div4,axiom,
% 5.01/5.30 ! [N: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_div4
% 5.01/5.30 thf(fact_7441_floor__divide__of__int__eq,axiom,
% 5.01/5.30 ! [K: int,L: int] :
% 5.01/5.30 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.01/5.30 = ( divide_divide_int @ K @ L ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_of_int_eq
% 5.01/5.30 thf(fact_7442_floor__divide__of__int__eq,axiom,
% 5.01/5.30 ! [K: int,L: int] :
% 5.01/5.30 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.01/5.30 = ( divide_divide_int @ K @ L ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_of_int_eq
% 5.01/5.30 thf(fact_7443_floor__power,axiom,
% 5.01/5.30 ! [X2: real,N: nat] :
% 5.01/5.30 ( ( X2
% 5.01/5.30 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X2 @ N ) )
% 5.01/5.30 = ( power_power_int @ ( archim6058952711729229775r_real @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_power
% 5.01/5.30 thf(fact_7444_floor__power,axiom,
% 5.01/5.30 ! [X2: rat,N: nat] :
% 5.01/5.30 ( ( X2
% 5.01/5.30 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.01/5.30 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X2 @ N ) )
% 5.01/5.30 = ( power_power_int @ ( archim3151403230148437115or_rat @ X2 ) @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_power
% 5.01/5.30 thf(fact_7445_real__of__int__div,axiom,
% 5.01/5.30 ! [D: int,N: int] :
% 5.01/5.30 ( ( dvd_dvd_int @ D @ N )
% 5.01/5.30 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.01/5.30 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_div
% 5.01/5.30 thf(fact_7446_of__int__nonneg,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_nonneg
% 5.01/5.30 thf(fact_7447_of__int__nonneg,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_nonneg
% 5.01/5.30 thf(fact_7448_of__int__nonneg,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_nonneg
% 5.01/5.30 thf(fact_7449_of__int__leD,axiom,
% 5.01/5.30 ! [N: int,X2: code_integer] :
% 5.01/5.30 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_leD
% 5.01/5.30 thf(fact_7450_of__int__leD,axiom,
% 5.01/5.30 ! [N: int,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_leD
% 5.01/5.30 thf(fact_7451_of__int__leD,axiom,
% 5.01/5.30 ! [N: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_leD
% 5.01/5.30 thf(fact_7452_of__int__leD,axiom,
% 5.01/5.30 ! [N: int,X2: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_leD
% 5.01/5.30 thf(fact_7453_of__int__pos,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_pos
% 5.01/5.30 thf(fact_7454_of__int__pos,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_pos
% 5.01/5.30 thf(fact_7455_of__int__pos,axiom,
% 5.01/5.30 ! [Z: int] :
% 5.01/5.30 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.01/5.30 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_pos
% 5.01/5.30 thf(fact_7456_of__int__lessD,axiom,
% 5.01/5.30 ! [N: int,X2: code_integer] :
% 5.01/5.30 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_lessD
% 5.01/5.30 thf(fact_7457_of__int__lessD,axiom,
% 5.01/5.30 ! [N: int,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_lessD
% 5.01/5.30 thf(fact_7458_of__int__lessD,axiom,
% 5.01/5.30 ! [N: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_lessD
% 5.01/5.30 thf(fact_7459_of__int__lessD,axiom,
% 5.01/5.30 ! [N: int,X2: int] :
% 5.01/5.30 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.01/5.30 => ( ( N = zero_zero_int )
% 5.01/5.30 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_lessD
% 5.01/5.30 thf(fact_7460_floor__exists,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [Z3: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_exists
% 5.01/5.30 thf(fact_7461_floor__exists,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ? [Z3: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 5.01/5.30 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_exists
% 5.01/5.30 thf(fact_7462_floor__exists1,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ? [X4: int] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.01/5.30 & ! [Y4: int] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_exists1
% 5.01/5.30 thf(fact_7463_floor__exists1,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ? [X4: int] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X2 )
% 5.01/5.30 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.01/5.30 & ! [Y4: int] :
% 5.01/5.30 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X2 )
% 5.01/5.30 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.01/5.30 => ( Y4 = X4 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_exists1
% 5.01/5.30 thf(fact_7464_of__int__ceiling__le__add__one,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ ( plus_plus_real @ R @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_le_add_one
% 5.01/5.30 thf(fact_7465_of__int__ceiling__le__add__one,axiom,
% 5.01/5.30 ! [R: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ ( plus_plus_rat @ R @ one_one_rat ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_le_add_one
% 5.01/5.30 thf(fact_7466_of__int__neg__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.30 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_neg_numeral
% 5.01/5.30 thf(fact_7467_of__int__neg__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_neg_numeral
% 5.01/5.30 thf(fact_7468_of__int__neg__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.30 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_neg_numeral
% 5.01/5.30 thf(fact_7469_of__int__neg__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.30 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_neg_numeral
% 5.01/5.30 thf(fact_7470_of__int__neg__numeral,axiom,
% 5.01/5.30 ! [K: num] :
% 5.01/5.30 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.30 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_neg_numeral
% 5.01/5.30 thf(fact_7471_of__int__ceiling__diff__one__le,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R ) ) @ one_one_real ) @ R ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_diff_one_le
% 5.01/5.30 thf(fact_7472_of__int__ceiling__diff__one__le,axiom,
% 5.01/5.30 ! [R: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R ) ) @ one_one_rat ) @ R ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_ceiling_diff_one_le
% 5.01/5.30 thf(fact_7473_of__nat__less__of__int__iff,axiom,
% 5.01/5.30 ! [N: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_less_of_int_iff
% 5.01/5.30 thf(fact_7474_of__nat__less__of__int__iff,axiom,
% 5.01/5.30 ! [N: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_less_of_int_iff
% 5.01/5.30 thf(fact_7475_of__nat__less__of__int__iff,axiom,
% 5.01/5.30 ! [N: nat,X2: int] :
% 5.01/5.30 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_less_of_int_iff
% 5.01/5.30 thf(fact_7476_of__nat__less__of__int__iff,axiom,
% 5.01/5.30 ! [N: nat,X2: int] :
% 5.01/5.30 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( ring_18347121197199848620nteger @ X2 ) )
% 5.01/5.30 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_nat_less_of_int_iff
% 5.01/5.30 thf(fact_7477_int__le__real__less,axiom,
% 5.01/5.30 ( ord_less_eq_int
% 5.01/5.30 = ( ^ [N4: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % int_le_real_less
% 5.01/5.30 thf(fact_7478_int__less__real__le,axiom,
% 5.01/5.30 ( ord_less_int
% 5.01/5.30 = ( ^ [N4: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % int_less_real_le
% 5.01/5.30 thf(fact_7479_ceiling__divide__eq__div,axiom,
% 5.01/5.30 ! [A: int,B: int] :
% 5.01/5.30 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_eq_div
% 5.01/5.30 thf(fact_7480_ceiling__divide__eq__div,axiom,
% 5.01/5.30 ! [A: int,B: int] :
% 5.01/5.30 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_eq_div
% 5.01/5.30 thf(fact_7481_sin__zero__iff__int2,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( sin_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( ? [I4: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % sin_zero_iff_int2
% 5.01/5.30 thf(fact_7482_ceiling__altdef,axiom,
% 5.01/5.30 ( archim7802044766580827645g_real
% 5.01/5.30 = ( ^ [X3: real] :
% 5.01/5.30 ( if_int
% 5.01/5.30 @ ( X3
% 5.01/5.30 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) )
% 5.01/5.30 @ ( archim6058952711729229775r_real @ X3 )
% 5.01/5.30 @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X3 ) @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_altdef
% 5.01/5.30 thf(fact_7483_ceiling__altdef,axiom,
% 5.01/5.30 ( archim2889992004027027881ng_rat
% 5.01/5.30 = ( ^ [X3: rat] :
% 5.01/5.30 ( if_int
% 5.01/5.30 @ ( X3
% 5.01/5.30 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 5.01/5.30 @ ( archim3151403230148437115or_rat @ X3 )
% 5.01/5.30 @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_altdef
% 5.01/5.30 thf(fact_7484_real__of__int__div__aux,axiom,
% 5.01/5.30 ! [X2: int,D: int] :
% 5.01/5.30 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D ) )
% 5.01/5.30 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_div_aux
% 5.01/5.30 thf(fact_7485_real__of__int__floor__add__one__gt,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_floor_add_one_gt
% 5.01/5.30 thf(fact_7486_floor__eq,axiom,
% 5.01/5.30 ! [N: int,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ X2 )
% 5.01/5.30 = N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq
% 5.01/5.30 thf(fact_7487_real__of__int__floor__add__one__ge,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_floor_add_one_ge
% 5.01/5.30 thf(fact_7488_real__of__int__floor__gt__diff__one,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_floor_gt_diff_one
% 5.01/5.30 thf(fact_7489_real__of__int__floor__ge__diff__one,axiom,
% 5.01/5.30 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_floor_ge_diff_one
% 5.01/5.30 thf(fact_7490_floor__unique,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ X2 )
% 5.01/5.30 = Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_unique
% 5.01/5.30 thf(fact_7491_floor__unique,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 )
% 5.01/5.30 => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.01/5.30 => ( ( archim3151403230148437115or_rat @ X2 )
% 5.01/5.30 = Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_unique
% 5.01/5.30 thf(fact_7492_floor__eq__iff,axiom,
% 5.01/5.30 ! [X2: real,A: int] :
% 5.01/5.30 ( ( ( archim6058952711729229775r_real @ X2 )
% 5.01/5.30 = A )
% 5.01/5.30 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq_iff
% 5.01/5.30 thf(fact_7493_floor__eq__iff,axiom,
% 5.01/5.30 ! [X2: rat,A: int] :
% 5.01/5.30 ( ( ( archim3151403230148437115or_rat @ X2 )
% 5.01/5.30 = A )
% 5.01/5.30 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 5.01/5.30 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq_iff
% 5.01/5.30 thf(fact_7494_floor__split,axiom,
% 5.01/5.30 ! [P: int > $o,T: real] :
% 5.01/5.30 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.01/5.30 = ( ! [I4: int] :
% 5.01/5.30 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 5.01/5.30 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 5.01/5.30 => ( P @ I4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_split
% 5.01/5.30 thf(fact_7495_floor__split,axiom,
% 5.01/5.30 ! [P: int > $o,T: rat] :
% 5.01/5.30 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.01/5.30 = ( ! [I4: int] :
% 5.01/5.30 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 5.01/5.30 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.01/5.30 => ( P @ I4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_split
% 5.01/5.30 thf(fact_7496_ceiling__correct,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.01/5.30 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_correct
% 5.01/5.30 thf(fact_7497_ceiling__correct,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.01/5.30 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_correct
% 5.01/5.30 thf(fact_7498_ceiling__unique,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.30 => ( ( archim7802044766580827645g_real @ X2 )
% 5.01/5.30 = Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_unique
% 5.01/5.30 thf(fact_7499_ceiling__unique,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.30 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.01/5.30 = Z ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_unique
% 5.01/5.30 thf(fact_7500_ceiling__eq__iff,axiom,
% 5.01/5.30 ! [X2: real,A: int] :
% 5.01/5.30 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.01/5.30 = A )
% 5.01/5.30 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X2 )
% 5.01/5.30 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_eq_iff
% 5.01/5.30 thf(fact_7501_ceiling__eq__iff,axiom,
% 5.01/5.30 ! [X2: rat,A: int] :
% 5.01/5.30 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.01/5.30 = A )
% 5.01/5.30 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 5.01/5.30 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_eq_iff
% 5.01/5.30 thf(fact_7502_ceiling__split,axiom,
% 5.01/5.30 ! [P: int > $o,T: real] :
% 5.01/5.30 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.01/5.30 = ( ! [I4: int] :
% 5.01/5.30 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.01/5.30 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.01/5.30 => ( P @ I4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_split
% 5.01/5.30 thf(fact_7503_ceiling__split,axiom,
% 5.01/5.30 ! [P: int > $o,T: rat] :
% 5.01/5.30 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.01/5.30 = ( ! [I4: int] :
% 5.01/5.30 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.01/5.30 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.01/5.30 => ( P @ I4 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_split
% 5.01/5.30 thf(fact_7504_less__floor__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_floor_iff
% 5.01/5.30 thf(fact_7505_less__floor__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % less_floor_iff
% 5.01/5.30 thf(fact_7506_floor__le__iff,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_iff
% 5.01/5.30 thf(fact_7507_floor__le__iff,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_iff
% 5.01/5.30 thf(fact_7508_cot__def,axiom,
% 5.01/5.30 ( cot_complex
% 5.01/5.30 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X3 ) @ ( sin_complex @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_def
% 5.01/5.30 thf(fact_7509_cot__def,axiom,
% 5.01/5.30 ( cot_real
% 5.01/5.30 = ( ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_def
% 5.01/5.30 thf(fact_7510_ceiling__less__iff,axiom,
% 5.01/5.30 ! [X2: real,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_iff
% 5.01/5.30 thf(fact_7511_ceiling__less__iff,axiom,
% 5.01/5.30 ! [X2: rat,Z: int] :
% 5.01/5.30 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.01/5.30 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_less_iff
% 5.01/5.30 thf(fact_7512_le__ceiling__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.01/5.30 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_ceiling_iff
% 5.01/5.30 thf(fact_7513_le__ceiling__iff,axiom,
% 5.01/5.30 ! [Z: int,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.01/5.30 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % le_ceiling_iff
% 5.01/5.30 thf(fact_7514_floor__correct,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_correct
% 5.01/5.30 thf(fact_7515_floor__correct,axiom,
% 5.01/5.30 ! [X2: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 5.01/5.30 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_correct
% 5.01/5.30 thf(fact_7516_real__of__int__div2,axiom,
% 5.01/5.30 ! [N: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_div2
% 5.01/5.30 thf(fact_7517_real__of__int__div3,axiom,
% 5.01/5.30 ! [N: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % real_of_int_div3
% 5.01/5.30 thf(fact_7518_floor__eq2,axiom,
% 5.01/5.30 ! [N: int,X2: real] :
% 5.01/5.30 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ X2 )
% 5.01/5.30 = N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_eq2
% 5.01/5.30 thf(fact_7519_floor__divide__real__eq__div,axiom,
% 5.01/5.30 ! [B: int,A: real] :
% 5.01/5.30 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.01/5.30 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.01/5.30 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_real_eq_div
% 5.01/5.30 thf(fact_7520_floor__divide__lower,axiom,
% 5.01/5.30 ! [Q2: real,P4: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.01/5.30 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q2 ) ) ) @ Q2 ) @ P4 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_lower
% 5.01/5.30 thf(fact_7521_floor__divide__lower,axiom,
% 5.01/5.30 ! [Q2: rat,P4: rat] :
% 5.01/5.30 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.01/5.30 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q2 ) ) ) @ Q2 ) @ P4 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_lower
% 5.01/5.30 thf(fact_7522_ceiling__divide__upper,axiom,
% 5.01/5.30 ! [Q2: real,P4: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.01/5.30 => ( ord_less_eq_real @ P4 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_upper
% 5.01/5.30 thf(fact_7523_ceiling__divide__upper,axiom,
% 5.01/5.30 ! [Q2: rat,P4: rat] :
% 5.01/5.30 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.01/5.30 => ( ord_less_eq_rat @ P4 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_upper
% 5.01/5.30 thf(fact_7524_even__of__int__iff,axiom,
% 5.01/5.30 ! [K: int] :
% 5.01/5.30 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.01/5.30 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % even_of_int_iff
% 5.01/5.30 thf(fact_7525_even__of__int__iff,axiom,
% 5.01/5.30 ! [K: int] :
% 5.01/5.30 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.01/5.30 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.01/5.30
% 5.01/5.30 % even_of_int_iff
% 5.01/5.30 thf(fact_7526_of__int__of__nat,axiom,
% 5.01/5.30 ( ring_1_of_int_rat
% 5.01/5.30 = ( ^ [K2: int] : ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat
% 5.01/5.30 thf(fact_7527_of__int__of__nat,axiom,
% 5.01/5.30 ( ring_1_of_int_real
% 5.01/5.30 = ( ^ [K2: int] : ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat
% 5.01/5.30 thf(fact_7528_of__int__of__nat,axiom,
% 5.01/5.30 ( ring_1_of_int_int
% 5.01/5.30 = ( ^ [K2: int] : ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat
% 5.01/5.30 thf(fact_7529_of__int__of__nat,axiom,
% 5.01/5.30 ( ring_17405671764205052669omplex
% 5.01/5.30 = ( ^ [K2: int] : ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat
% 5.01/5.30 thf(fact_7530_of__int__of__nat,axiom,
% 5.01/5.30 ( ring_18347121197199848620nteger
% 5.01/5.30 = ( ^ [K2: int] : ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K2 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K2 ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_of_nat
% 5.01/5.30 thf(fact_7531_floor__divide__upper,axiom,
% 5.01/5.30 ! [Q2: real,P4: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.01/5.30 => ( ord_less_real @ P4 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_upper
% 5.01/5.30 thf(fact_7532_floor__divide__upper,axiom,
% 5.01/5.30 ! [Q2: rat,P4: rat] :
% 5.01/5.30 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.01/5.30 => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_divide_upper
% 5.01/5.30 thf(fact_7533_ceiling__divide__lower,axiom,
% 5.01/5.30 ! [Q2: real,P4: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.01/5.30 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P4 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_lower
% 5.01/5.30 thf(fact_7534_ceiling__divide__lower,axiom,
% 5.01/5.30 ! [Q2: rat,P4: rat] :
% 5.01/5.30 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.01/5.30 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P4 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_divide_lower
% 5.01/5.30 thf(fact_7535_ceiling__eq,axiom,
% 5.01/5.30 ! [N: int,X2: real] :
% 5.01/5.30 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.01/5.30 => ( ( archim7802044766580827645g_real @ X2 )
% 5.01/5.30 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_eq
% 5.01/5.30 thf(fact_7536_ceiling__eq,axiom,
% 5.01/5.30 ! [N: int,X2: rat] :
% 5.01/5.30 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.01/5.30 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.01/5.30 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.01/5.30 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_eq
% 5.01/5.30 thf(fact_7537_cos__one__2pi__int,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 = one_one_real )
% 5.01/5.30 = ( ? [X3: int] :
% 5.01/5.30 ( X2
% 5.01/5.30 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_one_2pi_int
% 5.01/5.30 thf(fact_7538_arccos__cos__eq__abs__2pi,axiom,
% 5.01/5.30 ! [Theta: real] :
% 5.01/5.30 ~ ! [K3: int] :
% 5.01/5.30 ( ( arccos @ ( cos_real @ Theta ) )
% 5.01/5.30 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % arccos_cos_eq_abs_2pi
% 5.01/5.30 thf(fact_7539_floor__log__eq__powr__iff,axiom,
% 5.01/5.30 ! [X2: real,B: real,K: int] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ one_one_real @ B )
% 5.01/5.30 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X2 ) )
% 5.01/5.30 = K )
% 5.01/5.30 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.01/5.30 & ( ord_less_real @ X2 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_log_eq_powr_iff
% 5.01/5.30 thf(fact_7540_cot__gt__zero,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cot_gt_zero
% 5.01/5.30 thf(fact_7541_tan__cot_H,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.01/5.30 = ( cot_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % tan_cot'
% 5.01/5.30 thf(fact_7542_cos__zero__iff__int,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.30 ( ( ( cos_real @ X2 )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( ? [I4: int] :
% 5.01/5.30 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.01/5.30 & ( X2
% 5.01/5.30 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % cos_zero_iff_int
% 5.01/5.30 thf(fact_7543_round__unique,axiom,
% 5.01/5.30 ! [X2: real,Y: int] :
% 5.01/5.30 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.01/5.30 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 => ( ( archim8280529875227126926d_real @ X2 )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_unique
% 5.01/5.30 thf(fact_7544_round__unique,axiom,
% 5.01/5.30 ! [X2: rat,Y: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.01/5.30 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.01/5.30 = Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_unique
% 5.01/5.30 thf(fact_7545_round__unique_H,axiom,
% 5.01/5.30 ! [X2: real,N: int] :
% 5.01/5.30 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( archim8280529875227126926d_real @ X2 )
% 5.01/5.30 = N ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_unique'
% 5.01/5.30 thf(fact_7546_round__unique_H,axiom,
% 5.01/5.30 ! [X2: rat,N: int] :
% 5.01/5.30 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.01/5.30 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.01/5.30 = N ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_unique'
% 5.01/5.30 thf(fact_7547_of__int__round__abs__le,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_abs_le
% 5.01/5.30 thf(fact_7548_of__int__round__abs__le,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_abs_le
% 5.01/5.30 thf(fact_7549_of__int__round__gt,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_gt
% 5.01/5.30 thf(fact_7550_of__int__round__gt,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_gt
% 5.01/5.30 thf(fact_7551_of__int__round__ge,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_ge
% 5.01/5.30 thf(fact_7552_of__int__round__ge,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_ge
% 5.01/5.30 thf(fact_7553_round__0,axiom,
% 5.01/5.30 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.01/5.30 = zero_zero_int ) ).
% 5.01/5.30
% 5.01/5.30 % round_0
% 5.01/5.30 thf(fact_7554_round__0,axiom,
% 5.01/5.30 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.01/5.30 = zero_zero_int ) ).
% 5.01/5.30
% 5.01/5.30 % round_0
% 5.01/5.30 thf(fact_7555_round__numeral,axiom,
% 5.01/5.30 ! [N: num] :
% 5.01/5.30 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_numeral
% 5.01/5.30 thf(fact_7556_round__numeral,axiom,
% 5.01/5.30 ! [N: num] :
% 5.01/5.30 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.01/5.30 = ( numeral_numeral_int @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_numeral
% 5.01/5.30 thf(fact_7557_round__1,axiom,
% 5.01/5.30 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.01/5.30 = one_one_int ) ).
% 5.01/5.30
% 5.01/5.30 % round_1
% 5.01/5.30 thf(fact_7558_round__1,axiom,
% 5.01/5.30 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.01/5.30 = one_one_int ) ).
% 5.01/5.30
% 5.01/5.30 % round_1
% 5.01/5.30 thf(fact_7559_round__of__nat,axiom,
% 5.01/5.30 ! [N: nat] :
% 5.01/5.30 ( ( archim8280529875227126926d_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.01/5.30 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_of_nat
% 5.01/5.30 thf(fact_7560_round__neg__numeral,axiom,
% 5.01/5.30 ! [N: num] :
% 5.01/5.30 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_neg_numeral
% 5.01/5.30 thf(fact_7561_round__neg__numeral,axiom,
% 5.01/5.30 ! [N: num] :
% 5.01/5.30 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.01/5.30 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_neg_numeral
% 5.01/5.30 thf(fact_7562_round__mono,axiom,
% 5.01/5.30 ! [X2: rat,Y: rat] :
% 5.01/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.30 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_mono
% 5.01/5.30 thf(fact_7563_floor__le__round,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim8280529875227126926d_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_round
% 5.01/5.30 thf(fact_7564_floor__le__round,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % floor_le_round
% 5.01/5.30 thf(fact_7565_ceiling__ge__round,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X2 ) @ ( archim7802044766580827645g_real @ X2 ) ) ).
% 5.01/5.30
% 5.01/5.30 % ceiling_ge_round
% 5.01/5.30 thf(fact_7566_round__diff__minimal,axiom,
% 5.01/5.30 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_diff_minimal
% 5.01/5.30 thf(fact_7567_round__diff__minimal,axiom,
% 5.01/5.30 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_diff_minimal
% 5.01/5.30 thf(fact_7568_round__def,axiom,
% 5.01/5.30 ( archim8280529875227126926d_real
% 5.01/5.30 = ( ^ [X3: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_def
% 5.01/5.30 thf(fact_7569_round__def,axiom,
% 5.01/5.30 ( archim7778729529865785530nd_rat
% 5.01/5.30 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_def
% 5.01/5.30 thf(fact_7570_of__int__round__le,axiom,
% 5.01/5.30 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_le
% 5.01/5.30 thf(fact_7571_of__int__round__le,axiom,
% 5.01/5.30 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % of_int_round_le
% 5.01/5.30 thf(fact_7572_round__altdef,axiom,
% 5.01/5.30 ( archim8280529875227126926d_real
% 5.01/5.30 = ( ^ [X3: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X3 ) ) @ ( archim7802044766580827645g_real @ X3 ) @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_altdef
% 5.01/5.30 thf(fact_7573_round__altdef,axiom,
% 5.01/5.30 ( archim7778729529865785530nd_rat
% 5.01/5.30 = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % round_altdef
% 5.01/5.30 thf(fact_7574_exp__two__pi__i,axiom,
% 5.01/5.30 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % exp_two_pi_i
% 5.01/5.30 thf(fact_7575_exp__two__pi__i_H,axiom,
% 5.01/5.30 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % exp_two_pi_i'
% 5.01/5.30 thf(fact_7576_powr__real__of__int,axiom,
% 5.01/5.30 ! [X2: real,N: int] :
% 5.01/5.30 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.30 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.01/5.30 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.01/5.30 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.01/5.30 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.01/5.30 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % powr_real_of_int
% 5.01/5.30 thf(fact_7577_cis__2pi,axiom,
% 5.01/5.30 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % cis_2pi
% 5.01/5.30 thf(fact_7578_inverse__eq__iff__eq,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( ( inverse_inverse_real @ A )
% 5.01/5.30 = ( inverse_inverse_real @ B ) )
% 5.01/5.30 = ( A = B ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_eq_iff_eq
% 5.01/5.30 thf(fact_7579_inverse__eq__iff__eq,axiom,
% 5.01/5.30 ! [A: complex,B: complex] :
% 5.01/5.30 ( ( ( invers8013647133539491842omplex @ A )
% 5.01/5.30 = ( invers8013647133539491842omplex @ B ) )
% 5.01/5.30 = ( A = B ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_eq_iff_eq
% 5.01/5.30 thf(fact_7580_inverse__eq__iff__eq,axiom,
% 5.01/5.30 ! [A: rat,B: rat] :
% 5.01/5.30 ( ( ( inverse_inverse_rat @ A )
% 5.01/5.30 = ( inverse_inverse_rat @ B ) )
% 5.01/5.30 = ( A = B ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_eq_iff_eq
% 5.01/5.30 thf(fact_7581_inverse__inverse__eq,axiom,
% 5.01/5.30 ! [A: real] :
% 5.01/5.30 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.30 = A ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_inverse_eq
% 5.01/5.30 thf(fact_7582_inverse__inverse__eq,axiom,
% 5.01/5.30 ! [A: complex] :
% 5.01/5.30 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.30 = A ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_inverse_eq
% 5.01/5.30 thf(fact_7583_inverse__inverse__eq,axiom,
% 5.01/5.30 ! [A: rat] :
% 5.01/5.30 ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.30 = A ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_inverse_eq
% 5.01/5.30 thf(fact_7584_inverse__zero,axiom,
% 5.01/5.30 ( ( inverse_inverse_real @ zero_zero_real )
% 5.01/5.30 = zero_zero_real ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_zero
% 5.01/5.30 thf(fact_7585_inverse__zero,axiom,
% 5.01/5.30 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.01/5.30 = zero_zero_complex ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_zero
% 5.01/5.30 thf(fact_7586_inverse__zero,axiom,
% 5.01/5.30 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.01/5.30 = zero_zero_rat ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_zero
% 5.01/5.30 thf(fact_7587_inverse__nonzero__iff__nonzero,axiom,
% 5.01/5.30 ! [A: real] :
% 5.01/5.30 ( ( ( inverse_inverse_real @ A )
% 5.01/5.30 = zero_zero_real )
% 5.01/5.30 = ( A = zero_zero_real ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_nonzero_iff_nonzero
% 5.01/5.30 thf(fact_7588_inverse__nonzero__iff__nonzero,axiom,
% 5.01/5.30 ! [A: complex] :
% 5.01/5.30 ( ( ( invers8013647133539491842omplex @ A )
% 5.01/5.30 = zero_zero_complex )
% 5.01/5.30 = ( A = zero_zero_complex ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_nonzero_iff_nonzero
% 5.01/5.30 thf(fact_7589_inverse__nonzero__iff__nonzero,axiom,
% 5.01/5.30 ! [A: rat] :
% 5.01/5.30 ( ( ( inverse_inverse_rat @ A )
% 5.01/5.30 = zero_zero_rat )
% 5.01/5.30 = ( A = zero_zero_rat ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_nonzero_iff_nonzero
% 5.01/5.30 thf(fact_7590_inverse__mult__distrib,axiom,
% 5.01/5.30 ! [A: real,B: real] :
% 5.01/5.30 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.01/5.30 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_mult_distrib
% 5.01/5.30 thf(fact_7591_inverse__mult__distrib,axiom,
% 5.01/5.30 ! [A: complex,B: complex] :
% 5.01/5.30 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.01/5.30 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_mult_distrib
% 5.01/5.30 thf(fact_7592_inverse__mult__distrib,axiom,
% 5.01/5.30 ! [A: rat,B: rat] :
% 5.01/5.30 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.30 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_mult_distrib
% 5.01/5.30 thf(fact_7593_inverse__1,axiom,
% 5.01/5.30 ( ( inverse_inverse_real @ one_one_real )
% 5.01/5.30 = one_one_real ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_1
% 5.01/5.30 thf(fact_7594_inverse__1,axiom,
% 5.01/5.30 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.01/5.30 = one_one_complex ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_1
% 5.01/5.30 thf(fact_7595_inverse__1,axiom,
% 5.01/5.30 ( ( inverse_inverse_rat @ one_one_rat )
% 5.01/5.30 = one_one_rat ) ).
% 5.01/5.30
% 5.01/5.30 % inverse_1
% 5.01/5.30 thf(fact_7596_inverse__eq__1__iff,axiom,
% 5.01/5.30 ! [X2: real] :
% 5.01/5.31 ( ( ( inverse_inverse_real @ X2 )
% 5.01/5.31 = one_one_real )
% 5.01/5.31 = ( X2 = one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_1_iff
% 5.01/5.31 thf(fact_7597_inverse__eq__1__iff,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( ( invers8013647133539491842omplex @ X2 )
% 5.01/5.31 = one_one_complex )
% 5.01/5.31 = ( X2 = one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_1_iff
% 5.01/5.31 thf(fact_7598_inverse__eq__1__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ( inverse_inverse_rat @ X2 )
% 5.01/5.31 = one_one_rat )
% 5.01/5.31 = ( X2 = one_one_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_1_iff
% 5.01/5.31 thf(fact_7599_inverse__divide,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.01/5.31 = ( divide_divide_real @ B @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_divide
% 5.01/5.31 thf(fact_7600_inverse__divide,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.31 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_divide
% 5.01/5.31 thf(fact_7601_inverse__divide,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.01/5.31 = ( divide_divide_rat @ B @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_divide
% 5.01/5.31 thf(fact_7602_inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_minus_eq
% 5.01/5.31 thf(fact_7603_inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_minus_eq
% 5.01/5.31 thf(fact_7604_inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.01/5.31 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_minus_eq
% 5.01/5.31 thf(fact_7605_abs__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % abs_inverse
% 5.01/5.31 thf(fact_7606_abs__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.31 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % abs_inverse
% 5.01/5.31 thf(fact_7607_abs__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % abs_inverse
% 5.01/5.31 thf(fact_7608_sgn__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sgn_inverse
% 5.01/5.31 thf(fact_7609_sgn__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.31 = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sgn_inverse
% 5.01/5.31 thf(fact_7610_sgn__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sgn_inverse
% 5.01/5.31 thf(fact_7611_inverse__sgn,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 5.01/5.31 = ( sgn_sgn_real @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_sgn
% 5.01/5.31 thf(fact_7612_inverse__sgn,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 5.01/5.31 = ( sgn_sgn_rat @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_sgn
% 5.01/5.31 thf(fact_7613_inverse__nonnegative__iff__nonnegative,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_nonnegative_iff_nonnegative
% 5.01/5.31 thf(fact_7614_inverse__nonnegative__iff__nonnegative,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_nonnegative_iff_nonnegative
% 5.01/5.31 thf(fact_7615_inverse__nonpositive__iff__nonpositive,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.01/5.31 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_nonpositive_iff_nonpositive
% 5.01/5.31 thf(fact_7616_inverse__nonpositive__iff__nonpositive,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.01/5.31 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_nonpositive_iff_nonpositive
% 5.01/5.31 thf(fact_7617_inverse__less__iff__less,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.31 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff_less
% 5.01/5.31 thf(fact_7618_inverse__less__iff__less,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.31 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff_less
% 5.01/5.31 thf(fact_7619_inverse__less__iff__less__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff_less_neg
% 5.01/5.31 thf(fact_7620_inverse__less__iff__less__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff_less_neg
% 5.01/5.31 thf(fact_7621_inverse__negative__iff__negative,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.01/5.31 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_negative_iff_negative
% 5.01/5.31 thf(fact_7622_inverse__negative__iff__negative,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.01/5.31 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_negative_iff_negative
% 5.01/5.31 thf(fact_7623_inverse__positive__iff__positive,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_positive_iff_positive
% 5.01/5.31 thf(fact_7624_inverse__positive__iff__positive,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_positive_iff_positive
% 5.01/5.31 thf(fact_7625_frac__of__int,axiom,
% 5.01/5.31 ! [Z: int] :
% 5.01/5.31 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 5.01/5.31 = zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % frac_of_int
% 5.01/5.31 thf(fact_7626_frac__of__int,axiom,
% 5.01/5.31 ! [Z: int] :
% 5.01/5.31 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.01/5.31 = zero_zero_rat ) ).
% 5.01/5.31
% 5.01/5.31 % frac_of_int
% 5.01/5.31 thf(fact_7627_norm__ii,axiom,
% 5.01/5.31 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % norm_ii
% 5.01/5.31 thf(fact_7628_norm__cis,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % norm_cis
% 5.01/5.31 thf(fact_7629_cis__zero,axiom,
% 5.01/5.31 ( ( cis @ zero_zero_real )
% 5.01/5.31 = one_one_complex ) ).
% 5.01/5.31
% 5.01/5.31 % cis_zero
% 5.01/5.31 thf(fact_7630_inverse__le__iff__le,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.31 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff_le
% 5.01/5.31 thf(fact_7631_inverse__le__iff__le,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.01/5.31 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff_le
% 5.01/5.31 thf(fact_7632_inverse__le__iff__le__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff_le_neg
% 5.01/5.31 thf(fact_7633_inverse__le__iff__le__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff_le_neg
% 5.01/5.31 thf(fact_7634_right__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % right_inverse
% 5.01/5.31 thf(fact_7635_right__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.31 = one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % right_inverse
% 5.01/5.31 thf(fact_7636_right__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = one_one_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % right_inverse
% 5.01/5.31 thf(fact_7637_left__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.01/5.31 = one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % left_inverse
% 5.01/5.31 thf(fact_7638_left__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.01/5.31 = one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % left_inverse
% 5.01/5.31 thf(fact_7639_left__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.01/5.31 = one_one_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % left_inverse
% 5.01/5.31 thf(fact_7640_inverse__eq__divide__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.01/5.31 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_numeral
% 5.01/5.31 thf(fact_7641_inverse__eq__divide__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.01/5.31 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_numeral
% 5.01/5.31 thf(fact_7642_inverse__eq__divide__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.01/5.31 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_numeral
% 5.01/5.31 thf(fact_7643_inverse__eq__divide__neg__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.01/5.31 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_neg_numeral
% 5.01/5.31 thf(fact_7644_inverse__eq__divide__neg__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.31 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_neg_numeral
% 5.01/5.31 thf(fact_7645_inverse__eq__divide__neg__numeral,axiom,
% 5.01/5.31 ! [W: num] :
% 5.01/5.31 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.01/5.31 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide_neg_numeral
% 5.01/5.31 thf(fact_7646_power2__i,axiom,
% 5.01/5.31 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % power2_i
% 5.01/5.31 thf(fact_7647_cis__pi__half,axiom,
% 5.01/5.31 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = imaginary_unit ) ).
% 5.01/5.31
% 5.01/5.31 % cis_pi_half
% 5.01/5.31 thf(fact_7648_i__even__power,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.01/5.31
% 5.01/5.31 % i_even_power
% 5.01/5.31 thf(fact_7649_cis__minus__pi__half,axiom,
% 5.01/5.31 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_minus_pi_half
% 5.01/5.31 thf(fact_7650_nonzero__norm__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( real_V7735802525324610683m_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_norm_inverse
% 5.01/5.31 thf(fact_7651_nonzero__norm__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( real_V1022390504157884413omplex @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_norm_inverse
% 5.01/5.31 thf(fact_7652_mult__commute__imp__mult__inverse__commute,axiom,
% 5.01/5.31 ! [Y: real,X2: real] :
% 5.01/5.31 ( ( ( times_times_real @ Y @ X2 )
% 5.01/5.31 = ( times_times_real @ X2 @ Y ) )
% 5.01/5.31 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X2 )
% 5.01/5.31 = ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_commute_imp_mult_inverse_commute
% 5.01/5.31 thf(fact_7653_mult__commute__imp__mult__inverse__commute,axiom,
% 5.01/5.31 ! [Y: complex,X2: complex] :
% 5.01/5.31 ( ( ( times_times_complex @ Y @ X2 )
% 5.01/5.31 = ( times_times_complex @ X2 @ Y ) )
% 5.01/5.31 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X2 )
% 5.01/5.31 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_commute_imp_mult_inverse_commute
% 5.01/5.31 thf(fact_7654_mult__commute__imp__mult__inverse__commute,axiom,
% 5.01/5.31 ! [Y: rat,X2: rat] :
% 5.01/5.31 ( ( ( times_times_rat @ Y @ X2 )
% 5.01/5.31 = ( times_times_rat @ X2 @ Y ) )
% 5.01/5.31 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y ) @ X2 )
% 5.01/5.31 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_commute_imp_mult_inverse_commute
% 5.01/5.31 thf(fact_7655_field__class_Ofield__inverse__zero,axiom,
% 5.01/5.31 ( ( inverse_inverse_real @ zero_zero_real )
% 5.01/5.31 = zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse_zero
% 5.01/5.31 thf(fact_7656_field__class_Ofield__inverse__zero,axiom,
% 5.01/5.31 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.01/5.31 = zero_zero_complex ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse_zero
% 5.01/5.31 thf(fact_7657_field__class_Ofield__inverse__zero,axiom,
% 5.01/5.31 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.01/5.31 = zero_zero_rat ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse_zero
% 5.01/5.31 thf(fact_7658_inverse__zero__imp__zero,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ( inverse_inverse_real @ A )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 => ( A = zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_zero_imp_zero
% 5.01/5.31 thf(fact_7659_inverse__zero__imp__zero,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 = zero_zero_complex )
% 5.01/5.31 => ( A = zero_zero_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_zero_imp_zero
% 5.01/5.31 thf(fact_7660_inverse__zero__imp__zero,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ( inverse_inverse_rat @ A )
% 5.01/5.31 = zero_zero_rat )
% 5.01/5.31 => ( A = zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_zero_imp_zero
% 5.01/5.31 thf(fact_7661_nonzero__inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ( inverse_inverse_real @ A )
% 5.01/5.31 = ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( A = B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7662_nonzero__inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 = ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 => ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( A = B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7663_nonzero__inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ( inverse_inverse_rat @ A )
% 5.01/5.31 = ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( A = B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7664_nonzero__inverse__inverse__eq,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = A ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_inverse_eq
% 5.01/5.31 thf(fact_7665_nonzero__inverse__inverse__eq,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.01/5.31 = A ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_inverse_eq
% 5.01/5.31 thf(fact_7666_nonzero__inverse__inverse__eq,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = A ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_inverse_eq
% 5.01/5.31 thf(fact_7667_nonzero__imp__inverse__nonzero,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ A )
% 5.01/5.31 != zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_imp_inverse_nonzero
% 5.01/5.31 thf(fact_7668_nonzero__imp__inverse__nonzero,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 != zero_zero_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_imp_inverse_nonzero
% 5.01/5.31 thf(fact_7669_nonzero__imp__inverse__nonzero,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ A )
% 5.01/5.31 != zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_imp_inverse_nonzero
% 5.01/5.31 thf(fact_7670_power__inverse,axiom,
% 5.01/5.31 ! [A: real,N: nat] :
% 5.01/5.31 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 5.01/5.31 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_inverse
% 5.01/5.31 thf(fact_7671_power__inverse,axiom,
% 5.01/5.31 ! [A: complex,N: nat] :
% 5.01/5.31 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N )
% 5.01/5.31 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_inverse
% 5.01/5.31 thf(fact_7672_power__inverse,axiom,
% 5.01/5.31 ! [A: rat,N: nat] :
% 5.01/5.31 ( ( power_power_rat @ ( inverse_inverse_rat @ A ) @ N )
% 5.01/5.31 = ( inverse_inverse_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_inverse
% 5.01/5.31 thf(fact_7673_inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ( inverse_inverse_real @ A )
% 5.01/5.31 = ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( A = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7674_inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 = ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 => ( A = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7675_inverse__eq__imp__eq,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ( inverse_inverse_rat @ A )
% 5.01/5.31 = ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( A = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_imp_eq
% 5.01/5.31 thf(fact_7676_real__sqrt__inverse,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( sqrt @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % real_sqrt_inverse
% 5.01/5.31 thf(fact_7677_nonzero__of__real__inverse,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( X2 != zero_zero_real )
% 5.01/5.31 => ( ( real_V1803761363581548252l_real @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( real_V1803761363581548252l_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_of_real_inverse
% 5.01/5.31 thf(fact_7678_nonzero__of__real__inverse,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( X2 != zero_zero_real )
% 5.01/5.31 => ( ( real_V4546457046886955230omplex @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( invers8013647133539491842omplex @ ( real_V4546457046886955230omplex @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_of_real_inverse
% 5.01/5.31 thf(fact_7679_cis__divide,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.01/5.31 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_divide
% 5.01/5.31 thf(fact_7680_complex__i__not__zero,axiom,
% 5.01/5.31 imaginary_unit != zero_zero_complex ).
% 5.01/5.31
% 5.01/5.31 % complex_i_not_zero
% 5.01/5.31 thf(fact_7681_cis__neq__zero,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( cis @ A )
% 5.01/5.31 != zero_zero_complex ) ).
% 5.01/5.31
% 5.01/5.31 % cis_neq_zero
% 5.01/5.31 thf(fact_7682_norm__inverse__le__norm,axiom,
% 5.01/5.31 ! [R: real,X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ R @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.01/5.31 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X2 ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % norm_inverse_le_norm
% 5.01/5.31 thf(fact_7683_norm__inverse__le__norm,axiom,
% 5.01/5.31 ! [R: real,X2: complex] :
% 5.01/5.31 ( ( ord_less_eq_real @ R @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.01/5.31 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X2 ) ) @ ( inverse_inverse_real @ R ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % norm_inverse_le_norm
% 5.01/5.31 thf(fact_7684_positive__imp__inverse__positive,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % positive_imp_inverse_positive
% 5.01/5.31 thf(fact_7685_positive__imp__inverse__positive,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % positive_imp_inverse_positive
% 5.01/5.31 thf(fact_7686_negative__imp__inverse__negative,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ A @ zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % negative_imp_inverse_negative
% 5.01/5.31 thf(fact_7687_negative__imp__inverse__negative,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % negative_imp_inverse_negative
% 5.01/5.31 thf(fact_7688_inverse__positive__imp__positive,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 => ( ( A != zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_positive_imp_positive
% 5.01/5.31 thf(fact_7689_inverse__positive__imp__positive,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 => ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_positive_imp_positive
% 5.01/5.31 thf(fact_7690_inverse__negative__imp__negative,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.01/5.31 => ( ( A != zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_negative_imp_negative
% 5.01/5.31 thf(fact_7691_inverse__negative__imp__negative,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.01/5.31 => ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_negative_imp_negative
% 5.01/5.31 thf(fact_7692_less__imp__inverse__less__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ A @ B )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % less_imp_inverse_less_neg
% 5.01/5.31 thf(fact_7693_less__imp__inverse__less__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ A @ B )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % less_imp_inverse_less_neg
% 5.01/5.31 thf(fact_7694_inverse__less__imp__less__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_imp_less_neg
% 5.01/5.31 thf(fact_7695_inverse__less__imp__less__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_imp_less_neg
% 5.01/5.31 thf(fact_7696_less__imp__inverse__less,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ A @ B )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % less_imp_inverse_less
% 5.01/5.31 thf(fact_7697_less__imp__inverse__less,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ A @ B )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % less_imp_inverse_less
% 5.01/5.31 thf(fact_7698_inverse__less__imp__less,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ord_less_real @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_imp_less
% 5.01/5.31 thf(fact_7699_inverse__less__imp__less,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_imp_less
% 5.01/5.31 thf(fact_7700_nonzero__inverse__mult__distrib,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.01/5.31 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_mult_distrib
% 5.01/5.31 thf(fact_7701_nonzero__inverse__mult__distrib,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.01/5.31 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_mult_distrib
% 5.01/5.31 thf(fact_7702_nonzero__inverse__mult__distrib,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.31 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_mult_distrib
% 5.01/5.31 thf(fact_7703_nonzero__inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_minus_eq
% 5.01/5.31 thf(fact_7704_nonzero__inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_minus_eq
% 5.01/5.31 thf(fact_7705_nonzero__inverse__minus__eq,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.01/5.31 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_minus_eq
% 5.01/5.31 thf(fact_7706_inverse__numeral__1,axiom,
% 5.01/5.31 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.01/5.31 = ( numeral_numeral_real @ one ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_numeral_1
% 5.01/5.31 thf(fact_7707_inverse__numeral__1,axiom,
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.01/5.31 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_numeral_1
% 5.01/5.31 thf(fact_7708_inverse__numeral__1,axiom,
% 5.01/5.31 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.01/5.31 = ( numeral_numeral_rat @ one ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_numeral_1
% 5.01/5.31 thf(fact_7709_inverse__unique,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ( times_times_real @ A @ B )
% 5.01/5.31 = one_one_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ A )
% 5.01/5.31 = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_unique
% 5.01/5.31 thf(fact_7710_inverse__unique,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( ( times_times_complex @ A @ B )
% 5.01/5.31 = one_one_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_unique
% 5.01/5.31 thf(fact_7711_inverse__unique,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ( times_times_rat @ A @ B )
% 5.01/5.31 = one_one_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ A )
% 5.01/5.31 = B ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_unique
% 5.01/5.31 thf(fact_7712_field__class_Ofield__divide__inverse,axiom,
% 5.01/5.31 ( divide_divide_real
% 5.01/5.31 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_divide_inverse
% 5.01/5.31 thf(fact_7713_field__class_Ofield__divide__inverse,axiom,
% 5.01/5.31 ( divide1717551699836669952omplex
% 5.01/5.31 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_divide_inverse
% 5.01/5.31 thf(fact_7714_field__class_Ofield__divide__inverse,axiom,
% 5.01/5.31 ( divide_divide_rat
% 5.01/5.31 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_divide_inverse
% 5.01/5.31 thf(fact_7715_divide__inverse,axiom,
% 5.01/5.31 ( divide_divide_real
% 5.01/5.31 = ( ^ [A4: real,B3: real] : ( times_times_real @ A4 @ ( inverse_inverse_real @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse
% 5.01/5.31 thf(fact_7716_divide__inverse,axiom,
% 5.01/5.31 ( divide1717551699836669952omplex
% 5.01/5.31 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ A4 @ ( invers8013647133539491842omplex @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse
% 5.01/5.31 thf(fact_7717_divide__inverse,axiom,
% 5.01/5.31 ( divide_divide_rat
% 5.01/5.31 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ A4 @ ( inverse_inverse_rat @ B3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse
% 5.01/5.31 thf(fact_7718_divide__inverse__commute,axiom,
% 5.01/5.31 ( divide_divide_real
% 5.01/5.31 = ( ^ [A4: real,B3: real] : ( times_times_real @ ( inverse_inverse_real @ B3 ) @ A4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse_commute
% 5.01/5.31 thf(fact_7719_divide__inverse__commute,axiom,
% 5.01/5.31 ( divide1717551699836669952omplex
% 5.01/5.31 = ( ^ [A4: complex,B3: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B3 ) @ A4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse_commute
% 5.01/5.31 thf(fact_7720_divide__inverse__commute,axiom,
% 5.01/5.31 ( divide_divide_rat
% 5.01/5.31 = ( ^ [A4: rat,B3: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B3 ) @ A4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_inverse_commute
% 5.01/5.31 thf(fact_7721_inverse__eq__divide,axiom,
% 5.01/5.31 ( inverse_inverse_real
% 5.01/5.31 = ( divide_divide_real @ one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide
% 5.01/5.31 thf(fact_7722_inverse__eq__divide,axiom,
% 5.01/5.31 ( invers8013647133539491842omplex
% 5.01/5.31 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide
% 5.01/5.31 thf(fact_7723_inverse__eq__divide,axiom,
% 5.01/5.31 ( inverse_inverse_rat
% 5.01/5.31 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_eq_divide
% 5.01/5.31 thf(fact_7724_power__mult__inverse__distrib,axiom,
% 5.01/5.31 ! [X2: real,M: nat] :
% 5.01/5.31 ( ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( times_times_real @ ( inverse_inverse_real @ X2 ) @ ( power_power_real @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_inverse_distrib
% 5.01/5.31 thf(fact_7725_power__mult__inverse__distrib,axiom,
% 5.01/5.31 ! [X2: complex,M: nat] :
% 5.01/5.31 ( ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( invers8013647133539491842omplex @ X2 ) )
% 5.01/5.31 = ( times_times_complex @ ( invers8013647133539491842omplex @ X2 ) @ ( power_power_complex @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_inverse_distrib
% 5.01/5.31 thf(fact_7726_power__mult__inverse__distrib,axiom,
% 5.01/5.31 ! [X2: rat,M: nat] :
% 5.01/5.31 ( ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( inverse_inverse_rat @ X2 ) )
% 5.01/5.31 = ( times_times_rat @ ( inverse_inverse_rat @ X2 ) @ ( power_power_rat @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_inverse_distrib
% 5.01/5.31 thf(fact_7727_power__mult__power__inverse__commute,axiom,
% 5.01/5.31 ! [X2: real,M: nat,N: nat] :
% 5.01/5.31 ( ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ N ) )
% 5.01/5.31 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ N ) @ ( power_power_real @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_power_inverse_commute
% 5.01/5.31 thf(fact_7728_power__mult__power__inverse__commute,axiom,
% 5.01/5.31 ! [X2: complex,M: nat,N: nat] :
% 5.01/5.31 ( ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ N ) )
% 5.01/5.31 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ N ) @ ( power_power_complex @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_power_inverse_commute
% 5.01/5.31 thf(fact_7729_power__mult__power__inverse__commute,axiom,
% 5.01/5.31 ! [X2: rat,M: nat,N: nat] :
% 5.01/5.31 ( ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ N ) )
% 5.01/5.31 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ N ) @ ( power_power_rat @ X2 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_mult_power_inverse_commute
% 5.01/5.31 thf(fact_7730_mult__inverse__of__nat__commute,axiom,
% 5.01/5.31 ! [Xa: nat,X2: real] :
% 5.01/5.31 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_real @ X2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_nat_commute
% 5.01/5.31 thf(fact_7731_mult__inverse__of__nat__commute,axiom,
% 5.01/5.31 ! [Xa: nat,X2: complex] :
% 5.01/5.31 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_nat_commute
% 5.01/5.31 thf(fact_7732_mult__inverse__of__nat__commute,axiom,
% 5.01/5.31 ! [Xa: nat,X2: rat] :
% 5.01/5.31 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_nat_commute
% 5.01/5.31 thf(fact_7733_nonzero__abs__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_abs_inverse
% 5.01/5.31 thf(fact_7734_nonzero__abs__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.01/5.31 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_abs_inverse
% 5.01/5.31 thf(fact_7735_mult__inverse__of__int__commute,axiom,
% 5.01/5.31 ! [Xa: int,X2: real] :
% 5.01/5.31 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_real @ X2 @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_int_commute
% 5.01/5.31 thf(fact_7736_mult__inverse__of__int__commute,axiom,
% 5.01/5.31 ! [Xa: int,X2: complex] :
% 5.01/5.31 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_int_commute
% 5.01/5.31 thf(fact_7737_mult__inverse__of__int__commute,axiom,
% 5.01/5.31 ! [Xa: int,X2: rat] :
% 5.01/5.31 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) @ X2 )
% 5.01/5.31 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_inverse_of_int_commute
% 5.01/5.31 thf(fact_7738_exp__minus,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( exp_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_minus
% 5.01/5.31 thf(fact_7739_exp__minus,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.31 = ( invers8013647133539491842omplex @ ( exp_complex @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_minus
% 5.01/5.31 thf(fact_7740_powr__minus,axiom,
% 5.01/5.31 ! [X2: real,A: real] :
% 5.01/5.31 ( ( powr_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( powr_real @ X2 @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % powr_minus
% 5.01/5.31 thf(fact_7741_divide__real__def,axiom,
% 5.01/5.31 ( divide_divide_real
% 5.01/5.31 = ( ^ [X3: real,Y2: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % divide_real_def
% 5.01/5.31 thf(fact_7742_DeMoivre,axiom,
% 5.01/5.31 ! [A: real,N: nat] :
% 5.01/5.31 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.01/5.31 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DeMoivre
% 5.01/5.31 thf(fact_7743_frac__ge__0,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_ge_0
% 5.01/5.31 thf(fact_7744_frac__ge__0,axiom,
% 5.01/5.31 ! [X2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_ge_0
% 5.01/5.31 thf(fact_7745_cis__mult,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.01/5.31 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_mult
% 5.01/5.31 thf(fact_7746_frac__lt__1,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X2 ) @ one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % frac_lt_1
% 5.01/5.31 thf(fact_7747_frac__lt__1,axiom,
% 5.01/5.31 ! [X2: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X2 ) @ one_one_rat ) ).
% 5.01/5.31
% 5.01/5.31 % frac_lt_1
% 5.01/5.31 thf(fact_7748_frac__1__eq,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.01/5.31 = ( archim2898591450579166408c_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_1_eq
% 5.01/5.31 thf(fact_7749_frac__1__eq,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.01/5.31 = ( archimedean_frac_rat @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_1_eq
% 5.01/5.31 thf(fact_7750_inverse__le__imp__le,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_imp_le
% 5.01/5.31 thf(fact_7751_inverse__le__imp__le,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_imp_le
% 5.01/5.31 thf(fact_7752_le__imp__inverse__le,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_imp_inverse_le
% 5.01/5.31 thf(fact_7753_le__imp__inverse__le,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_imp_inverse_le
% 5.01/5.31 thf(fact_7754_inverse__le__imp__le__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_imp_le_neg
% 5.01/5.31 thf(fact_7755_inverse__le__imp__le__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_imp_le_neg
% 5.01/5.31 thf(fact_7756_le__imp__inverse__le__neg,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.31 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.01/5.31 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_imp_inverse_le_neg
% 5.01/5.31 thf(fact_7757_le__imp__inverse__le__neg,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_imp_inverse_le_neg
% 5.01/5.31 thf(fact_7758_inverse__le__1__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X2 ) @ one_one_real )
% 5.01/5.31 = ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.31 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_1_iff
% 5.01/5.31 thf(fact_7759_inverse__le__1__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X2 ) @ one_one_rat )
% 5.01/5.31 = ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.31 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_1_iff
% 5.01/5.31 thf(fact_7760_one__less__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( ord_less_real @ A @ one_one_real )
% 5.01/5.31 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_less_inverse
% 5.01/5.31 thf(fact_7761_one__less__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.01/5.31 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_less_inverse
% 5.01/5.31 thf(fact_7762_one__less__inverse__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_less_inverse_iff
% 5.01/5.31 thf(fact_7763_one__less__inverse__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X2 ) )
% 5.01/5.31 = ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.31 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_less_inverse_iff
% 5.01/5.31 thf(fact_7764_division__ring__inverse__add,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_add
% 5.01/5.31 thf(fact_7765_division__ring__inverse__add,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_add
% 5.01/5.31 thf(fact_7766_division__ring__inverse__add,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_add
% 5.01/5.31 thf(fact_7767_inverse__add,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_add
% 5.01/5.31 thf(fact_7768_inverse__add,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_add
% 5.01/5.31 thf(fact_7769_inverse__add,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_add
% 5.01/5.31 thf(fact_7770_field__class_Ofield__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.01/5.31 = one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse
% 5.01/5.31 thf(fact_7771_field__class_Ofield__inverse,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.01/5.31 = one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse
% 5.01/5.31 thf(fact_7772_field__class_Ofield__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.01/5.31 = one_one_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % field_class.field_inverse
% 5.01/5.31 thf(fact_7773_division__ring__inverse__diff,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_diff
% 5.01/5.31 thf(fact_7774_division__ring__inverse__diff,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_diff
% 5.01/5.31 thf(fact_7775_division__ring__inverse__diff,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % division_ring_inverse_diff
% 5.01/5.31 thf(fact_7776_nonzero__inverse__eq__divide,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( inverse_inverse_real @ A )
% 5.01/5.31 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_divide
% 5.01/5.31 thf(fact_7777_nonzero__inverse__eq__divide,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( invers8013647133539491842omplex @ A )
% 5.01/5.31 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_divide
% 5.01/5.31 thf(fact_7778_nonzero__inverse__eq__divide,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( inverse_inverse_rat @ A )
% 5.01/5.31 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % nonzero_inverse_eq_divide
% 5.01/5.31 thf(fact_7779_inverse__powr,axiom,
% 5.01/5.31 ! [Y: real,A: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.31 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.01/5.31 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_powr
% 5.01/5.31 thf(fact_7780_imaginary__unit_Ocode,axiom,
% 5.01/5.31 ( imaginary_unit
% 5.01/5.31 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % imaginary_unit.code
% 5.01/5.31 thf(fact_7781_Complex__eq__i,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ( complex2 @ X2 @ Y )
% 5.01/5.31 = imaginary_unit )
% 5.01/5.31 = ( ( X2 = zero_zero_real )
% 5.01/5.31 & ( Y = one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Complex_eq_i
% 5.01/5.31 thf(fact_7782_inverse__le__iff,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.31 => ( ord_less_eq_real @ B @ A ) )
% 5.01/5.31 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.01/5.31 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff
% 5.01/5.31 thf(fact_7783_inverse__le__iff,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.31 => ( ord_less_eq_rat @ B @ A ) )
% 5.01/5.31 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_le_iff
% 5.01/5.31 thf(fact_7784_inverse__less__iff,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.01/5.31 => ( ord_less_real @ B @ A ) )
% 5.01/5.31 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.01/5.31 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff
% 5.01/5.31 thf(fact_7785_inverse__less__iff,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.01/5.31 => ( ord_less_rat @ B @ A ) )
% 5.01/5.31 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.01/5.31 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_iff
% 5.01/5.31 thf(fact_7786_one__le__inverse__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 & ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_le_inverse_iff
% 5.01/5.31 thf(fact_7787_one__le__inverse__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X2 ) )
% 5.01/5.31 = ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.31 & ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_le_inverse_iff
% 5.01/5.31 thf(fact_7788_inverse__less__1__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ ( inverse_inverse_real @ X2 ) @ one_one_real )
% 5.01/5.31 = ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.31 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_1_iff
% 5.01/5.31 thf(fact_7789_inverse__less__1__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_rat @ ( inverse_inverse_rat @ X2 ) @ one_one_rat )
% 5.01/5.31 = ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.01/5.31 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_less_1_iff
% 5.01/5.31 thf(fact_7790_one__le__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.01/5.31 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_le_inverse
% 5.01/5.31 thf(fact_7791_one__le__inverse,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_le_inverse
% 5.01/5.31 thf(fact_7792_inverse__diff__inverse,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( A != zero_zero_real )
% 5.01/5.31 => ( ( B != zero_zero_real )
% 5.01/5.31 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_diff_inverse
% 5.01/5.31 thf(fact_7793_inverse__diff__inverse,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( A != zero_zero_complex )
% 5.01/5.31 => ( ( B != zero_zero_complex )
% 5.01/5.31 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_diff_inverse
% 5.01/5.31 thf(fact_7794_inverse__diff__inverse,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( A != zero_zero_rat )
% 5.01/5.31 => ( ( B != zero_zero_rat )
% 5.01/5.31 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.01/5.31 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % inverse_diff_inverse
% 5.01/5.31 thf(fact_7795_reals__Archimedean,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ? [N3: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % reals_Archimedean
% 5.01/5.31 thf(fact_7796_reals__Archimedean,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.31 => ? [N3: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % reals_Archimedean
% 5.01/5.31 thf(fact_7797_i__mult__Complex,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.01/5.31 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % i_mult_Complex
% 5.01/5.31 thf(fact_7798_Complex__mult__i,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.01/5.31 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % Complex_mult_i
% 5.01/5.31 thf(fact_7799_forall__pos__mono__1,axiom,
% 5.01/5.31 ! [P: real > $o,E: real] :
% 5.01/5.31 ( ! [D2: real,E2: real] :
% 5.01/5.31 ( ( ord_less_real @ D2 @ E2 )
% 5.01/5.31 => ( ( P @ D2 )
% 5.01/5.31 => ( P @ E2 ) ) )
% 5.01/5.31 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.31 => ( P @ E ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % forall_pos_mono_1
% 5.01/5.31 thf(fact_7800_real__arch__inverse,axiom,
% 5.01/5.31 ! [E: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.31 = ( ? [N4: nat] :
% 5.01/5.31 ( ( N4 != zero_zero_nat )
% 5.01/5.31 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.01/5.31 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % real_arch_inverse
% 5.01/5.31 thf(fact_7801_forall__pos__mono,axiom,
% 5.01/5.31 ! [P: real > $o,E: real] :
% 5.01/5.31 ( ! [D2: real,E2: real] :
% 5.01/5.31 ( ( ord_less_real @ D2 @ E2 )
% 5.01/5.31 => ( ( P @ D2 )
% 5.01/5.31 => ( P @ E2 ) ) )
% 5.01/5.31 => ( ! [N3: nat] :
% 5.01/5.31 ( ( N3 != zero_zero_nat )
% 5.01/5.31 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.31 => ( P @ E ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % forall_pos_mono
% 5.01/5.31 thf(fact_7802_sqrt__divide__self__eq,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.01/5.31 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sqrt_divide_self_eq
% 5.01/5.31 thf(fact_7803_ln__inverse,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( ln_ln_real @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ln_inverse
% 5.01/5.31 thf(fact_7804_frac__def,axiom,
% 5.01/5.31 ( archim2898591450579166408c_real
% 5.01/5.31 = ( ^ [X3: real] : ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_def
% 5.01/5.31 thf(fact_7805_frac__def,axiom,
% 5.01/5.31 ( archimedean_frac_rat
% 5.01/5.31 = ( ^ [X3: rat] : ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_def
% 5.01/5.31 thf(fact_7806_ex__inverse__of__nat__less,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ? [N3: nat] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.31 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ex_inverse_of_nat_less
% 5.01/5.31 thf(fact_7807_ex__inverse__of__nat__less,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.01/5.31 => ? [N3: nat] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.01/5.31 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N3 ) ) @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ex_inverse_of_nat_less
% 5.01/5.31 thf(fact_7808_power__diff__conv__inverse,axiom,
% 5.01/5.31 ! [X2: real,M: nat,N: nat] :
% 5.01/5.31 ( ( X2 != zero_zero_real )
% 5.01/5.31 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 => ( ( power_power_real @ X2 @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.31 = ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ M ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_diff_conv_inverse
% 5.01/5.31 thf(fact_7809_power__diff__conv__inverse,axiom,
% 5.01/5.31 ! [X2: complex,M: nat,N: nat] :
% 5.01/5.31 ( ( X2 != zero_zero_complex )
% 5.01/5.31 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 => ( ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.31 = ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ M ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_diff_conv_inverse
% 5.01/5.31 thf(fact_7810_power__diff__conv__inverse,axiom,
% 5.01/5.31 ! [X2: rat,M: nat,N: nat] :
% 5.01/5.31 ( ( X2 != zero_zero_rat )
% 5.01/5.31 => ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 => ( ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ M ) )
% 5.01/5.31 = ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ M ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % power_diff_conv_inverse
% 5.01/5.31 thf(fact_7811_complex__of__real__i,axiom,
% 5.01/5.31 ! [R: real] :
% 5.01/5.31 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ imaginary_unit )
% 5.01/5.31 = ( complex2 @ zero_zero_real @ R ) ) ).
% 5.01/5.31
% 5.01/5.31 % complex_of_real_i
% 5.01/5.31 thf(fact_7812_i__complex__of__real,axiom,
% 5.01/5.31 ! [R: real] :
% 5.01/5.31 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R ) )
% 5.01/5.31 = ( complex2 @ zero_zero_real @ R ) ) ).
% 5.01/5.31
% 5.01/5.31 % i_complex_of_real
% 5.01/5.31 thf(fact_7813_log__inverse,axiom,
% 5.01/5.31 ! [A: real,X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( A != one_one_real )
% 5.01/5.31 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( log @ A @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( log @ A @ X2 ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % log_inverse
% 5.01/5.31 thf(fact_7814_frac__eq,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.01/5.31 = X2 )
% 5.01/5.31 = ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_eq
% 5.01/5.31 thf(fact_7815_frac__eq,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ( archimedean_frac_rat @ X2 )
% 5.01/5.31 = X2 )
% 5.01/5.31 = ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.01/5.31 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_eq
% 5.01/5.31 thf(fact_7816_frac__add,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.01/5.31 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 5.01/5.31 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.01/5.31 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_add
% 5.01/5.31 thf(fact_7817_frac__add,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.01/5.31 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 5.01/5.31 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.01/5.31 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_add
% 5.01/5.31 thf(fact_7818_Complex__eq,axiom,
% 5.01/5.31 ( complex2
% 5.01/5.31 = ( ^ [A4: real,B3: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A4 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Complex_eq
% 5.01/5.31 thf(fact_7819_exp__plus__inverse__exp,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_plus_inverse_exp
% 5.01/5.31 thf(fact_7820_complex__split__polar,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ? [R4: real,A3: real] :
% 5.01/5.31 ( Z
% 5.01/5.31 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % complex_split_polar
% 5.01/5.31 thf(fact_7821_plus__inverse__ge__2,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % plus_inverse_ge_2
% 5.01/5.31 thf(fact_7822_real__inv__sqrt__pow2,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % real_inv_sqrt_pow2
% 5.01/5.31 thf(fact_7823_tan__cot,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.01/5.31 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tan_cot
% 5.01/5.31 thf(fact_7824_floor__add,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.01/5.31 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 5.01/5.31 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X2 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.01/5.31 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % floor_add
% 5.01/5.31 thf(fact_7825_floor__add,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.01/5.31 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 5.01/5.31 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X2 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.01/5.31 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % floor_add
% 5.01/5.31 thf(fact_7826_real__le__x__sinh,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % real_le_x_sinh
% 5.01/5.31 thf(fact_7827_real__le__abs__sinh,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % real_le_abs_sinh
% 5.01/5.31 thf(fact_7828_tan__sec,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( cos_real @ X2 )
% 5.01/5.31 != zero_zero_real )
% 5.01/5.31 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tan_sec
% 5.01/5.31 thf(fact_7829_tan__sec,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( ( cos_complex @ X2 )
% 5.01/5.31 != zero_zero_complex )
% 5.01/5.31 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tan_sec
% 5.01/5.31 thf(fact_7830_cmod__unit__one,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % cmod_unit_one
% 5.01/5.31 thf(fact_7831_cmod__complex__polar,axiom,
% 5.01/5.31 ! [R: real,A: real] :
% 5.01/5.31 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.01/5.31 = ( abs_abs_real @ R ) ) ).
% 5.01/5.31
% 5.01/5.31 % cmod_complex_polar
% 5.01/5.31 thf(fact_7832_Arg__minus__ii,axiom,
% 5.01/5.31 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.01/5.31 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Arg_minus_ii
% 5.01/5.31 thf(fact_7833_csqrt__ii,axiom,
% 5.01/5.31 ( ( csqrt @ imaginary_unit )
% 5.01/5.31 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % csqrt_ii
% 5.01/5.31 thf(fact_7834_Arg__ii,axiom,
% 5.01/5.31 ( ( arg @ imaginary_unit )
% 5.01/5.31 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Arg_ii
% 5.01/5.31 thf(fact_7835_Arg__correct,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ( ( Z != zero_zero_complex )
% 5.01/5.31 => ( ( ( sgn_sgn_complex @ Z )
% 5.01/5.31 = ( cis @ ( arg @ Z ) ) )
% 5.01/5.31 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.01/5.31 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Arg_correct
% 5.01/5.31 thf(fact_7836_sinh__ln__real,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.31 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_ln_real
% 5.01/5.31 thf(fact_7837_sinh__0,axiom,
% 5.01/5.31 ( ( sinh_complex @ zero_zero_complex )
% 5.01/5.31 = zero_zero_complex ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_0
% 5.01/5.31 thf(fact_7838_sinh__0,axiom,
% 5.01/5.31 ( ( sinh_real @ zero_zero_real )
% 5.01/5.31 = zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_0
% 5.01/5.31 thf(fact_7839_sinh__minus,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( sinh_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( sinh_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_minus
% 5.01/5.31 thf(fact_7840_sinh__minus,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( sinh_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ ( sinh_complex @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_minus
% 5.01/5.31 thf(fact_7841_cis__inverse,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( cis @ A ) )
% 5.01/5.31 = ( cis @ ( uminus_uminus_real @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_inverse
% 5.01/5.31 thf(fact_7842_sinh__real__zero__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( sinh_real @ X2 )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 = ( X2 = zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_zero_iff
% 5.01/5.31 thf(fact_7843_sinh__real__less__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y ) )
% 5.01/5.31 = ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_less_iff
% 5.01/5.31 thf(fact_7844_sinh__real__le__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y ) )
% 5.01/5.31 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_le_iff
% 5.01/5.31 thf(fact_7845_csqrt__0,axiom,
% 5.01/5.31 ( ( csqrt @ zero_zero_complex )
% 5.01/5.31 = zero_zero_complex ) ).
% 5.01/5.31
% 5.01/5.31 % csqrt_0
% 5.01/5.31 thf(fact_7846_csqrt__eq__0,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ( ( ( csqrt @ Z )
% 5.01/5.31 = zero_zero_complex )
% 5.01/5.31 = ( Z = zero_zero_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % csqrt_eq_0
% 5.01/5.31 thf(fact_7847_sinh__real__neg__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.01/5.31 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_neg_iff
% 5.01/5.31 thf(fact_7848_sinh__real__pos__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.01/5.31 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_pos_iff
% 5.01/5.31 thf(fact_7849_sinh__real__nonpos__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.01/5.31 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_nonpos_iff
% 5.01/5.31 thf(fact_7850_sinh__real__nonneg__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.01/5.31 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_real_nonneg_iff
% 5.01/5.31 thf(fact_7851_power2__csqrt,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = Z ) ).
% 5.01/5.31
% 5.01/5.31 % power2_csqrt
% 5.01/5.31 thf(fact_7852_Arg__zero,axiom,
% 5.01/5.31 ( ( arg @ zero_zero_complex )
% 5.01/5.31 = zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % Arg_zero
% 5.01/5.31 thf(fact_7853_cis__Arg,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ( ( Z != zero_zero_complex )
% 5.01/5.31 => ( ( cis @ ( arg @ Z ) )
% 5.01/5.31 = ( sgn_sgn_complex @ Z ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_Arg
% 5.01/5.31 thf(fact_7854_of__real__sqrt,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X2 ) )
% 5.01/5.31 = ( csqrt @ ( real_V4546457046886955230omplex @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_real_sqrt
% 5.01/5.31 thf(fact_7855_Arg__bounded,axiom,
% 5.01/5.31 ! [Z: complex] :
% 5.01/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.01/5.31 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.01/5.31
% 5.01/5.31 % Arg_bounded
% 5.01/5.31 thf(fact_7856_complex__inverse,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.01/5.31 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % complex_inverse
% 5.01/5.31 thf(fact_7857_sinh__field__def,axiom,
% 5.01/5.31 ( sinh_real
% 5.01/5.31 = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_field_def
% 5.01/5.31 thf(fact_7858_sinh__field__def,axiom,
% 5.01/5.31 ( sinh_complex
% 5.01/5.31 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_field_def
% 5.01/5.31 thf(fact_7859_cis__Arg__unique,axiom,
% 5.01/5.31 ! [Z: complex,X2: real] :
% 5.01/5.31 ( ( ( sgn_sgn_complex @ Z )
% 5.01/5.31 = ( cis @ X2 ) )
% 5.01/5.31 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.01/5.31 => ( ( arg @ Z )
% 5.01/5.31 = X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_Arg_unique
% 5.01/5.31 thf(fact_7860_cis__multiple__2pi,axiom,
% 5.01/5.31 ! [N: real] :
% 5.01/5.31 ( ( member_real @ N @ ring_1_Ints_real )
% 5.01/5.31 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.01/5.31 = one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % cis_multiple_2pi
% 5.01/5.31 thf(fact_7861_cosh__ln__real,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.01/5.31 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_ln_real
% 5.01/5.31 thf(fact_7862_Suc__0__xor__eq,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.31 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.31 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.31 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Suc_0_xor_eq
% 5.01/5.31 thf(fact_7863_xor__Suc__0__eq,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.31 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.31 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.31 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_Suc_0_eq
% 5.01/5.31 thf(fact_7864_gbinomial__absorption_H,axiom,
% 5.01/5.31 ! [K: nat,A: rat] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_rat @ A @ K )
% 5.01/5.31 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption'
% 5.01/5.31 thf(fact_7865_gbinomial__absorption_H,axiom,
% 5.01/5.31 ! [K: nat,A: real] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_real @ A @ K )
% 5.01/5.31 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption'
% 5.01/5.31 thf(fact_7866_gbinomial__absorption_H,axiom,
% 5.01/5.31 ! [K: nat,A: complex] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_complex @ A @ K )
% 5.01/5.31 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption'
% 5.01/5.31 thf(fact_7867_bit_Oxor__left__self,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ X2 @ ( bit_se6526347334894502574or_int @ X2 @ Y ) )
% 5.01/5.31 = Y ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_left_self
% 5.01/5.31 thf(fact_7868_bit_Oxor__self,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ X2 @ X2 )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_self
% 5.01/5.31 thf(fact_7869_xor__self__eq,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ A @ A )
% 5.01/5.31 = zero_zero_nat ) ).
% 5.01/5.31
% 5.01/5.31 % xor_self_eq
% 5.01/5.31 thf(fact_7870_xor__self__eq,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ A @ A )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % xor_self_eq
% 5.01/5.31 thf(fact_7871_xor_Oleft__neutral,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 5.01/5.31 = A ) ).
% 5.01/5.31
% 5.01/5.31 % xor.left_neutral
% 5.01/5.31 thf(fact_7872_xor_Oleft__neutral,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 5.01/5.31 = A ) ).
% 5.01/5.31
% 5.01/5.31 % xor.left_neutral
% 5.01/5.31 thf(fact_7873_xor_Oright__neutral,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 5.01/5.31 = A ) ).
% 5.01/5.31
% 5.01/5.31 % xor.right_neutral
% 5.01/5.31 thf(fact_7874_xor_Oright__neutral,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 5.01/5.31 = A ) ).
% 5.01/5.31
% 5.01/5.31 % xor.right_neutral
% 5.01/5.31 thf(fact_7875_cosh__minus,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( cosh_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.31 = ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_minus
% 5.01/5.31 thf(fact_7876_cosh__minus,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( cosh_complex @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.31 = ( cosh_complex @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_minus
% 5.01/5.31 thf(fact_7877_take__bit__xor,axiom,
% 5.01/5.31 ! [N: nat,A: int,B: int] :
% 5.01/5.31 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_xor
% 5.01/5.31 thf(fact_7878_take__bit__xor,axiom,
% 5.01/5.31 ! [N: nat,A: nat,B: nat] :
% 5.01/5.31 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.01/5.31 = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_xor
% 5.01/5.31 thf(fact_7879_cosh__0,axiom,
% 5.01/5.31 ( ( cosh_complex @ zero_zero_complex )
% 5.01/5.31 = one_one_complex ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_0
% 5.01/5.31 thf(fact_7880_cosh__0,axiom,
% 5.01/5.31 ( ( cosh_real @ zero_zero_real )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_0
% 5.01/5.31 thf(fact_7881_gbinomial__0_I2_J,axiom,
% 5.01/5.31 ! [K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.01/5.31 = zero_zero_complex ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(2)
% 5.01/5.31 thf(fact_7882_gbinomial__0_I2_J,axiom,
% 5.01/5.31 ! [K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.01/5.31 = zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(2)
% 5.01/5.31 thf(fact_7883_gbinomial__0_I2_J,axiom,
% 5.01/5.31 ! [K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.01/5.31 = zero_zero_rat ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(2)
% 5.01/5.31 thf(fact_7884_gbinomial__0_I2_J,axiom,
% 5.01/5.31 ! [K: nat] :
% 5.01/5.31 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.01/5.31 = zero_zero_nat ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(2)
% 5.01/5.31 thf(fact_7885_gbinomial__0_I2_J,axiom,
% 5.01/5.31 ! [K: nat] :
% 5.01/5.31 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(2)
% 5.01/5.31 thf(fact_7886_gbinomial__0_I1_J,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.01/5.31 = one_one_complex ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(1)
% 5.01/5.31 thf(fact_7887_gbinomial__0_I1_J,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(1)
% 5.01/5.31 thf(fact_7888_gbinomial__0_I1_J,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.01/5.31 = one_one_rat ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(1)
% 5.01/5.31 thf(fact_7889_gbinomial__0_I1_J,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.01/5.31 = one_one_nat ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(1)
% 5.01/5.31 thf(fact_7890_gbinomial__0_I1_J,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.01/5.31 = one_one_int ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_0(1)
% 5.01/5.31 thf(fact_7891_frac__eq__0__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_eq_0_iff
% 5.01/5.31 thf(fact_7892_frac__eq__0__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ( archimedean_frac_rat @ X2 )
% 5.01/5.31 = zero_zero_rat )
% 5.01/5.31 = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_eq_0_iff
% 5.01/5.31 thf(fact_7893_floor__add2,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 | ( member_real @ Y @ ring_1_Ints_real ) )
% 5.01/5.31 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % floor_add2
% 5.01/5.31 thf(fact_7894_floor__add2,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 5.01/5.31 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % floor_add2
% 5.01/5.31 thf(fact_7895_frac__gt__0__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X2 ) )
% 5.01/5.31 = ( ~ ( member_real @ X2 @ ring_1_Ints_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_gt_0_iff
% 5.01/5.31 thf(fact_7896_frac__gt__0__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X2 ) )
% 5.01/5.31 = ( ~ ( member_rat @ X2 @ ring_1_Ints_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_gt_0_iff
% 5.01/5.31 thf(fact_7897_xor__numerals_I3_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(3)
% 5.01/5.31 thf(fact_7898_xor__numerals_I3_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(3)
% 5.01/5.31 thf(fact_7899_xor__numerals_I8_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(8)
% 5.01/5.31 thf(fact_7900_xor__numerals_I8_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit0 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(8)
% 5.01/5.31 thf(fact_7901_xor__numerals_I5_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(5)
% 5.01/5.31 thf(fact_7902_xor__numerals_I5_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit1 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(5)
% 5.01/5.31 thf(fact_7903_xor__numerals_I2_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(2)
% 5.01/5.31 thf(fact_7904_xor__numerals_I2_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(2)
% 5.01/5.31 thf(fact_7905_xor__numerals_I1_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(1)
% 5.01/5.31 thf(fact_7906_xor__numerals_I1_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(1)
% 5.01/5.31 thf(fact_7907_xor__numerals_I7_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(7)
% 5.01/5.31 thf(fact_7908_xor__numerals_I7_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(7)
% 5.01/5.31 thf(fact_7909_xor__nat__numerals_I1_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_numerals(1)
% 5.01/5.31 thf(fact_7910_xor__nat__numerals_I2_J,axiom,
% 5.01/5.31 ! [Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_numerals(2)
% 5.01/5.31 thf(fact_7911_xor__nat__numerals_I3_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_numerals(3)
% 5.01/5.31 thf(fact_7912_xor__nat__numerals_I4_J,axiom,
% 5.01/5.31 ! [X2: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.31 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_numerals(4)
% 5.01/5.31 thf(fact_7913_xor__numerals_I6_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(6)
% 5.01/5.31 thf(fact_7914_xor__numerals_I6_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.01/5.31 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(6)
% 5.01/5.31 thf(fact_7915_xor__numerals_I4_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(4)
% 5.01/5.31 thf(fact_7916_xor__numerals_I4_J,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.01/5.31 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_numerals(4)
% 5.01/5.31 thf(fact_7917_Ints__power,axiom,
% 5.01/5.31 ! [A: real,N: nat] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( member_real @ ( power_power_real @ A @ N ) @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_power
% 5.01/5.31 thf(fact_7918_Ints__power,axiom,
% 5.01/5.31 ! [A: int,N: nat] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_power
% 5.01/5.31 thf(fact_7919_Ints__power,axiom,
% 5.01/5.31 ! [A: complex,N: nat] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( member_complex @ ( power_power_complex @ A @ N ) @ ring_1_Ints_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_power
% 5.01/5.31 thf(fact_7920_of__int__xor__eq,axiom,
% 5.01/5.31 ! [K: int,L: int] :
% 5.01/5.31 ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_xor_eq
% 5.01/5.31 thf(fact_7921_Ints__minus,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( member_real @ ( uminus_uminus_real @ A ) @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_minus
% 5.01/5.31 thf(fact_7922_Ints__minus,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( member_int @ ( uminus_uminus_int @ A ) @ ring_1_Ints_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_minus
% 5.01/5.31 thf(fact_7923_Ints__minus,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( member_complex @ ( uminus1482373934393186551omplex @ A ) @ ring_1_Ints_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_minus
% 5.01/5.31 thf(fact_7924_Ints__minus,axiom,
% 5.01/5.31 ! [A: code_integer] :
% 5.01/5.31 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.01/5.31 => ( member_Code_integer @ ( uminus1351360451143612070nteger @ A ) @ ring_11222124179247155820nteger ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_minus
% 5.01/5.31 thf(fact_7925_Ints__minus,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( member_rat @ ( uminus_uminus_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_minus
% 5.01/5.31 thf(fact_7926_minus__in__Ints__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( member_real @ ( uminus_uminus_real @ X2 ) @ ring_1_Ints_real )
% 5.01/5.31 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_in_Ints_iff
% 5.01/5.31 thf(fact_7927_minus__in__Ints__iff,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( member_int @ ( uminus_uminus_int @ X2 ) @ ring_1_Ints_int )
% 5.01/5.31 = ( member_int @ X2 @ ring_1_Ints_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_in_Ints_iff
% 5.01/5.31 thf(fact_7928_minus__in__Ints__iff,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( member_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ring_1_Ints_complex )
% 5.01/5.31 = ( member_complex @ X2 @ ring_1_Ints_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_in_Ints_iff
% 5.01/5.31 thf(fact_7929_minus__in__Ints__iff,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( member_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ ring_11222124179247155820nteger )
% 5.01/5.31 = ( member_Code_integer @ X2 @ ring_11222124179247155820nteger ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_in_Ints_iff
% 5.01/5.31 thf(fact_7930_minus__in__Ints__iff,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( member_rat @ ( uminus_uminus_rat @ X2 ) @ ring_1_Ints_rat )
% 5.01/5.31 = ( member_rat @ X2 @ ring_1_Ints_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_in_Ints_iff
% 5.01/5.31 thf(fact_7931_Ints__of__nat,axiom,
% 5.01/5.31 ! [N: nat] : ( member_real @ ( semiri5074537144036343181t_real @ N ) @ ring_1_Ints_real ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_of_nat
% 5.01/5.31 thf(fact_7932_Ints__of__nat,axiom,
% 5.01/5.31 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ring_1_Ints_int ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_of_nat
% 5.01/5.31 thf(fact_7933_Ints__of__nat,axiom,
% 5.01/5.31 ! [N: nat] : ( member_complex @ ( semiri8010041392384452111omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_of_nat
% 5.01/5.31 thf(fact_7934_Ints__of__nat,axiom,
% 5.01/5.31 ! [N: nat] : ( member_Code_integer @ ( semiri4939895301339042750nteger @ N ) @ ring_11222124179247155820nteger ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_of_nat
% 5.01/5.31 thf(fact_7935_bit_Oconj__xor__distrib2,axiom,
% 5.01/5.31 ! [Y: int,Z: int,X2: int] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y @ Z ) @ X2 )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y @ X2 ) @ ( bit_se725231765392027082nd_int @ Z @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.conj_xor_distrib2
% 5.01/5.31 thf(fact_7936_bit_Oconj__xor__distrib,axiom,
% 5.01/5.31 ! [X2: int,Y: int,Z: int] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ X2 @ ( bit_se6526347334894502574or_int @ Y @ Z ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se725231765392027082nd_int @ X2 @ Z ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.conj_xor_distrib
% 5.01/5.31 thf(fact_7937_bit__xor__iff,axiom,
% 5.01/5.31 ! [A: nat,B: nat,N: nat] :
% 5.01/5.31 ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ N )
% 5.01/5.31 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.01/5.31 != ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_xor_iff
% 5.01/5.31 thf(fact_7938_bit__xor__iff,axiom,
% 5.01/5.31 ! [A: int,B: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ N )
% 5.01/5.31 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.01/5.31 != ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_xor_iff
% 5.01/5.31 thf(fact_7939_cosh__real__nonzero,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( cosh_real @ X2 )
% 5.01/5.31 != zero_zero_real ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonzero
% 5.01/5.31 thf(fact_7940_Ints__0,axiom,
% 5.01/5.31 member_complex @ zero_zero_complex @ ring_1_Ints_complex ).
% 5.01/5.31
% 5.01/5.31 % Ints_0
% 5.01/5.31 thf(fact_7941_Ints__0,axiom,
% 5.01/5.31 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 5.01/5.31
% 5.01/5.31 % Ints_0
% 5.01/5.31 thf(fact_7942_Ints__0,axiom,
% 5.01/5.31 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 5.01/5.31
% 5.01/5.31 % Ints_0
% 5.01/5.31 thf(fact_7943_Ints__0,axiom,
% 5.01/5.31 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 5.01/5.31
% 5.01/5.31 % Ints_0
% 5.01/5.31 thf(fact_7944_xor_Oassoc,axiom,
% 5.01/5.31 ! [A: nat,B: nat,C: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 5.01/5.31 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.assoc
% 5.01/5.31 thf(fact_7945_xor_Oassoc,axiom,
% 5.01/5.31 ! [A: int,B: int,C: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.assoc
% 5.01/5.31 thf(fact_7946_xor_Ocommute,axiom,
% 5.01/5.31 ( bit_se6528837805403552850or_nat
% 5.01/5.31 = ( ^ [A4: nat,B3: nat] : ( bit_se6528837805403552850or_nat @ B3 @ A4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.commute
% 5.01/5.31 thf(fact_7947_xor_Ocommute,axiom,
% 5.01/5.31 ( bit_se6526347334894502574or_int
% 5.01/5.31 = ( ^ [A4: int,B3: int] : ( bit_se6526347334894502574or_int @ B3 @ A4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.commute
% 5.01/5.31 thf(fact_7948_xor_Oleft__commute,axiom,
% 5.01/5.31 ! [B: nat,A: nat,C: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 5.01/5.31 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.left_commute
% 5.01/5.31 thf(fact_7949_xor_Oleft__commute,axiom,
% 5.01/5.31 ! [B: int,A: int,C: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor.left_commute
% 5.01/5.31 thf(fact_7950_of__nat__xor__eq,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri4939895301339042750nteger @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se3222712562003087583nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_xor_eq
% 5.01/5.31 thf(fact_7951_of__nat__xor__eq,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_xor_eq
% 5.01/5.31 thf(fact_7952_of__nat__xor__eq,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_xor_eq
% 5.01/5.31 thf(fact_7953_of__nat__gbinomial,axiom,
% 5.01/5.31 ! [N: nat,K: nat] :
% 5.01/5.31 ( ( semiri5074537144036343181t_real @ ( gbinomial_nat @ N @ K ) )
% 5.01/5.31 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_gbinomial
% 5.01/5.31 thf(fact_7954_of__nat__gbinomial,axiom,
% 5.01/5.31 ! [N: nat,K: nat] :
% 5.01/5.31 ( ( semiri8010041392384452111omplex @ ( gbinomial_nat @ N @ K ) )
% 5.01/5.31 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_gbinomial
% 5.01/5.31 thf(fact_7955_Ints__diff,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.01/5.31 => ( member_real @ ( minus_minus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_diff
% 5.01/5.31 thf(fact_7956_Ints__diff,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.01/5.31 => ( member_rat @ ( minus_minus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_diff
% 5.01/5.31 thf(fact_7957_Ints__diff,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.01/5.31 => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_diff
% 5.01/5.31 thf(fact_7958_Ints__diff,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.01/5.31 => ( member_complex @ ( minus_minus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_diff
% 5.01/5.31 thf(fact_7959_Ints__1,axiom,
% 5.01/5.31 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 5.01/5.31
% 5.01/5.31 % Ints_1
% 5.01/5.31 thf(fact_7960_Ints__1,axiom,
% 5.01/5.31 member_int @ one_one_int @ ring_1_Ints_int ).
% 5.01/5.31
% 5.01/5.31 % Ints_1
% 5.01/5.31 thf(fact_7961_Ints__1,axiom,
% 5.01/5.31 member_real @ one_one_real @ ring_1_Ints_real ).
% 5.01/5.31
% 5.01/5.31 % Ints_1
% 5.01/5.31 thf(fact_7962_Ints__1,axiom,
% 5.01/5.31 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 5.01/5.31
% 5.01/5.31 % Ints_1
% 5.01/5.31 thf(fact_7963_Ints__add,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.01/5.31 => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_add
% 5.01/5.31 thf(fact_7964_Ints__add,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.01/5.31 => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_add
% 5.01/5.31 thf(fact_7965_Ints__add,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.01/5.31 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_add
% 5.01/5.31 thf(fact_7966_Ints__add,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.01/5.31 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_add
% 5.01/5.31 thf(fact_7967_Ints__mult,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.01/5.31 => ( member_real @ ( times_times_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_mult
% 5.01/5.31 thf(fact_7968_Ints__mult,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.01/5.31 => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_mult
% 5.01/5.31 thf(fact_7969_Ints__mult,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.01/5.31 => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_mult
% 5.01/5.31 thf(fact_7970_Ints__mult,axiom,
% 5.01/5.31 ! [A: complex,B: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.01/5.31 => ( member_complex @ ( times_times_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_mult
% 5.01/5.31 thf(fact_7971_Ints__numeral,axiom,
% 5.01/5.31 ! [N: num] : ( member_complex @ ( numera6690914467698888265omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_numeral
% 5.01/5.31 thf(fact_7972_Ints__numeral,axiom,
% 5.01/5.31 ! [N: num] : ( member_real @ ( numeral_numeral_real @ N ) @ ring_1_Ints_real ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_numeral
% 5.01/5.31 thf(fact_7973_Ints__numeral,axiom,
% 5.01/5.31 ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_numeral
% 5.01/5.31 thf(fact_7974_Ints__numeral,axiom,
% 5.01/5.31 ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_numeral
% 5.01/5.31 thf(fact_7975_cosh__real__pos,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_pos
% 5.01/5.31 thf(fact_7976_cosh__real__nonpos__le__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) )
% 5.01/5.31 = ( ord_less_eq_real @ Y @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonpos_le_iff
% 5.01/5.31 thf(fact_7977_cosh__real__nonneg__le__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.31 => ( ( ord_less_eq_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) )
% 5.01/5.31 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonneg_le_iff
% 5.01/5.31 thf(fact_7978_cosh__real__nonneg,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonneg
% 5.01/5.31 thf(fact_7979_cosh__real__ge__1,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_ge_1
% 5.01/5.31 thf(fact_7980_Ints__double__eq__0__iff,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( ( ( plus_plus_complex @ A @ A )
% 5.01/5.31 = zero_zero_complex )
% 5.01/5.31 = ( A = zero_zero_complex ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_double_eq_0_iff
% 5.01/5.31 thf(fact_7981_Ints__double__eq__0__iff,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( ( plus_plus_real @ A @ A )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 = ( A = zero_zero_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_double_eq_0_iff
% 5.01/5.31 thf(fact_7982_Ints__double__eq__0__iff,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( ( plus_plus_rat @ A @ A )
% 5.01/5.31 = zero_zero_rat )
% 5.01/5.31 = ( A = zero_zero_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_double_eq_0_iff
% 5.01/5.31 thf(fact_7983_Ints__double__eq__0__iff,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( ( plus_plus_int @ A @ A )
% 5.01/5.31 = zero_zero_int )
% 5.01/5.31 = ( A = zero_zero_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_double_eq_0_iff
% 5.01/5.31 thf(fact_7984_binomial__gbinomial,axiom,
% 5.01/5.31 ! [N: nat,K: nat] :
% 5.01/5.31 ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.01/5.31 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % binomial_gbinomial
% 5.01/5.31 thf(fact_7985_binomial__gbinomial,axiom,
% 5.01/5.31 ! [N: nat,K: nat] :
% 5.01/5.31 ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.01/5.31 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % binomial_gbinomial
% 5.01/5.31 thf(fact_7986_sinh__less__cosh__real,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_less_cosh_real
% 5.01/5.31 thf(fact_7987_sinh__le__cosh__real,axiom,
% 5.01/5.31 ! [X2: real] : ( ord_less_eq_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_le_cosh_real
% 5.01/5.31 thf(fact_7988_gbinomial__Suc__Suc,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_Suc_Suc
% 5.01/5.31 thf(fact_7989_gbinomial__Suc__Suc,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_Suc_Suc
% 5.01/5.31 thf(fact_7990_gbinomial__Suc__Suc,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_Suc_Suc
% 5.01/5.31 thf(fact_7991_cosh__real__strict__mono,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.31 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_strict_mono
% 5.01/5.31 thf(fact_7992_cosh__real__nonneg__less__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.31 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) )
% 5.01/5.31 = ( ord_less_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonneg_less_iff
% 5.01/5.31 thf(fact_7993_cosh__real__nonpos__less__iff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.01/5.31 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) )
% 5.01/5.31 = ( ord_less_real @ Y @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_real_nonpos_less_iff
% 5.01/5.31 thf(fact_7994_gbinomial__of__nat__symmetric,axiom,
% 5.01/5.31 ! [K: nat,N: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.31 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.01/5.31 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_of_nat_symmetric
% 5.01/5.31 thf(fact_7995_gbinomial__of__nat__symmetric,axiom,
% 5.01/5.31 ! [K: nat,N: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ K @ N )
% 5.01/5.31 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.01/5.31 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_of_nat_symmetric
% 5.01/5.31 thf(fact_7996_Ints__odd__nonzero,axiom,
% 5.01/5.31 ! [A: complex] :
% 5.01/5.31 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.01/5.31 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 5.01/5.31 != zero_zero_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_nonzero
% 5.01/5.31 thf(fact_7997_Ints__odd__nonzero,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 5.01/5.31 != zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_nonzero
% 5.01/5.31 thf(fact_7998_Ints__odd__nonzero,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 5.01/5.31 != zero_zero_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_nonzero
% 5.01/5.31 thf(fact_7999_Ints__odd__nonzero,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 5.01/5.31 != zero_zero_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_nonzero
% 5.01/5.31 thf(fact_8000_of__int__divide__in__Ints,axiom,
% 5.01/5.31 ! [B: int,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.31 => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_divide_in_Ints
% 5.01/5.31 thf(fact_8001_of__int__divide__in__Ints,axiom,
% 5.01/5.31 ! [B: int,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.31 => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_divide_in_Ints
% 5.01/5.31 thf(fact_8002_of__int__divide__in__Ints,axiom,
% 5.01/5.31 ! [B: int,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.31 => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_divide_in_Ints
% 5.01/5.31 thf(fact_8003_of__int__divide__in__Ints,axiom,
% 5.01/5.31 ! [B: int,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ B @ A )
% 5.01/5.31 => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_divide_in_Ints
% 5.01/5.31 thf(fact_8004_arcosh__cosh__real,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.31 => ( ( arcosh_real @ ( cosh_real @ X2 ) )
% 5.01/5.31 = X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % arcosh_cosh_real
% 5.01/5.31 thf(fact_8005_cosh__add,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( cosh_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_add
% 5.01/5.31 thf(fact_8006_cosh__add,axiom,
% 5.01/5.31 ! [X2: complex,Y: complex] :
% 5.01/5.31 ( ( cosh_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_complex @ ( times_times_complex @ ( cosh_complex @ X2 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X2 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_add
% 5.01/5.31 thf(fact_8007_sinh__add,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( sinh_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X2 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X2 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_add
% 5.01/5.31 thf(fact_8008_sinh__add,axiom,
% 5.01/5.31 ! [X2: complex,Y: complex] :
% 5.01/5.31 ( ( sinh_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.31 = ( plus_plus_complex @ ( times_times_complex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X2 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_add
% 5.01/5.31 thf(fact_8009_sinh__diff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( sinh_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X2 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X2 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_diff
% 5.01/5.31 thf(fact_8010_sinh__diff,axiom,
% 5.01/5.31 ! [X2: complex,Y: complex] :
% 5.01/5.31 ( ( sinh_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_complex @ ( times_times_complex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X2 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_diff
% 5.01/5.31 thf(fact_8011_cosh__diff,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( cosh_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_diff
% 5.01/5.31 thf(fact_8012_cosh__diff,axiom,
% 5.01/5.31 ! [X2: complex,Y: complex] :
% 5.01/5.31 ( ( cosh_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.31 = ( minus_minus_complex @ ( times_times_complex @ ( cosh_complex @ X2 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X2 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_diff
% 5.01/5.31 thf(fact_8013_cosh__plus__sinh,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( plus_plus_complex @ ( cosh_complex @ X2 ) @ ( sinh_complex @ X2 ) )
% 5.01/5.31 = ( exp_complex @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_plus_sinh
% 5.01/5.31 thf(fact_8014_cosh__plus__sinh,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( plus_plus_real @ ( cosh_real @ X2 ) @ ( sinh_real @ X2 ) )
% 5.01/5.31 = ( exp_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_plus_sinh
% 5.01/5.31 thf(fact_8015_sinh__plus__cosh,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( plus_plus_complex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ X2 ) )
% 5.01/5.31 = ( exp_complex @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_plus_cosh
% 5.01/5.31 thf(fact_8016_sinh__plus__cosh,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( plus_plus_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) )
% 5.01/5.31 = ( exp_real @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_plus_cosh
% 5.01/5.31 thf(fact_8017_tanh__def,axiom,
% 5.01/5.31 ( tanh_complex
% 5.01/5.31 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X3 ) @ ( cosh_complex @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tanh_def
% 5.01/5.31 thf(fact_8018_tanh__def,axiom,
% 5.01/5.31 ( tanh_real
% 5.01/5.31 = ( ^ [X3: real] : ( divide_divide_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tanh_def
% 5.01/5.31 thf(fact_8019_gbinomial__addition__formula,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_addition_formula
% 5.01/5.31 thf(fact_8020_gbinomial__addition__formula,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_addition_formula
% 5.01/5.31 thf(fact_8021_gbinomial__addition__formula,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.01/5.31 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_addition_formula
% 5.01/5.31 thf(fact_8022_gbinomial__absorb__comp,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.01/5.31 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorb_comp
% 5.01/5.31 thf(fact_8023_gbinomial__absorb__comp,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.01/5.31 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorb_comp
% 5.01/5.31 thf(fact_8024_gbinomial__absorb__comp,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.01/5.31 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorb_comp
% 5.01/5.31 thf(fact_8025_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.01/5.31 ! [K: nat,A: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.01/5.31 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_ge_n_over_k_pow_k
% 5.01/5.31 thf(fact_8026_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.01/5.31 ! [K: nat,A: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.01/5.31 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_ge_n_over_k_pow_k
% 5.01/5.31 thf(fact_8027_gbinomial__mult__1,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.01/5.31 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1
% 5.01/5.31 thf(fact_8028_gbinomial__mult__1,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.01/5.31 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1
% 5.01/5.31 thf(fact_8029_gbinomial__mult__1,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.01/5.31 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1
% 5.01/5.31 thf(fact_8030_gbinomial__mult__1_H,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.01/5.31 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1'
% 5.01/5.31 thf(fact_8031_gbinomial__mult__1_H,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.01/5.31 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K ) @ ( gbinomial_real @ A @ K ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1'
% 5.01/5.31 thf(fact_8032_gbinomial__mult__1_H,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.01/5.31 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_mult_1'
% 5.01/5.31 thf(fact_8033_even__xor__iff,axiom,
% 5.01/5.31 ! [A: code_integer,B: code_integer] :
% 5.01/5.31 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 5.01/5.31 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.01/5.31 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_xor_iff
% 5.01/5.31 thf(fact_8034_even__xor__iff,axiom,
% 5.01/5.31 ! [A: nat,B: nat] :
% 5.01/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.01/5.31 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.01/5.31 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_xor_iff
% 5.01/5.31 thf(fact_8035_even__xor__iff,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.01/5.31 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.01/5.31 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_xor_iff
% 5.01/5.31 thf(fact_8036_Ints__odd__less__0,axiom,
% 5.01/5.31 ! [A: real] :
% 5.01/5.31 ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 5.01/5.31 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_less_0
% 5.01/5.31 thf(fact_8037_Ints__odd__less__0,axiom,
% 5.01/5.31 ! [A: rat] :
% 5.01/5.31 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.01/5.31 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_less_0
% 5.01/5.31 thf(fact_8038_Ints__odd__less__0,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( member_int @ A @ ring_1_Ints_int )
% 5.01/5.31 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.01/5.31 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_odd_less_0
% 5.01/5.31 thf(fact_8039_Ints__nonzero__abs__ge1,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.01/5.31 => ( ( X2 != zero_z3403309356797280102nteger )
% 5.01/5.31 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_ge1
% 5.01/5.31 thf(fact_8040_Ints__nonzero__abs__ge1,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 => ( ( X2 != zero_zero_real )
% 5.01/5.31 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_ge1
% 5.01/5.31 thf(fact_8041_Ints__nonzero__abs__ge1,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( X2 != zero_zero_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_ge1
% 5.01/5.31 thf(fact_8042_Ints__nonzero__abs__ge1,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.01/5.31 => ( ( X2 != zero_zero_int )
% 5.01/5.31 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_ge1
% 5.01/5.31 thf(fact_8043_Ints__nonzero__abs__less1,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.01/5.31 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer )
% 5.01/5.31 => ( X2 = zero_z3403309356797280102nteger ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_less1
% 5.01/5.31 thf(fact_8044_Ints__nonzero__abs__less1,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 => ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.31 => ( X2 = zero_zero_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_less1
% 5.01/5.31 thf(fact_8045_Ints__nonzero__abs__less1,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat )
% 5.01/5.31 => ( X2 = zero_zero_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_less1
% 5.01/5.31 thf(fact_8046_Ints__nonzero__abs__less1,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.01/5.31 => ( ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int )
% 5.01/5.31 => ( X2 = zero_zero_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_nonzero_abs_less1
% 5.01/5.31 thf(fact_8047_Ints__eq__abs__less1,axiom,
% 5.01/5.31 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.31 ( ( member_Code_integer @ X2 @ ring_11222124179247155820nteger )
% 5.01/5.31 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 5.01/5.31 => ( ( X2 = Y )
% 5.01/5.31 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_eq_abs_less1
% 5.01/5.31 thf(fact_8048_Ints__eq__abs__less1,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 => ( ( member_real @ Y @ ring_1_Ints_real )
% 5.01/5.31 => ( ( X2 = Y )
% 5.01/5.31 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_eq_abs_less1
% 5.01/5.31 thf(fact_8049_Ints__eq__abs__less1,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( X2 = Y )
% 5.01/5.31 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_eq_abs_less1
% 5.01/5.31 thf(fact_8050_Ints__eq__abs__less1,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( member_int @ X2 @ ring_1_Ints_int )
% 5.01/5.31 => ( ( member_int @ Y @ ring_1_Ints_int )
% 5.01/5.31 => ( ( X2 = Y )
% 5.01/5.31 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Ints_eq_abs_less1
% 5.01/5.31 thf(fact_8051_sin__times__pi__eq__0,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( sin_real @ ( times_times_real @ X2 @ pi ) )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sin_times_pi_eq_0
% 5.01/5.31 thf(fact_8052_cosh__minus__sinh,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( minus_minus_real @ ( cosh_real @ X2 ) @ ( sinh_real @ X2 ) )
% 5.01/5.31 = ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_minus_sinh
% 5.01/5.31 thf(fact_8053_cosh__minus__sinh,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( minus_minus_complex @ ( cosh_complex @ X2 ) @ ( sinh_complex @ X2 ) )
% 5.01/5.31 = ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_minus_sinh
% 5.01/5.31 thf(fact_8054_sinh__minus__cosh,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( minus_minus_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) )
% 5.01/5.31 = ( uminus_uminus_real @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_minus_cosh
% 5.01/5.31 thf(fact_8055_sinh__minus__cosh,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( minus_minus_complex @ ( sinh_complex @ X2 ) @ ( cosh_complex @ X2 ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_minus_cosh
% 5.01/5.31 thf(fact_8056_Suc__times__gbinomial,axiom,
% 5.01/5.31 ! [K: nat,A: rat] :
% 5.01/5.31 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Suc_times_gbinomial
% 5.01/5.31 thf(fact_8057_Suc__times__gbinomial,axiom,
% 5.01/5.31 ! [K: nat,A: real] :
% 5.01/5.31 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Suc_times_gbinomial
% 5.01/5.31 thf(fact_8058_Suc__times__gbinomial,axiom,
% 5.01/5.31 ! [K: nat,A: complex] :
% 5.01/5.31 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Suc_times_gbinomial
% 5.01/5.31 thf(fact_8059_gbinomial__absorption,axiom,
% 5.01/5.31 ! [K: nat,A: rat] :
% 5.01/5.31 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption
% 5.01/5.31 thf(fact_8060_gbinomial__absorption,axiom,
% 5.01/5.31 ! [K: nat,A: real] :
% 5.01/5.31 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption
% 5.01/5.31 thf(fact_8061_gbinomial__absorption,axiom,
% 5.01/5.31 ! [K: nat,A: complex] :
% 5.01/5.31 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.01/5.31 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_absorption
% 5.01/5.31 thf(fact_8062_gbinomial__trinomial__revision,axiom,
% 5.01/5.31 ! [K: nat,M: nat,A: rat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ K @ M )
% 5.01/5.31 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.01/5.31 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_trinomial_revision
% 5.01/5.31 thf(fact_8063_gbinomial__trinomial__revision,axiom,
% 5.01/5.31 ! [K: nat,M: nat,A: real] :
% 5.01/5.31 ( ( ord_less_eq_nat @ K @ M )
% 5.01/5.31 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.01/5.31 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_trinomial_revision
% 5.01/5.31 thf(fact_8064_gbinomial__trinomial__revision,axiom,
% 5.01/5.31 ! [K: nat,M: nat,A: complex] :
% 5.01/5.31 ( ( ord_less_eq_nat @ K @ M )
% 5.01/5.31 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.01/5.31 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_trinomial_revision
% 5.01/5.31 thf(fact_8065_frac__neg,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.31 = zero_zero_real ) )
% 5.01/5.31 & ( ~ ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.31 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.31 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X2 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_neg
% 5.01/5.31 thf(fact_8066_frac__neg,axiom,
% 5.01/5.31 ! [X2: rat] :
% 5.01/5.31 ( ( ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.01/5.31 = zero_zero_rat ) )
% 5.01/5.31 & ( ~ ( member_rat @ X2 @ ring_1_Ints_rat )
% 5.01/5.31 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X2 ) )
% 5.01/5.31 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X2 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_neg
% 5.01/5.31 thf(fact_8067_sinh__double,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.31 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X2 ) ) @ ( cosh_complex @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_double
% 5.01/5.31 thf(fact_8068_sinh__double,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.31 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X2 ) ) @ ( cosh_real @ X2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_double
% 5.01/5.31 thf(fact_8069_gbinomial__factors,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_factors
% 5.01/5.31 thf(fact_8070_gbinomial__factors,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_factors
% 5.01/5.31 thf(fact_8071_gbinomial__factors,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_factors
% 5.01/5.31 thf(fact_8072_gbinomial__rec,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_rec
% 5.01/5.31 thf(fact_8073_gbinomial__rec,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_rec
% 5.01/5.31 thf(fact_8074_gbinomial__rec,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.01/5.31 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_rec
% 5.01/5.31 thf(fact_8075_gbinomial__index__swap,axiom,
% 5.01/5.31 ! [K: nat,N: nat] :
% 5.01/5.31 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K ) )
% 5.01/5.31 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_index_swap
% 5.01/5.31 thf(fact_8076_gbinomial__index__swap,axiom,
% 5.01/5.31 ! [K: nat,N: nat] :
% 5.01/5.31 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K ) )
% 5.01/5.31 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_index_swap
% 5.01/5.31 thf(fact_8077_gbinomial__index__swap,axiom,
% 5.01/5.31 ! [K: nat,N: nat] :
% 5.01/5.31 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.01/5.31 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_index_swap
% 5.01/5.31 thf(fact_8078_gbinomial__negated__upper,axiom,
% 5.01/5.31 ( gbinomial_rat
% 5.01/5.31 = ( ^ [A4: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A4 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_negated_upper
% 5.01/5.31 thf(fact_8079_gbinomial__negated__upper,axiom,
% 5.01/5.31 ( gbinomial_real
% 5.01/5.31 = ( ^ [A4: real,K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A4 ) @ one_one_real ) @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_negated_upper
% 5.01/5.31 thf(fact_8080_gbinomial__negated__upper,axiom,
% 5.01/5.31 ( gbinomial_complex
% 5.01/5.31 = ( ^ [A4: complex,K2: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A4 ) @ one_one_complex ) @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_negated_upper
% 5.01/5.31 thf(fact_8081_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8082_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8083_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8084_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8085_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8086_le__mult__floor__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % le_mult_floor_Ints
% 5.01/5.31 thf(fact_8087_frac__unique__iff,axiom,
% 5.01/5.31 ! [X2: real,A: real] :
% 5.01/5.31 ( ( ( archim2898591450579166408c_real @ X2 )
% 5.01/5.31 = A )
% 5.01/5.31 = ( ( member_real @ ( minus_minus_real @ X2 @ A ) @ ring_1_Ints_real )
% 5.01/5.31 & ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_unique_iff
% 5.01/5.31 thf(fact_8088_frac__unique__iff,axiom,
% 5.01/5.31 ! [X2: rat,A: rat] :
% 5.01/5.31 ( ( ( archimedean_frac_rat @ X2 )
% 5.01/5.31 = A )
% 5.01/5.31 = ( ( member_rat @ ( minus_minus_rat @ X2 @ A ) @ ring_1_Ints_rat )
% 5.01/5.31 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % frac_unique_iff
% 5.01/5.31 thf(fact_8089_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8090_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8091_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: real,B: real] :
% 5.01/5.31 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.01/5.31 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.01/5.31 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8092_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8093_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8094_mult__ceiling__le__Ints,axiom,
% 5.01/5.31 ! [A: rat,B: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.01/5.31 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.01/5.31 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % mult_ceiling_le_Ints
% 5.01/5.31 thf(fact_8095_tanh__add,axiom,
% 5.01/5.31 ! [X2: complex,Y: complex] :
% 5.01/5.31 ( ( ( cosh_complex @ X2 )
% 5.01/5.31 != zero_zero_complex )
% 5.01/5.31 => ( ( ( cosh_complex @ Y )
% 5.01/5.31 != zero_zero_complex )
% 5.01/5.31 => ( ( tanh_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.31 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X2 ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X2 ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tanh_add
% 5.01/5.31 thf(fact_8096_tanh__add,axiom,
% 5.01/5.31 ! [X2: real,Y: real] :
% 5.01/5.31 ( ( ( cosh_real @ X2 )
% 5.01/5.31 != zero_zero_real )
% 5.01/5.31 => ( ( ( cosh_real @ Y )
% 5.01/5.31 != zero_zero_real )
% 5.01/5.31 => ( ( tanh_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.01/5.31 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % tanh_add
% 5.01/5.31 thf(fact_8097_gbinomial__minus,axiom,
% 5.01/5.31 ! [A: rat,K: nat] :
% 5.01/5.31 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.01/5.31 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_minus
% 5.01/5.31 thf(fact_8098_gbinomial__minus,axiom,
% 5.01/5.31 ! [A: real,K: nat] :
% 5.01/5.31 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.01/5.31 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_minus
% 5.01/5.31 thf(fact_8099_gbinomial__minus,axiom,
% 5.01/5.31 ! [A: complex,K: nat] :
% 5.01/5.31 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.01/5.31 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_minus
% 5.01/5.31 thf(fact_8100_gbinomial__reduce__nat,axiom,
% 5.01/5.31 ! [K: nat,A: real] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_real @ A @ K )
% 5.01/5.31 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_reduce_nat
% 5.01/5.31 thf(fact_8101_gbinomial__reduce__nat,axiom,
% 5.01/5.31 ! [K: nat,A: rat] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_rat @ A @ K )
% 5.01/5.31 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_reduce_nat
% 5.01/5.31 thf(fact_8102_gbinomial__reduce__nat,axiom,
% 5.01/5.31 ! [K: nat,A: complex] :
% 5.01/5.31 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.01/5.31 => ( ( gbinomial_complex @ A @ K )
% 5.01/5.31 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_reduce_nat
% 5.01/5.31 thf(fact_8103_gbinomial__pochhammer,axiom,
% 5.01/5.31 ( gbinomial_rat
% 5.01/5.31 = ( ^ [A4: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A4 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer
% 5.01/5.31 thf(fact_8104_gbinomial__pochhammer,axiom,
% 5.01/5.31 ( gbinomial_real
% 5.01/5.31 = ( ^ [A4: real,K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A4 ) @ K2 ) ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer
% 5.01/5.31 thf(fact_8105_gbinomial__pochhammer,axiom,
% 5.01/5.31 ( gbinomial_complex
% 5.01/5.31 = ( ^ [A4: complex,K2: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A4 ) @ K2 ) ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer
% 5.01/5.31 thf(fact_8106_gbinomial__pochhammer_H,axiom,
% 5.01/5.31 ( gbinomial_rat
% 5.01/5.31 = ( ^ [A4: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer'
% 5.01/5.31 thf(fact_8107_gbinomial__pochhammer_H,axiom,
% 5.01/5.31 ( gbinomial_real
% 5.01/5.31 = ( ^ [A4: real,K2: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer'
% 5.01/5.31 thf(fact_8108_gbinomial__pochhammer_H,axiom,
% 5.01/5.31 ( gbinomial_complex
% 5.01/5.31 = ( ^ [A4: complex,K2: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % gbinomial_pochhammer'
% 5.01/5.31 thf(fact_8109_sin__integer__2pi,axiom,
% 5.01/5.31 ! [N: real] :
% 5.01/5.31 ( ( member_real @ N @ ring_1_Ints_real )
% 5.01/5.31 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.01/5.31 = zero_zero_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sin_integer_2pi
% 5.01/5.31 thf(fact_8110_cos__integer__2pi,axiom,
% 5.01/5.31 ! [N: real] :
% 5.01/5.31 ( ( member_real @ N @ ring_1_Ints_real )
% 5.01/5.31 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.01/5.31 = one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % cos_integer_2pi
% 5.01/5.31 thf(fact_8111_cosh__field__def,axiom,
% 5.01/5.31 ( cosh_real
% 5.01/5.31 = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_field_def
% 5.01/5.31 thf(fact_8112_cosh__field__def,axiom,
% 5.01/5.31 ( cosh_complex
% 5.01/5.31 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_field_def
% 5.01/5.31 thf(fact_8113_xor__nat__unfold,axiom,
% 5.01/5.31 ( bit_se6528837805403552850or_nat
% 5.01/5.31 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_unfold
% 5.01/5.31 thf(fact_8114_cosh__square__eq,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( power_power_real @ ( cosh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_square_eq
% 5.01/5.31 thf(fact_8115_cosh__square__eq,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( power_power_complex @ ( cosh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_square_eq
% 5.01/5.31 thf(fact_8116_sinh__square__eq,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( power_power_real @ ( sinh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_square_eq
% 5.01/5.31 thf(fact_8117_sinh__square__eq,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( power_power_complex @ ( sinh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.01/5.31
% 5.01/5.31 % sinh_square_eq
% 5.01/5.31 thf(fact_8118_hyperbolic__pythagoras,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = one_one_real ) ).
% 5.01/5.31
% 5.01/5.31 % hyperbolic_pythagoras
% 5.01/5.31 thf(fact_8119_hyperbolic__pythagoras,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = one_one_complex ) ).
% 5.01/5.31
% 5.01/5.31 % hyperbolic_pythagoras
% 5.01/5.31 thf(fact_8120_xor__nat__rec,axiom,
% 5.01/5.31 ( bit_se6528837805403552850or_nat
% 5.01/5.31 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.31 ( plus_plus_nat
% 5.01/5.31 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.31 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.01/5.31 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.01/5.31 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_rec
% 5.01/5.31 thf(fact_8121_one__xor__eq,axiom,
% 5.01/5.31 ! [A: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 5.01/5.31 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n356916108424825756nteger
% 5.01/5.31 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_xor_eq
% 5.01/5.31 thf(fact_8122_one__xor__eq,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 5.01/5.31 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.31 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_xor_eq
% 5.01/5.31 thf(fact_8123_one__xor__eq,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 5.01/5.31 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n2684676970156552555ol_int
% 5.01/5.31 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % one_xor_eq
% 5.01/5.31 thf(fact_8124_xor__one__eq,axiom,
% 5.01/5.31 ! [A: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 5.01/5.31 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n356916108424825756nteger
% 5.01/5.31 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_one_eq
% 5.01/5.31 thf(fact_8125_xor__one__eq,axiom,
% 5.01/5.31 ! [A: nat] :
% 5.01/5.31 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 5.01/5.31 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.31 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_one_eq
% 5.01/5.31 thf(fact_8126_xor__one__eq,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 5.01/5.31 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.01/5.31 @ ( zero_n2684676970156552555ol_int
% 5.01/5.31 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_one_eq
% 5.01/5.31 thf(fact_8127_cosh__zero__iff,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( ( cosh_real @ X2 )
% 5.01/5.31 = zero_zero_real )
% 5.01/5.31 = ( ( power_power_real @ ( exp_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_zero_iff
% 5.01/5.31 thf(fact_8128_cosh__zero__iff,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( ( cosh_complex @ X2 )
% 5.01/5.31 = zero_zero_complex )
% 5.01/5.31 = ( ( power_power_complex @ ( exp_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_zero_iff
% 5.01/5.31 thf(fact_8129_cosh__double,axiom,
% 5.01/5.31 ! [X2: complex] :
% 5.01/5.31 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.31 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_double
% 5.01/5.31 thf(fact_8130_cosh__double,axiom,
% 5.01/5.31 ! [X2: real] :
% 5.01/5.31 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.01/5.31 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % cosh_double
% 5.01/5.31 thf(fact_8131_horner__sum__of__bool__2__less,axiom,
% 5.01/5.31 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % horner_sum_of_bool_2_less
% 5.01/5.31 thf(fact_8132_push__bit__numeral__minus__1,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_numeral_minus_1
% 5.01/5.31 thf(fact_8133_push__bit__numeral__minus__1,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_numeral_minus_1
% 5.01/5.31 thf(fact_8134_subset__antisym,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.01/5.31 => ( A2 = B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_antisym
% 5.01/5.31 thf(fact_8135_subsetI,axiom,
% 5.01/5.31 ! [A2: set_real,B4: set_real] :
% 5.01/5.31 ( ! [X4: real] :
% 5.01/5.31 ( ( member_real @ X4 @ A2 )
% 5.01/5.31 => ( member_real @ X4 @ B4 ) )
% 5.01/5.31 => ( ord_less_eq_set_real @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetI
% 5.01/5.31 thf(fact_8136_subsetI,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ! [X4: nat] :
% 5.01/5.31 ( ( member_nat @ X4 @ A2 )
% 5.01/5.31 => ( member_nat @ X4 @ B4 ) )
% 5.01/5.31 => ( ord_less_eq_set_nat @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetI
% 5.01/5.31 thf(fact_8137_subsetI,axiom,
% 5.01/5.31 ! [A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ! [X4: complex] :
% 5.01/5.31 ( ( member_complex @ X4 @ A2 )
% 5.01/5.31 => ( member_complex @ X4 @ B4 ) )
% 5.01/5.31 => ( ord_le211207098394363844omplex @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetI
% 5.01/5.31 thf(fact_8138_subsetI,axiom,
% 5.01/5.31 ! [A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ! [X4: set_nat] :
% 5.01/5.31 ( ( member_set_nat @ X4 @ A2 )
% 5.01/5.31 => ( member_set_nat @ X4 @ B4 ) )
% 5.01/5.31 => ( ord_le6893508408891458716et_nat @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetI
% 5.01/5.31 thf(fact_8139_subsetI,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ! [X4: int] :
% 5.01/5.31 ( ( member_int @ X4 @ A2 )
% 5.01/5.31 => ( member_int @ X4 @ B4 ) )
% 5.01/5.31 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetI
% 5.01/5.31 thf(fact_8140_Compl__subset__Compl__iff,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B4 ) )
% 5.01/5.31 = ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % Compl_subset_Compl_iff
% 5.01/5.31 thf(fact_8141_psubsetI,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( A2 != B4 )
% 5.01/5.31 => ( ord_less_set_int @ A2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubsetI
% 5.01/5.31 thf(fact_8142_push__bit__nonnegative__int__iff,axiom,
% 5.01/5.31 ! [N: nat,K: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.01/5.31 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_nonnegative_int_iff
% 5.01/5.31 thf(fact_8143_push__bit__negative__int__iff,axiom,
% 5.01/5.31 ! [N: nat,K: int] :
% 5.01/5.31 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.31 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_negative_int_iff
% 5.01/5.31 thf(fact_8144_push__bit__eq__0__iff,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( ( bit_se545348938243370406it_int @ N @ A )
% 5.01/5.31 = zero_zero_int )
% 5.01/5.31 = ( A = zero_zero_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_eq_0_iff
% 5.01/5.31 thf(fact_8145_push__bit__eq__0__iff,axiom,
% 5.01/5.31 ! [N: nat,A: nat] :
% 5.01/5.31 ( ( ( bit_se547839408752420682it_nat @ N @ A )
% 5.01/5.31 = zero_zero_nat )
% 5.01/5.31 = ( A = zero_zero_nat ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_eq_0_iff
% 5.01/5.31 thf(fact_8146_push__bit__of__0,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ zero_zero_int )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_0
% 5.01/5.31 thf(fact_8147_push__bit__of__0,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ zero_zero_nat )
% 5.01/5.31 = zero_zero_nat ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_0
% 5.01/5.31 thf(fact_8148_Compl__anti__mono,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B4 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Compl_anti_mono
% 5.01/5.31 thf(fact_8149_push__bit__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_push_bit
% 5.01/5.31 thf(fact_8150_push__bit__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_push_bit
% 5.01/5.31 thf(fact_8151_push__bit__and,axiom,
% 5.01/5.31 ! [N: nat,A: int,B: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.01/5.31 = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_and
% 5.01/5.31 thf(fact_8152_push__bit__and,axiom,
% 5.01/5.31 ! [N: nat,A: nat,B: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.01/5.31 = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_and
% 5.01/5.31 thf(fact_8153_push__bit__xor,axiom,
% 5.01/5.31 ! [N: nat,A: int,B: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.01/5.31 = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_xor
% 5.01/5.31 thf(fact_8154_push__bit__xor,axiom,
% 5.01/5.31 ! [N: nat,A: nat,B: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.01/5.31 = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_xor
% 5.01/5.31 thf(fact_8155_concat__bit__of__zero__1,axiom,
% 5.01/5.31 ! [N: nat,L: int] :
% 5.01/5.31 ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 5.01/5.31
% 5.01/5.31 % concat_bit_of_zero_1
% 5.01/5.31 thf(fact_8156_xor__nonnegative__int__iff,axiom,
% 5.01/5.31 ! [K: int,L: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.01/5.31 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.31 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nonnegative_int_iff
% 5.01/5.31 thf(fact_8157_xor__negative__int__iff,axiom,
% 5.01/5.31 ! [K: int,L: int] :
% 5.01/5.31 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.01/5.31 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.31 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_negative_int_iff
% 5.01/5.31 thf(fact_8158_push__bit__Suc__numeral,axiom,
% 5.01/5.31 ! [N: nat,K: num] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( numeral_numeral_int @ K ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ N @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc_numeral
% 5.01/5.31 thf(fact_8159_push__bit__Suc__numeral,axiom,
% 5.01/5.31 ! [N: nat,K: num] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc_numeral
% 5.01/5.31 thf(fact_8160_push__bit__Suc__minus__numeral,axiom,
% 5.01/5.31 ! [N: nat,K: num] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.01/5.31 = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc_minus_numeral
% 5.01/5.31 thf(fact_8161_push__bit__Suc__minus__numeral,axiom,
% 5.01/5.31 ! [N: nat,K: num] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc_minus_numeral
% 5.01/5.31 thf(fact_8162_push__bit__numeral,axiom,
% 5.01/5.31 ! [L: num,K: num] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ K ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_numeral
% 5.01/5.31 thf(fact_8163_push__bit__numeral,axiom,
% 5.01/5.31 ! [L: num,K: num] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_numeral
% 5.01/5.31 thf(fact_8164_push__bit__Suc,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc
% 5.01/5.31 thf(fact_8165_push__bit__Suc,axiom,
% 5.01/5.31 ! [N: nat,A: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_Suc
% 5.01/5.31 thf(fact_8166_push__bit__of__1,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 5.01/5.31 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_1
% 5.01/5.31 thf(fact_8167_push__bit__of__1,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 5.01/5.31 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_1
% 5.01/5.31 thf(fact_8168_push__bit__of__Suc__0,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.31 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_Suc_0
% 5.01/5.31 thf(fact_8169_even__push__bit__iff,axiom,
% 5.01/5.31 ! [N: nat,A: code_integer] :
% 5.01/5.31 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N @ A ) )
% 5.01/5.31 = ( ( N != zero_zero_nat )
% 5.01/5.31 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_push_bit_iff
% 5.01/5.31 thf(fact_8170_even__push__bit__iff,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.01/5.31 = ( ( N != zero_zero_nat )
% 5.01/5.31 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_push_bit_iff
% 5.01/5.31 thf(fact_8171_even__push__bit__iff,axiom,
% 5.01/5.31 ! [N: nat,A: nat] :
% 5.01/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.01/5.31 = ( ( N != zero_zero_nat )
% 5.01/5.31 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_push_bit_iff
% 5.01/5.31 thf(fact_8172_push__bit__minus__numeral,axiom,
% 5.01/5.31 ! [L: num,K: num] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.01/5.31 = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus_numeral
% 5.01/5.31 thf(fact_8173_push__bit__minus__numeral,axiom,
% 5.01/5.31 ! [L: num,K: num] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus_numeral
% 5.01/5.31 thf(fact_8174_bit__xor__int__iff,axiom,
% 5.01/5.31 ! [K: int,L: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 5.01/5.31 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.01/5.31 != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_xor_int_iff
% 5.01/5.31 thf(fact_8175_flip__bit__int__def,axiom,
% 5.01/5.31 ( bit_se2159334234014336723it_int
% 5.01/5.31 = ( ^ [N4: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % flip_bit_int_def
% 5.01/5.31 thf(fact_8176_push__bit__add,axiom,
% 5.01/5.31 ! [N: nat,A: int,B: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( plus_plus_int @ A @ B ) )
% 5.01/5.31 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_add
% 5.01/5.31 thf(fact_8177_push__bit__add,axiom,
% 5.01/5.31 ! [N: nat,A: nat,B: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( plus_plus_nat @ A @ B ) )
% 5.01/5.31 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_add
% 5.01/5.31 thf(fact_8178_push__bit__minus,axiom,
% 5.01/5.31 ! [N: nat,A: code_integer] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus
% 5.01/5.31 thf(fact_8179_push__bit__minus,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 5.01/5.31 = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus
% 5.01/5.31 thf(fact_8180_push__bit__nat__eq,axiom,
% 5.01/5.31 ! [N: nat,K: int] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.01/5.31 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_nat_eq
% 5.01/5.31 thf(fact_8181_push__bit__of__nat,axiom,
% 5.01/5.31 ! [N: nat,M: nat] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ N @ ( semiri4939895301339042750nteger @ M ) )
% 5.01/5.31 = ( semiri4939895301339042750nteger @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_nat
% 5.01/5.31 thf(fact_8182_push__bit__of__nat,axiom,
% 5.01/5.31 ! [N: nat,M: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.01/5.31 = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_nat
% 5.01/5.31 thf(fact_8183_push__bit__of__nat,axiom,
% 5.01/5.31 ! [N: nat,M: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.01/5.31 = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_nat
% 5.01/5.31 thf(fact_8184_of__nat__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri4939895301339042750nteger @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se7788150548672797655nteger @ M @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_push_bit
% 5.01/5.31 thf(fact_8185_of__nat__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_push_bit
% 5.01/5.31 thf(fact_8186_of__nat__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_nat_push_bit
% 5.01/5.31 thf(fact_8187_push__bit__of__int,axiom,
% 5.01/5.31 ! [N: nat,K: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.01/5.31 = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_of_int
% 5.01/5.31 thf(fact_8188_XOR__lower,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.31 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % XOR_lower
% 5.01/5.31 thf(fact_8189_push__bit__take__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.01/5.31 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_take_bit
% 5.01/5.31 thf(fact_8190_push__bit__take__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.01/5.31 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_take_bit
% 5.01/5.31 thf(fact_8191_take__bit__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: int] :
% 5.01/5.31 ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.01/5.31 = ( bit_se545348938243370406it_int @ N @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_push_bit
% 5.01/5.31 thf(fact_8192_take__bit__push__bit,axiom,
% 5.01/5.31 ! [M: nat,N: nat,A: nat] :
% 5.01/5.31 ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.01/5.31 = ( bit_se547839408752420682it_nat @ N @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_push_bit
% 5.01/5.31 thf(fact_8193_flip__bit__nat__def,axiom,
% 5.01/5.31 ( bit_se2161824704523386999it_nat
% 5.01/5.31 = ( ^ [M3: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % flip_bit_nat_def
% 5.01/5.31 thf(fact_8194_bit__push__bit__iff__int,axiom,
% 5.01/5.31 ! [M: nat,K: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.01/5.31 = ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_push_bit_iff_int
% 5.01/5.31 thf(fact_8195_xor__nat__def,axiom,
% 5.01/5.31 ( bit_se6528837805403552850or_nat
% 5.01/5.31 = ( ^ [M3: nat,N4: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_nat_def
% 5.01/5.31 thf(fact_8196_psubsetE,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_set_int @ A2 @ B4 )
% 5.01/5.31 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubsetE
% 5.01/5.31 thf(fact_8197_psubset__eq,axiom,
% 5.01/5.31 ( ord_less_set_int
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.01/5.31 & ( A6 != B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_eq
% 5.01/5.31 thf(fact_8198_psubset__imp__subset,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_subset
% 5.01/5.31 thf(fact_8199_psubset__subset__trans,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,C5: set_int] :
% 5.01/5.31 ( ( ord_less_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 5.01/5.31 => ( ord_less_set_int @ A2 @ C5 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_subset_trans
% 5.01/5.31 thf(fact_8200_subset__not__subset__eq,axiom,
% 5.01/5.31 ( ord_less_set_int
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.01/5.31 & ~ ( ord_less_eq_set_int @ B7 @ A6 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_not_subset_eq
% 5.01/5.31 thf(fact_8201_subset__psubset__trans,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,C5: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_set_int @ B4 @ C5 )
% 5.01/5.31 => ( ord_less_set_int @ A2 @ C5 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_psubset_trans
% 5.01/5.31 thf(fact_8202_subset__iff__psubset__eq,axiom,
% 5.01/5.31 ( ord_less_eq_set_int
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ( ( ord_less_set_int @ A6 @ B7 )
% 5.01/5.31 | ( A6 = B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff_psubset_eq
% 5.01/5.31 thf(fact_8203_in__mono,axiom,
% 5.01/5.31 ! [A2: set_real,B4: set_real,X2: real] :
% 5.01/5.31 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.01/5.31 => ( ( member_real @ X2 @ A2 )
% 5.01/5.31 => ( member_real @ X2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % in_mono
% 5.01/5.31 thf(fact_8204_in__mono,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat,X2: nat] :
% 5.01/5.31 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.01/5.31 => ( ( member_nat @ X2 @ A2 )
% 5.01/5.31 => ( member_nat @ X2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % in_mono
% 5.01/5.31 thf(fact_8205_in__mono,axiom,
% 5.01/5.31 ! [A2: set_complex,B4: set_complex,X2: complex] :
% 5.01/5.31 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.01/5.31 => ( ( member_complex @ X2 @ A2 )
% 5.01/5.31 => ( member_complex @ X2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % in_mono
% 5.01/5.31 thf(fact_8206_in__mono,axiom,
% 5.01/5.31 ! [A2: set_set_nat,B4: set_set_nat,X2: set_nat] :
% 5.01/5.31 ( ( ord_le6893508408891458716et_nat @ A2 @ B4 )
% 5.01/5.31 => ( ( member_set_nat @ X2 @ A2 )
% 5.01/5.31 => ( member_set_nat @ X2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % in_mono
% 5.01/5.31 thf(fact_8207_in__mono,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,X2: int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( member_int @ X2 @ A2 )
% 5.01/5.31 => ( member_int @ X2 @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % in_mono
% 5.01/5.31 thf(fact_8208_subsetD,axiom,
% 5.01/5.31 ! [A2: set_real,B4: set_real,C: real] :
% 5.01/5.31 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.01/5.31 => ( ( member_real @ C @ A2 )
% 5.01/5.31 => ( member_real @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetD
% 5.01/5.31 thf(fact_8209_subsetD,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat,C: nat] :
% 5.01/5.31 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.01/5.31 => ( ( member_nat @ C @ A2 )
% 5.01/5.31 => ( member_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetD
% 5.01/5.31 thf(fact_8210_subsetD,axiom,
% 5.01/5.31 ! [A2: set_complex,B4: set_complex,C: complex] :
% 5.01/5.31 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.01/5.31 => ( ( member_complex @ C @ A2 )
% 5.01/5.31 => ( member_complex @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetD
% 5.01/5.31 thf(fact_8211_subsetD,axiom,
% 5.01/5.31 ! [A2: set_set_nat,B4: set_set_nat,C: set_nat] :
% 5.01/5.31 ( ( ord_le6893508408891458716et_nat @ A2 @ B4 )
% 5.01/5.31 => ( ( member_set_nat @ C @ A2 )
% 5.01/5.31 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetD
% 5.01/5.31 thf(fact_8212_subsetD,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,C: int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( member_int @ C @ A2 )
% 5.01/5.31 => ( member_int @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subsetD
% 5.01/5.31 thf(fact_8213_equalityE,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( A2 = B4 )
% 5.01/5.31 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ~ ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % equalityE
% 5.01/5.31 thf(fact_8214_subset__eq,axiom,
% 5.01/5.31 ( ord_less_eq_set_real
% 5.01/5.31 = ( ^ [A6: set_real,B7: set_real] :
% 5.01/5.31 ! [X3: real] :
% 5.01/5.31 ( ( member_real @ X3 @ A6 )
% 5.01/5.31 => ( member_real @ X3 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_eq
% 5.01/5.31 thf(fact_8215_subset__eq,axiom,
% 5.01/5.31 ( ord_less_eq_set_nat
% 5.01/5.31 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.01/5.31 ! [X3: nat] :
% 5.01/5.31 ( ( member_nat @ X3 @ A6 )
% 5.01/5.31 => ( member_nat @ X3 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_eq
% 5.01/5.31 thf(fact_8216_subset__eq,axiom,
% 5.01/5.31 ( ord_le211207098394363844omplex
% 5.01/5.31 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.01/5.31 ! [X3: complex] :
% 5.01/5.31 ( ( member_complex @ X3 @ A6 )
% 5.01/5.31 => ( member_complex @ X3 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_eq
% 5.01/5.31 thf(fact_8217_subset__eq,axiom,
% 5.01/5.31 ( ord_le6893508408891458716et_nat
% 5.01/5.31 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.01/5.31 ! [X3: set_nat] :
% 5.01/5.31 ( ( member_set_nat @ X3 @ A6 )
% 5.01/5.31 => ( member_set_nat @ X3 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_eq
% 5.01/5.31 thf(fact_8218_subset__eq,axiom,
% 5.01/5.31 ( ord_less_eq_set_int
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ! [X3: int] :
% 5.01/5.31 ( ( member_int @ X3 @ A6 )
% 5.01/5.31 => ( member_int @ X3 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_eq
% 5.01/5.31 thf(fact_8219_equalityD1,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( A2 = B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % equalityD1
% 5.01/5.31 thf(fact_8220_equalityD2,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( A2 = B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % equalityD2
% 5.01/5.31 thf(fact_8221_subset__iff,axiom,
% 5.01/5.31 ( ord_less_eq_set_real
% 5.01/5.31 = ( ^ [A6: set_real,B7: set_real] :
% 5.01/5.31 ! [T2: real] :
% 5.01/5.31 ( ( member_real @ T2 @ A6 )
% 5.01/5.31 => ( member_real @ T2 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff
% 5.01/5.31 thf(fact_8222_subset__iff,axiom,
% 5.01/5.31 ( ord_less_eq_set_nat
% 5.01/5.31 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.01/5.31 ! [T2: nat] :
% 5.01/5.31 ( ( member_nat @ T2 @ A6 )
% 5.01/5.31 => ( member_nat @ T2 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff
% 5.01/5.31 thf(fact_8223_subset__iff,axiom,
% 5.01/5.31 ( ord_le211207098394363844omplex
% 5.01/5.31 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.01/5.31 ! [T2: complex] :
% 5.01/5.31 ( ( member_complex @ T2 @ A6 )
% 5.01/5.31 => ( member_complex @ T2 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff
% 5.01/5.31 thf(fact_8224_subset__iff,axiom,
% 5.01/5.31 ( ord_le6893508408891458716et_nat
% 5.01/5.31 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.01/5.31 ! [T2: set_nat] :
% 5.01/5.31 ( ( member_set_nat @ T2 @ A6 )
% 5.01/5.31 => ( member_set_nat @ T2 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff
% 5.01/5.31 thf(fact_8225_subset__iff,axiom,
% 5.01/5.31 ( ord_less_eq_set_int
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ! [T2: int] :
% 5.01/5.31 ( ( member_int @ T2 @ A6 )
% 5.01/5.31 => ( member_int @ T2 @ B7 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_iff
% 5.01/5.31 thf(fact_8226_subset__refl,axiom,
% 5.01/5.31 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.01/5.31
% 5.01/5.31 % subset_refl
% 5.01/5.31 thf(fact_8227_Collect__mono,axiom,
% 5.01/5.31 ! [P: complex > $o,Q: complex > $o] :
% 5.01/5.31 ( ! [X4: complex] :
% 5.01/5.31 ( ( P @ X4 )
% 5.01/5.31 => ( Q @ X4 ) )
% 5.01/5.31 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono
% 5.01/5.31 thf(fact_8228_Collect__mono,axiom,
% 5.01/5.31 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.01/5.31 ( ! [X4: list_nat] :
% 5.01/5.31 ( ( P @ X4 )
% 5.01/5.31 => ( Q @ X4 ) )
% 5.01/5.31 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono
% 5.01/5.31 thf(fact_8229_Collect__mono,axiom,
% 5.01/5.31 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.01/5.31 ( ! [X4: set_nat] :
% 5.01/5.31 ( ( P @ X4 )
% 5.01/5.31 => ( Q @ X4 ) )
% 5.01/5.31 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono
% 5.01/5.31 thf(fact_8230_Collect__mono,axiom,
% 5.01/5.31 ! [P: nat > $o,Q: nat > $o] :
% 5.01/5.31 ( ! [X4: nat] :
% 5.01/5.31 ( ( P @ X4 )
% 5.01/5.31 => ( Q @ X4 ) )
% 5.01/5.31 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono
% 5.01/5.31 thf(fact_8231_Collect__mono,axiom,
% 5.01/5.31 ! [P: int > $o,Q: int > $o] :
% 5.01/5.31 ( ! [X4: int] :
% 5.01/5.31 ( ( P @ X4 )
% 5.01/5.31 => ( Q @ X4 ) )
% 5.01/5.31 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono
% 5.01/5.31 thf(fact_8232_subset__trans,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,C5: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 5.01/5.31 => ( ord_less_eq_set_int @ A2 @ C5 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % subset_trans
% 5.01/5.31 thf(fact_8233_set__eq__subset,axiom,
% 5.01/5.31 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.01/5.31 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A6 @ B7 )
% 5.01/5.31 & ( ord_less_eq_set_int @ B7 @ A6 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % set_eq_subset
% 5.01/5.31 thf(fact_8234_Collect__mono__iff,axiom,
% 5.01/5.31 ! [P: complex > $o,Q: complex > $o] :
% 5.01/5.31 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.01/5.31 = ( ! [X3: complex] :
% 5.01/5.31 ( ( P @ X3 )
% 5.01/5.31 => ( Q @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono_iff
% 5.01/5.31 thf(fact_8235_Collect__mono__iff,axiom,
% 5.01/5.31 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.01/5.31 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.01/5.31 = ( ! [X3: list_nat] :
% 5.01/5.31 ( ( P @ X3 )
% 5.01/5.31 => ( Q @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono_iff
% 5.01/5.31 thf(fact_8236_Collect__mono__iff,axiom,
% 5.01/5.31 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.01/5.31 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.01/5.31 = ( ! [X3: set_nat] :
% 5.01/5.31 ( ( P @ X3 )
% 5.01/5.31 => ( Q @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono_iff
% 5.01/5.31 thf(fact_8237_Collect__mono__iff,axiom,
% 5.01/5.31 ! [P: nat > $o,Q: nat > $o] :
% 5.01/5.31 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.01/5.31 = ( ! [X3: nat] :
% 5.01/5.31 ( ( P @ X3 )
% 5.01/5.31 => ( Q @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono_iff
% 5.01/5.31 thf(fact_8238_Collect__mono__iff,axiom,
% 5.01/5.31 ! [P: int > $o,Q: int > $o] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.01/5.31 = ( ! [X3: int] :
% 5.01/5.31 ( ( P @ X3 )
% 5.01/5.31 => ( Q @ X3 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Collect_mono_iff
% 5.01/5.31 thf(fact_8239_double__diff,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat,C5: set_nat] :
% 5.01/5.31 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.01/5.31 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C5 @ A2 ) )
% 5.01/5.31 = A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % double_diff
% 5.01/5.31 thf(fact_8240_double__diff,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int,C5: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 5.01/5.31 => ( ( minus_minus_set_int @ B4 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 5.01/5.31 = A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % double_diff
% 5.01/5.31 thf(fact_8241_Diff__subset,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ A2 ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_subset
% 5.01/5.31 thf(fact_8242_Diff__subset,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ A2 ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_subset
% 5.01/5.31 thf(fact_8243_Diff__mono,axiom,
% 5.01/5.31 ! [A2: set_nat,C5: set_nat,D4: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( ord_less_eq_set_nat @ A2 @ C5 )
% 5.01/5.31 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 5.01/5.31 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ ( minus_minus_set_nat @ C5 @ D4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_mono
% 5.01/5.31 thf(fact_8244_Diff__mono,axiom,
% 5.01/5.31 ! [A2: set_int,C5: set_int,D4: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ A2 @ C5 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ D4 @ B4 )
% 5.01/5.31 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ ( minus_minus_set_int @ C5 @ D4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_mono
% 5.01/5.31 thf(fact_8245_bit__push__bit__iff__nat,axiom,
% 5.01/5.31 ! [M: nat,Q2: nat,N: nat] :
% 5.01/5.31 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.01/5.31 = ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_push_bit_iff_nat
% 5.01/5.31 thf(fact_8246_concat__bit__eq,axiom,
% 5.01/5.31 ( bit_concat_bit
% 5.01/5.31 = ( ^ [N4: nat,K2: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N4 @ K2 ) @ ( bit_se545348938243370406it_int @ N4 @ L2 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % concat_bit_eq
% 5.01/5.31 thf(fact_8247_flip__bit__eq__xor,axiom,
% 5.01/5.31 ( bit_se2159334234014336723it_int
% 5.01/5.31 = ( ^ [N4: nat,A4: int] : ( bit_se6526347334894502574or_int @ A4 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % flip_bit_eq_xor
% 5.01/5.31 thf(fact_8248_flip__bit__eq__xor,axiom,
% 5.01/5.31 ( bit_se2161824704523386999it_nat
% 5.01/5.31 = ( ^ [N4: nat,A4: nat] : ( bit_se6528837805403552850or_nat @ A4 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % flip_bit_eq_xor
% 5.01/5.31 thf(fact_8249_push__bit__double,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_double
% 5.01/5.31 thf(fact_8250_push__bit__double,axiom,
% 5.01/5.31 ! [N: nat,A: nat] :
% 5.01/5.31 ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.31 = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_double
% 5.01/5.31 thf(fact_8251_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.01/5.31 ( bit_se1146084159140164899it_int
% 5.01/5.31 = ( ^ [A4: int,N4: nat] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ A4 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) )
% 5.01/5.31 != zero_zero_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_iff_and_push_bit_not_eq_0
% 5.01/5.31 thf(fact_8252_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.01/5.31 ( bit_se1148574629649215175it_nat
% 5.01/5.31 = ( ^ [A4: nat,N4: nat] :
% 5.01/5.31 ( ( bit_se727722235901077358nd_nat @ A4 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) )
% 5.01/5.31 != zero_zero_nat ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_iff_and_push_bit_not_eq_0
% 5.01/5.31 thf(fact_8253_push__bit__int__def,axiom,
% 5.01/5.31 ( bit_se545348938243370406it_int
% 5.01/5.31 = ( ^ [N4: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_int_def
% 5.01/5.31 thf(fact_8254_push__bit__nat__def,axiom,
% 5.01/5.31 ( bit_se547839408752420682it_nat
% 5.01/5.31 = ( ^ [N4: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_nat_def
% 5.01/5.31 thf(fact_8255_push__bit__eq__mult,axiom,
% 5.01/5.31 ( bit_se545348938243370406it_int
% 5.01/5.31 = ( ^ [N4: nat,A4: int] : ( times_times_int @ A4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_eq_mult
% 5.01/5.31 thf(fact_8256_push__bit__eq__mult,axiom,
% 5.01/5.31 ( bit_se547839408752420682it_nat
% 5.01/5.31 = ( ^ [N4: nat,A4: nat] : ( times_times_nat @ A4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_eq_mult
% 5.01/5.31 thf(fact_8257_exp__dvdE,axiom,
% 5.01/5.31 ! [N: nat,A: code_integer] :
% 5.01/5.31 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A )
% 5.01/5.31 => ~ ! [B2: code_integer] :
% 5.01/5.31 ( A
% 5.01/5.31 != ( bit_se7788150548672797655nteger @ N @ B2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_dvdE
% 5.01/5.31 thf(fact_8258_exp__dvdE,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A )
% 5.01/5.31 => ~ ! [B2: int] :
% 5.01/5.31 ( A
% 5.01/5.31 != ( bit_se545348938243370406it_int @ N @ B2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_dvdE
% 5.01/5.31 thf(fact_8259_exp__dvdE,axiom,
% 5.01/5.31 ! [N: nat,A: nat] :
% 5.01/5.31 ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A )
% 5.01/5.31 => ~ ! [B2: nat] :
% 5.01/5.31 ( A
% 5.01/5.31 != ( bit_se547839408752420682it_nat @ N @ B2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % exp_dvdE
% 5.01/5.31 thf(fact_8260_push__bit__minus__one,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus_one
% 5.01/5.31 thf(fact_8261_XOR__upper,axiom,
% 5.01/5.31 ! [X2: int,N: nat,Y: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.31 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.31 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.31 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % XOR_upper
% 5.01/5.31 thf(fact_8262_xor__int__rec,axiom,
% 5.01/5.31 ( bit_se6526347334894502574or_int
% 5.01/5.31 = ( ^ [K2: int,L2: int] :
% 5.01/5.31 ( plus_plus_int
% 5.01/5.31 @ ( zero_n2684676970156552555ol_int
% 5.01/5.31 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.01/5.31 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.01/5.31 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_int_rec
% 5.01/5.31 thf(fact_8263_bit__horner__sum__bit__iff,axiom,
% 5.01/5.31 ! [Bs: list_o,N: nat] :
% 5.01/5.31 ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.01/5.31 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.01/5.31 & ( nth_o @ Bs @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_horner_sum_bit_iff
% 5.01/5.31 thf(fact_8264_bit__horner__sum__bit__iff,axiom,
% 5.01/5.31 ! [Bs: list_o,N: nat] :
% 5.01/5.31 ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.01/5.31 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.01/5.31 & ( nth_o @ Bs @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_horner_sum_bit_iff
% 5.01/5.31 thf(fact_8265_bit__horner__sum__bit__iff,axiom,
% 5.01/5.31 ! [Bs: list_o,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.01/5.31 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.01/5.31 & ( nth_o @ Bs @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_horner_sum_bit_iff
% 5.01/5.31 thf(fact_8266_xor__int__unfold,axiom,
% 5.01/5.31 ( bit_se6526347334894502574or_int
% 5.01/5.31 = ( ^ [K2: int,L2: int] :
% 5.01/5.31 ( if_int
% 5.01/5.31 @ ( K2
% 5.01/5.31 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.01/5.31 @ ( if_int
% 5.01/5.31 @ ( L2
% 5.01/5.31 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.01/5.31 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % xor_int_unfold
% 5.01/5.31 thf(fact_8267_valid__eq,axiom,
% 5.01/5.31 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.01/5.31
% 5.01/5.31 % valid_eq
% 5.01/5.31 thf(fact_8268_valid__eq1,axiom,
% 5.01/5.31 ! [T: vEBT_VEBT,D: nat] :
% 5.01/5.31 ( ( vEBT_invar_vebt @ T @ D )
% 5.01/5.31 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.01/5.31
% 5.01/5.31 % valid_eq1
% 5.01/5.31 thf(fact_8269_valid__eq2,axiom,
% 5.01/5.31 ! [T: vEBT_VEBT,D: nat] :
% 5.01/5.31 ( ( vEBT_VEBT_valid @ T @ D )
% 5.01/5.31 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.01/5.31
% 5.01/5.31 % valid_eq2
% 5.01/5.31 thf(fact_8270_Diff__idemp,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ B4 )
% 5.01/5.31 = ( minus_minus_set_nat @ A2 @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_idemp
% 5.01/5.31 thf(fact_8271_Diff__iff,axiom,
% 5.01/5.31 ! [C: real,A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.01/5.31 = ( ( member_real @ C @ A2 )
% 5.01/5.31 & ~ ( member_real @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_iff
% 5.01/5.31 thf(fact_8272_Diff__iff,axiom,
% 5.01/5.31 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.01/5.31 = ( ( member_complex @ C @ A2 )
% 5.01/5.31 & ~ ( member_complex @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_iff
% 5.01/5.31 thf(fact_8273_Diff__iff,axiom,
% 5.01/5.31 ! [C: int,A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.01/5.31 = ( ( member_int @ C @ A2 )
% 5.01/5.31 & ~ ( member_int @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_iff
% 5.01/5.31 thf(fact_8274_Diff__iff,axiom,
% 5.01/5.31 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.01/5.31 = ( ( member_set_nat @ C @ A2 )
% 5.01/5.31 & ~ ( member_set_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_iff
% 5.01/5.31 thf(fact_8275_Diff__iff,axiom,
% 5.01/5.31 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.01/5.31 = ( ( member_nat @ C @ A2 )
% 5.01/5.31 & ~ ( member_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Diff_iff
% 5.01/5.31 thf(fact_8276_DiffI,axiom,
% 5.01/5.31 ! [C: real,A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( member_real @ C @ A2 )
% 5.01/5.31 => ( ~ ( member_real @ C @ B4 )
% 5.01/5.31 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffI
% 5.01/5.31 thf(fact_8277_DiffI,axiom,
% 5.01/5.31 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( member_complex @ C @ A2 )
% 5.01/5.31 => ( ~ ( member_complex @ C @ B4 )
% 5.01/5.31 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffI
% 5.01/5.31 thf(fact_8278_DiffI,axiom,
% 5.01/5.31 ! [C: int,A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( member_int @ C @ A2 )
% 5.01/5.31 => ( ~ ( member_int @ C @ B4 )
% 5.01/5.31 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffI
% 5.01/5.31 thf(fact_8279_DiffI,axiom,
% 5.01/5.31 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( member_set_nat @ C @ A2 )
% 5.01/5.31 => ( ~ ( member_set_nat @ C @ B4 )
% 5.01/5.31 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffI
% 5.01/5.31 thf(fact_8280_DiffI,axiom,
% 5.01/5.31 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( member_nat @ C @ A2 )
% 5.01/5.31 => ( ~ ( member_nat @ C @ B4 )
% 5.01/5.31 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffI
% 5.01/5.31 thf(fact_8281_bit_Odouble__compl,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X2 ) )
% 5.01/5.31 = X2 ) ).
% 5.01/5.31
% 5.01/5.31 % bit.double_compl
% 5.01/5.31 thf(fact_8282_bit_Ocompl__eq__compl__iff,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( ( bit_ri7919022796975470100ot_int @ X2 )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ Y ) )
% 5.01/5.31 = ( X2 = Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.compl_eq_compl_iff
% 5.01/5.31 thf(fact_8283_bit_Oxor__compl__left,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X2 ) @ Y )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_compl_left
% 5.01/5.31 thf(fact_8284_bit_Oxor__compl__right,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ X2 @ ( bit_ri7919022796975470100ot_int @ Y ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_compl_right
% 5.01/5.31 thf(fact_8285_bit_Oconj__cancel__right,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ X2 @ ( bit_ri7919022796975470100ot_int @ X2 ) )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % bit.conj_cancel_right
% 5.01/5.31 thf(fact_8286_bit_Oconj__cancel__left,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X2 ) @ X2 )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % bit.conj_cancel_left
% 5.01/5.31 thf(fact_8287_bit_Ocompl__one,axiom,
% 5.01/5.31 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.31 = zero_z3403309356797280102nteger ) ).
% 5.01/5.31
% 5.01/5.31 % bit.compl_one
% 5.01/5.31 thf(fact_8288_bit_Ocompl__one,axiom,
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % bit.compl_one
% 5.01/5.31 thf(fact_8289_bit_Ocompl__zero,axiom,
% 5.01/5.31 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.compl_zero
% 5.01/5.31 thf(fact_8290_bit_Ocompl__zero,axiom,
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.01/5.31 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.compl_zero
% 5.01/5.31 thf(fact_8291_bit_Oxor__one__left,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.01/5.31 = ( bit_ri7632146776885996613nteger @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_one_left
% 5.01/5.31 thf(fact_8292_bit_Oxor__one__left,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_one_left
% 5.01/5.31 thf(fact_8293_bit_Oxor__one__right,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.31 = ( bit_ri7632146776885996613nteger @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_one_right
% 5.01/5.31 thf(fact_8294_bit_Oxor__one__right,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_one_right
% 5.01/5.31 thf(fact_8295_bit_Oxor__cancel__left,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X2 ) @ X2 )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_cancel_left
% 5.01/5.31 thf(fact_8296_bit_Oxor__cancel__left,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X2 ) @ X2 )
% 5.01/5.31 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_cancel_left
% 5.01/5.31 thf(fact_8297_bit_Oxor__cancel__right,axiom,
% 5.01/5.31 ! [X2: code_integer] :
% 5.01/5.31 ( ( bit_se3222712562003087583nteger @ X2 @ ( bit_ri7632146776885996613nteger @ X2 ) )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_cancel_right
% 5.01/5.31 thf(fact_8298_bit_Oxor__cancel__right,axiom,
% 5.01/5.31 ! [X2: int] :
% 5.01/5.31 ( ( bit_se6526347334894502574or_int @ X2 @ ( bit_ri7919022796975470100ot_int @ X2 ) )
% 5.01/5.31 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit.xor_cancel_right
% 5.01/5.31 thf(fact_8299_not__nonnegative__int__iff,axiom,
% 5.01/5.31 ! [K: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.01/5.31 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_nonnegative_int_iff
% 5.01/5.31 thf(fact_8300_not__negative__int__iff,axiom,
% 5.01/5.31 ! [K: int] :
% 5.01/5.31 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.01/5.31 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_negative_int_iff
% 5.01/5.31 thf(fact_8301_minus__not__numeral__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.01/5.31 = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_not_numeral_eq
% 5.01/5.31 thf(fact_8302_minus__not__numeral__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.31 = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_not_numeral_eq
% 5.01/5.31 thf(fact_8303_even__not__iff,axiom,
% 5.01/5.31 ! [A: code_integer] :
% 5.01/5.31 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 5.01/5.31 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_not_iff
% 5.01/5.31 thf(fact_8304_even__not__iff,axiom,
% 5.01/5.31 ! [A: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.01/5.31 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_not_iff
% 5.01/5.31 thf(fact_8305_push__bit__minus__one__eq__not__mask,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.01/5.31 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus_one_eq_not_mask
% 5.01/5.31 thf(fact_8306_push__bit__minus__one__eq__not__mask,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_minus_one_eq_not_mask
% 5.01/5.31 thf(fact_8307_not__one__eq,axiom,
% 5.01/5.31 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_one_eq
% 5.01/5.31 thf(fact_8308_not__one__eq,axiom,
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 5.01/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_one_eq
% 5.01/5.31 thf(fact_8309_DiffD2,axiom,
% 5.01/5.31 ! [C: real,A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( member_real @ C @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD2
% 5.01/5.31 thf(fact_8310_DiffD2,axiom,
% 5.01/5.31 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( member_complex @ C @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD2
% 5.01/5.31 thf(fact_8311_DiffD2,axiom,
% 5.01/5.31 ! [C: int,A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( member_int @ C @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD2
% 5.01/5.31 thf(fact_8312_DiffD2,axiom,
% 5.01/5.31 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( member_set_nat @ C @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD2
% 5.01/5.31 thf(fact_8313_DiffD2,axiom,
% 5.01/5.31 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( member_nat @ C @ B4 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD2
% 5.01/5.31 thf(fact_8314_DiffD1,axiom,
% 5.01/5.31 ! [C: real,A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.01/5.31 => ( member_real @ C @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD1
% 5.01/5.31 thf(fact_8315_DiffD1,axiom,
% 5.01/5.31 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.01/5.31 => ( member_complex @ C @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD1
% 5.01/5.31 thf(fact_8316_DiffD1,axiom,
% 5.01/5.31 ! [C: int,A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.01/5.31 => ( member_int @ C @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD1
% 5.01/5.31 thf(fact_8317_DiffD1,axiom,
% 5.01/5.31 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.01/5.31 => ( member_set_nat @ C @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD1
% 5.01/5.31 thf(fact_8318_DiffD1,axiom,
% 5.01/5.31 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.01/5.31 => ( member_nat @ C @ A2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffD1
% 5.01/5.31 thf(fact_8319_DiffE,axiom,
% 5.01/5.31 ! [C: real,A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( ( member_real @ C @ A2 )
% 5.01/5.31 => ( member_real @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffE
% 5.01/5.31 thf(fact_8320_DiffE,axiom,
% 5.01/5.31 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( ( member_complex @ C @ A2 )
% 5.01/5.31 => ( member_complex @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffE
% 5.01/5.31 thf(fact_8321_DiffE,axiom,
% 5.01/5.31 ! [C: int,A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( ( member_int @ C @ A2 )
% 5.01/5.31 => ( member_int @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffE
% 5.01/5.31 thf(fact_8322_DiffE,axiom,
% 5.01/5.31 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( ( member_set_nat @ C @ A2 )
% 5.01/5.31 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffE
% 5.01/5.31 thf(fact_8323_DiffE,axiom,
% 5.01/5.31 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.01/5.31 => ~ ( ( member_nat @ C @ A2 )
% 5.01/5.31 => ( member_nat @ C @ B4 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % DiffE
% 5.01/5.31 thf(fact_8324_psubset__imp__ex__mem,axiom,
% 5.01/5.31 ! [A2: set_real,B4: set_real] :
% 5.01/5.31 ( ( ord_less_set_real @ A2 @ B4 )
% 5.01/5.31 => ? [B2: real] : ( member_real @ B2 @ ( minus_minus_set_real @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_ex_mem
% 5.01/5.31 thf(fact_8325_psubset__imp__ex__mem,axiom,
% 5.01/5.31 ! [A2: set_complex,B4: set_complex] :
% 5.01/5.31 ( ( ord_less_set_complex @ A2 @ B4 )
% 5.01/5.31 => ? [B2: complex] : ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_ex_mem
% 5.01/5.31 thf(fact_8326_psubset__imp__ex__mem,axiom,
% 5.01/5.31 ! [A2: set_int,B4: set_int] :
% 5.01/5.31 ( ( ord_less_set_int @ A2 @ B4 )
% 5.01/5.31 => ? [B2: int] : ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_ex_mem
% 5.01/5.31 thf(fact_8327_psubset__imp__ex__mem,axiom,
% 5.01/5.31 ! [A2: set_set_nat,B4: set_set_nat] :
% 5.01/5.31 ( ( ord_less_set_set_nat @ A2 @ B4 )
% 5.01/5.31 => ? [B2: set_nat] : ( member_set_nat @ B2 @ ( minus_2163939370556025621et_nat @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_ex_mem
% 5.01/5.31 thf(fact_8328_psubset__imp__ex__mem,axiom,
% 5.01/5.31 ! [A2: set_nat,B4: set_nat] :
% 5.01/5.31 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.01/5.31 => ? [B2: nat] : ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A2 ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % psubset_imp_ex_mem
% 5.01/5.31 thf(fact_8329_of__int__not__eq,axiom,
% 5.01/5.31 ! [K: int] :
% 5.01/5.31 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_not_eq
% 5.01/5.31 thf(fact_8330_bit__not__int__iff,axiom,
% 5.01/5.31 ! [K: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.01/5.31 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_not_int_iff
% 5.01/5.31 thf(fact_8331_take__bit__not__take__bit,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.01/5.31 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_not_take_bit
% 5.01/5.31 thf(fact_8332_take__bit__not__iff,axiom,
% 5.01/5.31 ! [N: nat,A: int,B: int] :
% 5.01/5.31 ( ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.01/5.31 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 5.01/5.31 = ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.01/5.31 = ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_not_iff
% 5.01/5.31 thf(fact_8333_of__int__not__numeral,axiom,
% 5.01/5.31 ! [K: num] :
% 5.01/5.31 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % of_int_not_numeral
% 5.01/5.31 thf(fact_8334_not__add__distrib,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 5.01/5.31 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_add_distrib
% 5.01/5.31 thf(fact_8335_not__diff__distrib,axiom,
% 5.01/5.31 ! [A: int,B: int] :
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 5.01/5.31 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_diff_distrib
% 5.01/5.31 thf(fact_8336_minus__eq__not__plus__1,axiom,
% 5.01/5.31 ( uminus1351360451143612070nteger
% 5.01/5.31 = ( ^ [A4: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_eq_not_plus_1
% 5.01/5.31 thf(fact_8337_minus__eq__not__plus__1,axiom,
% 5.01/5.31 ( uminus_uminus_int
% 5.01/5.31 = ( ^ [A4: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A4 ) @ one_one_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_eq_not_plus_1
% 5.01/5.31 thf(fact_8338_minus__eq__not__minus__1,axiom,
% 5.01/5.31 ( uminus1351360451143612070nteger
% 5.01/5.31 = ( ^ [A4: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A4 @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_eq_not_minus_1
% 5.01/5.31 thf(fact_8339_minus__eq__not__minus__1,axiom,
% 5.01/5.31 ( uminus_uminus_int
% 5.01/5.31 = ( ^ [A4: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A4 @ one_one_int ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_eq_not_minus_1
% 5.01/5.31 thf(fact_8340_not__eq__complement,axiom,
% 5.01/5.31 ( bit_ri7632146776885996613nteger
% 5.01/5.31 = ( ^ [A4: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A4 ) @ one_one_Code_integer ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_eq_complement
% 5.01/5.31 thf(fact_8341_not__eq__complement,axiom,
% 5.01/5.31 ( bit_ri7919022796975470100ot_int
% 5.01/5.31 = ( ^ [A4: int] : ( minus_minus_int @ ( uminus_uminus_int @ A4 ) @ one_one_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_eq_complement
% 5.01/5.31 thf(fact_8342_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.01/5.31 ! [Uu2: $o,Uv2: $o,D: nat] :
% 5.01/5.31 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 5.01/5.31 = ( D = one_one_nat ) ) ).
% 5.01/5.31
% 5.01/5.31 % VEBT_internal.valid'.simps(1)
% 5.01/5.31 thf(fact_8343_not__int__def,axiom,
% 5.01/5.31 ( bit_ri7919022796975470100ot_int
% 5.01/5.31 = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_int_def
% 5.01/5.31 thf(fact_8344_and__not__numerals_I1_J,axiom,
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(1)
% 5.01/5.31 thf(fact_8345_disjunctive__diff,axiom,
% 5.01/5.31 ! [B: int,A: int] :
% 5.01/5.31 ( ! [N3: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ B @ N3 )
% 5.01/5.31 => ( bit_se1146084159140164899it_int @ A @ N3 ) )
% 5.01/5.31 => ( ( minus_minus_int @ A @ B )
% 5.01/5.31 = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % disjunctive_diff
% 5.01/5.31 thf(fact_8346_take__bit__not__eq__mask__diff,axiom,
% 5.01/5.31 ! [N: nat,A: int] :
% 5.01/5.31 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.01/5.31 = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_not_eq_mask_diff
% 5.01/5.31 thf(fact_8347_minus__numeral__inc__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 5.01/5.31 = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_numeral_inc_eq
% 5.01/5.31 thf(fact_8348_minus__numeral__inc__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_numeral_inc_eq
% 5.01/5.31 thf(fact_8349_unset__bit__int__def,axiom,
% 5.01/5.31 ( bit_se4203085406695923979it_int
% 5.01/5.31 = ( ^ [N4: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % unset_bit_int_def
% 5.01/5.31 thf(fact_8350_not__int__div__2,axiom,
% 5.01/5.31 ! [K: int] :
% 5.01/5.31 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_int_div_2
% 5.01/5.31 thf(fact_8351_even__not__iff__int,axiom,
% 5.01/5.31 ! [K: int] :
% 5.01/5.31 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.01/5.31 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % even_not_iff_int
% 5.01/5.31 thf(fact_8352_not__numeral__Bit0__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_numeral_Bit0_eq
% 5.01/5.31 thf(fact_8353_not__numeral__Bit0__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 5.01/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_numeral_Bit0_eq
% 5.01/5.31 thf(fact_8354_and__not__numerals_I2_J,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.31 = one_one_int ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(2)
% 5.01/5.31 thf(fact_8355_and__not__numerals_I4_J,axiom,
% 5.01/5.31 ! [M: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(4)
% 5.01/5.31 thf(fact_8356_bit__minus__int__iff,axiom,
% 5.01/5.31 ! [K: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.01/5.31 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_minus_int_iff
% 5.01/5.31 thf(fact_8357_not__numeral__BitM__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N ) ) )
% 5.01/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_numeral_BitM_eq
% 5.01/5.31 thf(fact_8358_not__numeral__BitM__eq,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N ) ) )
% 5.01/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_numeral_BitM_eq
% 5.01/5.31 thf(fact_8359_take__bit__not__mask__eq__0,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.31 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) )
% 5.01/5.31 = zero_zero_int ) ) ).
% 5.01/5.31
% 5.01/5.31 % take_bit_not_mask_eq_0
% 5.01/5.31 thf(fact_8360_push__bit__mask__eq,axiom,
% 5.01/5.31 ! [M: nat,N: nat] :
% 5.01/5.31 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.01/5.31 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % push_bit_mask_eq
% 5.01/5.31 thf(fact_8361_unset__bit__eq__and__not,axiom,
% 5.01/5.31 ( bit_se4203085406695923979it_int
% 5.01/5.31 = ( ^ [N4: nat,A4: int] : ( bit_se725231765392027082nd_int @ A4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % unset_bit_eq_and_not
% 5.01/5.31 thf(fact_8362_and__not__numerals_I5_J,axiom,
% 5.01/5.31 ! [M: num,N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(5)
% 5.01/5.31 thf(fact_8363_and__not__numerals_I7_J,axiom,
% 5.01/5.31 ! [M: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.31 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(7)
% 5.01/5.31 thf(fact_8364_and__not__numerals_I3_J,axiom,
% 5.01/5.31 ! [N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.31 = zero_zero_int ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(3)
% 5.01/5.31 thf(fact_8365_and__not__numerals_I6_J,axiom,
% 5.01/5.31 ! [M: num,N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(6)
% 5.01/5.31 thf(fact_8366_and__not__numerals_I9_J,axiom,
% 5.01/5.31 ! [M: num,N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(9)
% 5.01/5.31 thf(fact_8367_bit__not__iff__eq,axiom,
% 5.01/5.31 ! [A: int,N: nat] :
% 5.01/5.31 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N )
% 5.01/5.31 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.01/5.31 != zero_zero_int )
% 5.01/5.31 & ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % bit_not_iff_eq
% 5.01/5.31 thf(fact_8368_minus__exp__eq__not__mask,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.31 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_exp_eq_not_mask
% 5.01/5.31 thf(fact_8369_minus__exp__eq__not__mask,axiom,
% 5.01/5.31 ! [N: nat] :
% 5.01/5.31 ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.31 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % minus_exp_eq_not_mask
% 5.01/5.31 thf(fact_8370_and__not__numerals_I8_J,axiom,
% 5.01/5.31 ! [M: num,N: num] :
% 5.01/5.31 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.31 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % and_not_numerals(8)
% 5.01/5.31 thf(fact_8371_not__int__rec,axiom,
% 5.01/5.31 ( bit_ri7919022796975470100ot_int
% 5.01/5.31 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % not_int_rec
% 5.01/5.31 thf(fact_8372_Cauchy__iff2,axiom,
% 5.01/5.31 ( topolo4055970368930404560y_real
% 5.01/5.31 = ( ^ [X5: nat > real] :
% 5.01/5.31 ! [J3: nat] :
% 5.01/5.31 ? [M8: nat] :
% 5.01/5.31 ! [M3: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.01/5.31 => ! [N4: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ M8 @ N4 )
% 5.01/5.31 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X5 @ M3 ) @ ( X5 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % Cauchy_iff2
% 5.01/5.31 thf(fact_8373_order__refl,axiom,
% 5.01/5.31 ! [X2: set_int] : ( ord_less_eq_set_int @ X2 @ X2 ) ).
% 5.01/5.31
% 5.01/5.31 % order_refl
% 5.01/5.31 thf(fact_8374_order__refl,axiom,
% 5.01/5.31 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 5.01/5.31
% 5.01/5.31 % order_refl
% 5.01/5.31 thf(fact_8375_order__refl,axiom,
% 5.01/5.31 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 5.01/5.31
% 5.01/5.31 % order_refl
% 5.01/5.31 thf(fact_8376_order__refl,axiom,
% 5.01/5.31 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 5.01/5.31
% 5.01/5.31 % order_refl
% 5.01/5.31 thf(fact_8377_order__refl,axiom,
% 5.01/5.31 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 5.01/5.31
% 5.01/5.31 % order_refl
% 5.01/5.31 thf(fact_8378_dual__order_Orefl,axiom,
% 5.01/5.31 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.01/5.31
% 5.01/5.31 % dual_order.refl
% 5.01/5.31 thf(fact_8379_dual__order_Orefl,axiom,
% 5.01/5.31 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.01/5.31
% 5.01/5.31 % dual_order.refl
% 5.01/5.31 thf(fact_8380_dual__order_Orefl,axiom,
% 5.01/5.31 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.01/5.31
% 5.01/5.31 % dual_order.refl
% 5.01/5.31 thf(fact_8381_dual__order_Orefl,axiom,
% 5.01/5.31 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.01/5.31
% 5.01/5.31 % dual_order.refl
% 5.01/5.31 thf(fact_8382_dual__order_Orefl,axiom,
% 5.01/5.31 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.01/5.31
% 5.01/5.31 % dual_order.refl
% 5.01/5.31 thf(fact_8383_order__antisym__conv,axiom,
% 5.01/5.31 ! [Y: set_int,X2: set_int] :
% 5.01/5.31 ( ( ord_less_eq_set_int @ Y @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.31 = ( X2 = Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_antisym_conv
% 5.01/5.31 thf(fact_8384_order__antisym__conv,axiom,
% 5.01/5.31 ! [Y: rat,X2: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.31 = ( X2 = Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_antisym_conv
% 5.01/5.31 thf(fact_8385_order__antisym__conv,axiom,
% 5.01/5.31 ! [Y: num,X2: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ Y @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.31 = ( X2 = Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_antisym_conv
% 5.01/5.31 thf(fact_8386_order__antisym__conv,axiom,
% 5.01/5.31 ! [Y: nat,X2: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.31 = ( X2 = Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_antisym_conv
% 5.01/5.31 thf(fact_8387_order__antisym__conv,axiom,
% 5.01/5.31 ! [Y: int,X2: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ Y @ X2 )
% 5.01/5.31 => ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.31 = ( X2 = Y ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_antisym_conv
% 5.01/5.31 thf(fact_8388_linorder__le__cases,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ~ ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.31 => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_le_cases
% 5.01/5.31 thf(fact_8389_linorder__le__cases,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ~ ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.31 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_le_cases
% 5.01/5.31 thf(fact_8390_linorder__le__cases,axiom,
% 5.01/5.31 ! [X2: nat,Y: nat] :
% 5.01/5.31 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.31 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_le_cases
% 5.01/5.31 thf(fact_8391_linorder__le__cases,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ~ ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.31 => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_le_cases
% 5.01/5.31 thf(fact_8392_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8393_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8394_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8395_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.01/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8396_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.01/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8397_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: num,B: num,F: num > num,C: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8398_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.01/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8399_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: num,B: num,F: num > int,C: int] :
% 5.01/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8400_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8401_ord__le__eq__subst,axiom,
% 5.01/5.31 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.01/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.31 => ( ( ( F @ B )
% 5.01/5.31 = C )
% 5.01/5.31 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_le_eq_subst
% 5.01/5.31 thf(fact_8402_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8403_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8404_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8405_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.31 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8406_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8407_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: num,F: num > num,B: num,C: num] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8408_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8409_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: int,F: num > int,B: num,C: num] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.31 => ( ! [X4: num,Y3: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8410_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.31 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8411_ord__eq__le__subst,axiom,
% 5.01/5.31 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.01/5.31 ( ( A
% 5.01/5.31 = ( F @ B ) )
% 5.01/5.31 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.31 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.31 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.31 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.31
% 5.01/5.31 % ord_eq_le_subst
% 5.01/5.31 thf(fact_8412_linorder__linear,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.31 | ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_linear
% 5.01/5.31 thf(fact_8413_linorder__linear,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.31 | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_linear
% 5.01/5.31 thf(fact_8414_linorder__linear,axiom,
% 5.01/5.31 ! [X2: nat,Y: nat] :
% 5.01/5.31 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.31 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_linear
% 5.01/5.31 thf(fact_8415_linorder__linear,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.31 | ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.01/5.31
% 5.01/5.31 % linorder_linear
% 5.01/5.31 thf(fact_8416_order__eq__refl,axiom,
% 5.01/5.31 ! [X2: set_int,Y: set_int] :
% 5.01/5.31 ( ( X2 = Y )
% 5.01/5.31 => ( ord_less_eq_set_int @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_eq_refl
% 5.01/5.31 thf(fact_8417_order__eq__refl,axiom,
% 5.01/5.31 ! [X2: rat,Y: rat] :
% 5.01/5.31 ( ( X2 = Y )
% 5.01/5.31 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_eq_refl
% 5.01/5.31 thf(fact_8418_order__eq__refl,axiom,
% 5.01/5.31 ! [X2: num,Y: num] :
% 5.01/5.31 ( ( X2 = Y )
% 5.01/5.31 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_eq_refl
% 5.01/5.31 thf(fact_8419_order__eq__refl,axiom,
% 5.01/5.31 ! [X2: nat,Y: nat] :
% 5.01/5.31 ( ( X2 = Y )
% 5.01/5.31 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_eq_refl
% 5.01/5.31 thf(fact_8420_order__eq__refl,axiom,
% 5.01/5.31 ! [X2: int,Y: int] :
% 5.01/5.31 ( ( X2 = Y )
% 5.01/5.31 => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.01/5.31
% 5.01/5.31 % order_eq_refl
% 5.01/5.31 thf(fact_8421_order__subst2,axiom,
% 5.01/5.31 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8422_order__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8423_order__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8424_order__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8425_order__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8426_order__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8427_order__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8428_order__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8429_order__subst2,axiom,
% 5.01/5.32 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8430_order__subst2,axiom,
% 5.01/5.32 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst2
% 5.01/5.32 thf(fact_8431_order__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8432_order__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8433_order__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8434_order__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8435_order__subst1,axiom,
% 5.01/5.32 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8436_order__subst1,axiom,
% 5.01/5.32 ! [A: num,F: num > num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8437_order__subst1,axiom,
% 5.01/5.32 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8438_order__subst1,axiom,
% 5.01/5.32 ! [A: num,F: int > num,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8439_order__subst1,axiom,
% 5.01/5.32 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8440_order__subst1,axiom,
% 5.01/5.32 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_subst1
% 5.01/5.32 thf(fact_8441_Orderings_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: set_int,B3: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.01/5.32 & ( ord_less_eq_set_int @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Orderings.order_eq_iff
% 5.01/5.32 thf(fact_8442_Orderings_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.01/5.32 & ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Orderings.order_eq_iff
% 5.01/5.32 thf(fact_8443_Orderings_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: num,B3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.01/5.32 & ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Orderings.order_eq_iff
% 5.01/5.32 thf(fact_8444_Orderings_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.01/5.32 & ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Orderings.order_eq_iff
% 5.01/5.32 thf(fact_8445_Orderings_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: int,B3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.01/5.32 & ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Orderings.order_eq_iff
% 5.01/5.32 thf(fact_8446_antisym,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ B @ A )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym
% 5.01/5.32 thf(fact_8447_antisym,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym
% 5.01/5.32 thf(fact_8448_antisym,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ A )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym
% 5.01/5.32 thf(fact_8449_antisym,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym
% 5.01/5.32 thf(fact_8450_antisym,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ A )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym
% 5.01/5.32 thf(fact_8451_dual__order_Otrans,axiom,
% 5.01/5.32 ! [B: set_int,A: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ C @ B )
% 5.01/5.32 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.trans
% 5.01/5.32 thf(fact_8452_dual__order_Otrans,axiom,
% 5.01/5.32 ! [B: rat,A: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_rat @ C @ B )
% 5.01/5.32 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.trans
% 5.01/5.32 thf(fact_8453_dual__order_Otrans,axiom,
% 5.01/5.32 ! [B: num,A: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_num @ C @ B )
% 5.01/5.32 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.trans
% 5.01/5.32 thf(fact_8454_dual__order_Otrans,axiom,
% 5.01/5.32 ! [B: nat,A: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_nat @ C @ B )
% 5.01/5.32 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.trans
% 5.01/5.32 thf(fact_8455_dual__order_Otrans,axiom,
% 5.01/5.32 ! [B: int,A: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_int @ C @ B )
% 5.01/5.32 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.trans
% 5.01/5.32 thf(fact_8456_dual__order_Oantisym,axiom,
% 5.01/5.32 ! [B: set_int,A: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.antisym
% 5.01/5.32 thf(fact_8457_dual__order_Oantisym,axiom,
% 5.01/5.32 ! [B: rat,A: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.antisym
% 5.01/5.32 thf(fact_8458_dual__order_Oantisym,axiom,
% 5.01/5.32 ! [B: num,A: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.antisym
% 5.01/5.32 thf(fact_8459_dual__order_Oantisym,axiom,
% 5.01/5.32 ! [B: nat,A: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.antisym
% 5.01/5.32 thf(fact_8460_dual__order_Oantisym,axiom,
% 5.01/5.32 ! [B: int,A: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.antisym
% 5.01/5.32 thf(fact_8461_dual__order_Oeq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: set_int,B3: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.01/5.32 & ( ord_less_eq_set_int @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.eq_iff
% 5.01/5.32 thf(fact_8462_dual__order_Oeq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.01/5.32 & ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.eq_iff
% 5.01/5.32 thf(fact_8463_dual__order_Oeq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: num,B3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.01/5.32 & ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.eq_iff
% 5.01/5.32 thf(fact_8464_dual__order_Oeq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.01/5.32 & ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.eq_iff
% 5.01/5.32 thf(fact_8465_dual__order_Oeq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [A4: int,B3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.01/5.32 & ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.eq_iff
% 5.01/5.32 thf(fact_8466_linorder__wlog,axiom,
% 5.01/5.32 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.01/5.32 ( ! [A3: rat,B2: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: rat,B2: rat] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_wlog
% 5.01/5.32 thf(fact_8467_linorder__wlog,axiom,
% 5.01/5.32 ! [P: num > num > $o,A: num,B: num] :
% 5.01/5.32 ( ! [A3: num,B2: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: num,B2: num] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_wlog
% 5.01/5.32 thf(fact_8468_linorder__wlog,axiom,
% 5.01/5.32 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.01/5.32 ( ! [A3: nat,B2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: nat,B2: nat] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_wlog
% 5.01/5.32 thf(fact_8469_linorder__wlog,axiom,
% 5.01/5.32 ! [P: int > int > $o,A: int,B: int] :
% 5.01/5.32 ( ! [A3: int,B2: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: int,B2: int] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_wlog
% 5.01/5.32 thf(fact_8470_order__trans,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int,Z: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_eq_set_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_trans
% 5.01/5.32 thf(fact_8471_order__trans,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.01/5.32 => ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_trans
% 5.01/5.32 thf(fact_8472_order__trans,axiom,
% 5.01/5.32 ! [X2: num,Y: num,Z: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_num @ Y @ Z )
% 5.01/5.32 => ( ord_less_eq_num @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_trans
% 5.01/5.32 thf(fact_8473_order__trans,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,Z: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.01/5.32 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_trans
% 5.01/5.32 thf(fact_8474_order__trans,axiom,
% 5.01/5.32 ! [X2: int,Y: int,Z: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_trans
% 5.01/5.32 thf(fact_8475_order_Otrans,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ B @ C )
% 5.01/5.32 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.trans
% 5.01/5.32 thf(fact_8476_order_Otrans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.trans
% 5.01/5.32 thf(fact_8477_order_Otrans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.trans
% 5.01/5.32 thf(fact_8478_order_Otrans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.trans
% 5.01/5.32 thf(fact_8479_order_Otrans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.32 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.trans
% 5.01/5.32 thf(fact_8480_order__antisym,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ Y @ X2 )
% 5.01/5.32 => ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_antisym
% 5.01/5.32 thf(fact_8481_order__antisym,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.32 => ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_antisym
% 5.01/5.32 thf(fact_8482_order__antisym,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_num @ Y @ X2 )
% 5.01/5.32 => ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_antisym
% 5.01/5.32 thf(fact_8483_order__antisym,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.32 => ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_antisym
% 5.01/5.32 thf(fact_8484_order__antisym,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_int @ Y @ X2 )
% 5.01/5.32 => ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_antisym
% 5.01/5.32 thf(fact_8485_ord__le__eq__trans,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_le_eq_trans
% 5.01/5.32 thf(fact_8486_ord__le__eq__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_le_eq_trans
% 5.01/5.32 thf(fact_8487_ord__le__eq__trans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_le_eq_trans
% 5.01/5.32 thf(fact_8488_ord__le__eq__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_le_eq_trans
% 5.01/5.32 thf(fact_8489_ord__le__eq__trans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_le_eq_trans
% 5.01/5.32 thf(fact_8490_ord__eq__le__trans,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int,C: set_int] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ B @ C )
% 5.01/5.32 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_le_trans
% 5.01/5.32 thf(fact_8491_ord__eq__le__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_le_trans
% 5.01/5.32 thf(fact_8492_ord__eq__le__trans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_le_trans
% 5.01/5.32 thf(fact_8493_ord__eq__le__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_le_trans
% 5.01/5.32 thf(fact_8494_ord__eq__le__trans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.32 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_le_trans
% 5.01/5.32 thf(fact_8495_order__class_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [X3: set_int,Y2: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 5.01/5.32 & ( ord_less_eq_set_int @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_class.order_eq_iff
% 5.01/5.32 thf(fact_8496_order__class_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [X3: rat,Y2: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 5.01/5.32 & ( ord_less_eq_rat @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_class.order_eq_iff
% 5.01/5.32 thf(fact_8497_order__class_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [X3: num,Y2: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X3 @ Y2 )
% 5.01/5.32 & ( ord_less_eq_num @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_class.order_eq_iff
% 5.01/5.32 thf(fact_8498_order__class_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [X3: nat,Y2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 5.01/5.32 & ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_class.order_eq_iff
% 5.01/5.32 thf(fact_8499_order__class_Oorder__eq__iff,axiom,
% 5.01/5.32 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.01/5.32 = ( ^ [X3: int,Y2: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X3 @ Y2 )
% 5.01/5.32 & ( ord_less_eq_int @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_class.order_eq_iff
% 5.01/5.32 thf(fact_8500_le__cases3,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ X2 @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_rat @ X2 @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.01/5.32 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ Y @ X2 ) )
% 5.01/5.32 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ Z @ X2 ) )
% 5.01/5.32 => ~ ( ( ord_less_eq_rat @ Z @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_rat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % le_cases3
% 5.01/5.32 thf(fact_8501_le__cases3,axiom,
% 5.01/5.32 ! [X2: num,Y: num,Z: num] :
% 5.01/5.32 ( ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_num @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.01/5.32 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 5.01/5.32 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 5.01/5.32 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % le_cases3
% 5.01/5.32 thf(fact_8502_le__cases3,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,Z: nat] :
% 5.01/5.32 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.01/5.32 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 5.01/5.32 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 5.01/5.32 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % le_cases3
% 5.01/5.32 thf(fact_8503_le__cases3,axiom,
% 5.01/5.32 ! [X2: int,Y: int,Z: int] :
% 5.01/5.32 ( ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_int @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_int @ X2 @ Z ) )
% 5.01/5.32 => ( ( ( ord_less_eq_int @ X2 @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.01/5.32 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.01/5.32 => ~ ( ord_less_eq_int @ Y @ X2 ) )
% 5.01/5.32 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.01/5.32 => ~ ( ord_less_eq_int @ Z @ X2 ) )
% 5.01/5.32 => ~ ( ( ord_less_eq_int @ Z @ X2 )
% 5.01/5.32 => ~ ( ord_less_eq_int @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % le_cases3
% 5.01/5.32 thf(fact_8504_nle__le,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.01/5.32 = ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.32 & ( B != A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nle_le
% 5.01/5.32 thf(fact_8505_nle__le,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.01/5.32 = ( ( ord_less_eq_num @ B @ A )
% 5.01/5.32 & ( B != A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nle_le
% 5.01/5.32 thf(fact_8506_nle__le,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.01/5.32 = ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.32 & ( B != A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nle_le
% 5.01/5.32 thf(fact_8507_nle__le,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.01/5.32 = ( ( ord_less_eq_int @ B @ A )
% 5.01/5.32 & ( B != A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nle_le
% 5.01/5.32 thf(fact_8508_lt__ex,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % lt_ex
% 5.01/5.32 thf(fact_8509_lt__ex,axiom,
% 5.01/5.32 ! [X2: rat] :
% 5.01/5.32 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % lt_ex
% 5.01/5.32 thf(fact_8510_lt__ex,axiom,
% 5.01/5.32 ! [X2: int] :
% 5.01/5.32 ? [Y3: int] : ( ord_less_int @ Y3 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % lt_ex
% 5.01/5.32 thf(fact_8511_gt__ex,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 5.01/5.32
% 5.01/5.32 % gt_ex
% 5.01/5.32 thf(fact_8512_gt__ex,axiom,
% 5.01/5.32 ! [X2: rat] :
% 5.01/5.32 ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 5.01/5.32
% 5.01/5.32 % gt_ex
% 5.01/5.32 thf(fact_8513_gt__ex,axiom,
% 5.01/5.32 ! [X2: nat] :
% 5.01/5.32 ? [X_12: nat] : ( ord_less_nat @ X2 @ X_12 ) ).
% 5.01/5.32
% 5.01/5.32 % gt_ex
% 5.01/5.32 thf(fact_8514_gt__ex,axiom,
% 5.01/5.32 ! [X2: int] :
% 5.01/5.32 ? [X_12: int] : ( ord_less_int @ X2 @ X_12 ) ).
% 5.01/5.32
% 5.01/5.32 % gt_ex
% 5.01/5.32 thf(fact_8515_dense,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ? [Z3: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Z3 )
% 5.01/5.32 & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense
% 5.01/5.32 thf(fact_8516_dense,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ? [Z3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Z3 )
% 5.01/5.32 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense
% 5.01/5.32 thf(fact_8517_less__imp__neq,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_imp_neq
% 5.01/5.32 thf(fact_8518_less__imp__neq,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_imp_neq
% 5.01/5.32 thf(fact_8519_less__imp__neq,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_imp_neq
% 5.01/5.32 thf(fact_8520_less__imp__neq,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_imp_neq
% 5.01/5.32 thf(fact_8521_less__imp__neq,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_imp_neq
% 5.01/5.32 thf(fact_8522_order_Oasym,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.asym
% 5.01/5.32 thf(fact_8523_order_Oasym,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.asym
% 5.01/5.32 thf(fact_8524_order_Oasym,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.asym
% 5.01/5.32 thf(fact_8525_order_Oasym,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.asym
% 5.01/5.32 thf(fact_8526_order_Oasym,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.asym
% 5.01/5.32 thf(fact_8527_ord__eq__less__trans,axiom,
% 5.01/5.32 ! [A: real,B: real,C: real] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_trans
% 5.01/5.32 thf(fact_8528_ord__eq__less__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_trans
% 5.01/5.32 thf(fact_8529_ord__eq__less__trans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_trans
% 5.01/5.32 thf(fact_8530_ord__eq__less__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_trans
% 5.01/5.32 thf(fact_8531_ord__eq__less__trans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_trans
% 5.01/5.32 thf(fact_8532_ord__less__eq__trans,axiom,
% 5.01/5.32 ! [A: real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_trans
% 5.01/5.32 thf(fact_8533_ord__less__eq__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_trans
% 5.01/5.32 thf(fact_8534_ord__less__eq__trans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_trans
% 5.01/5.32 thf(fact_8535_ord__less__eq__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_trans
% 5.01/5.32 thf(fact_8536_ord__less__eq__trans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ( B = C )
% 5.01/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_trans
% 5.01/5.32 thf(fact_8537_less__induct,axiom,
% 5.01/5.32 ! [P: nat > $o,A: nat] :
% 5.01/5.32 ( ! [X4: nat] :
% 5.01/5.32 ( ! [Y4: nat] :
% 5.01/5.32 ( ( ord_less_nat @ Y4 @ X4 )
% 5.01/5.32 => ( P @ Y4 ) )
% 5.01/5.32 => ( P @ X4 ) )
% 5.01/5.32 => ( P @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_induct
% 5.01/5.32 thf(fact_8538_antisym__conv3,axiom,
% 5.01/5.32 ! [Y: real,X2: real] :
% 5.01/5.32 ( ~ ( ord_less_real @ Y @ X2 )
% 5.01/5.32 => ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv3
% 5.01/5.32 thf(fact_8539_antisym__conv3,axiom,
% 5.01/5.32 ! [Y: rat,X2: rat] :
% 5.01/5.32 ( ~ ( ord_less_rat @ Y @ X2 )
% 5.01/5.32 => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv3
% 5.01/5.32 thf(fact_8540_antisym__conv3,axiom,
% 5.01/5.32 ! [Y: num,X2: num] :
% 5.01/5.32 ( ~ ( ord_less_num @ Y @ X2 )
% 5.01/5.32 => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv3
% 5.01/5.32 thf(fact_8541_antisym__conv3,axiom,
% 5.01/5.32 ! [Y: nat,X2: nat] :
% 5.01/5.32 ( ~ ( ord_less_nat @ Y @ X2 )
% 5.01/5.32 => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv3
% 5.01/5.32 thf(fact_8542_antisym__conv3,axiom,
% 5.01/5.32 ! [Y: int,X2: int] :
% 5.01/5.32 ( ~ ( ord_less_int @ Y @ X2 )
% 5.01/5.32 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv3
% 5.01/5.32 thf(fact_8543_linorder__cases,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ~ ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ( X2 != Y )
% 5.01/5.32 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_cases
% 5.01/5.32 thf(fact_8544_linorder__cases,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ( X2 != Y )
% 5.01/5.32 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_cases
% 5.01/5.32 thf(fact_8545_linorder__cases,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ~ ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ( X2 != Y )
% 5.01/5.32 => ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_cases
% 5.01/5.32 thf(fact_8546_linorder__cases,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ( X2 != Y )
% 5.01/5.32 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_cases
% 5.01/5.32 thf(fact_8547_linorder__cases,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ~ ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ( X2 != Y )
% 5.01/5.32 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_cases
% 5.01/5.32 thf(fact_8548_dual__order_Oasym,axiom,
% 5.01/5.32 ! [B: real,A: real] :
% 5.01/5.32 ( ( ord_less_real @ B @ A )
% 5.01/5.32 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.asym
% 5.01/5.32 thf(fact_8549_dual__order_Oasym,axiom,
% 5.01/5.32 ! [B: rat,A: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B @ A )
% 5.01/5.32 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.asym
% 5.01/5.32 thf(fact_8550_dual__order_Oasym,axiom,
% 5.01/5.32 ! [B: num,A: num] :
% 5.01/5.32 ( ( ord_less_num @ B @ A )
% 5.01/5.32 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.asym
% 5.01/5.32 thf(fact_8551_dual__order_Oasym,axiom,
% 5.01/5.32 ! [B: nat,A: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B @ A )
% 5.01/5.32 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.asym
% 5.01/5.32 thf(fact_8552_dual__order_Oasym,axiom,
% 5.01/5.32 ! [B: int,A: int] :
% 5.01/5.32 ( ( ord_less_int @ B @ A )
% 5.01/5.32 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.asym
% 5.01/5.32 thf(fact_8553_dual__order_Oirrefl,axiom,
% 5.01/5.32 ! [A: real] :
% 5.01/5.32 ~ ( ord_less_real @ A @ A ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.irrefl
% 5.01/5.32 thf(fact_8554_dual__order_Oirrefl,axiom,
% 5.01/5.32 ! [A: rat] :
% 5.01/5.32 ~ ( ord_less_rat @ A @ A ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.irrefl
% 5.01/5.32 thf(fact_8555_dual__order_Oirrefl,axiom,
% 5.01/5.32 ! [A: num] :
% 5.01/5.32 ~ ( ord_less_num @ A @ A ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.irrefl
% 5.01/5.32 thf(fact_8556_dual__order_Oirrefl,axiom,
% 5.01/5.32 ! [A: nat] :
% 5.01/5.32 ~ ( ord_less_nat @ A @ A ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.irrefl
% 5.01/5.32 thf(fact_8557_dual__order_Oirrefl,axiom,
% 5.01/5.32 ! [A: int] :
% 5.01/5.32 ~ ( ord_less_int @ A @ A ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.irrefl
% 5.01/5.32 thf(fact_8558_exists__least__iff,axiom,
% 5.01/5.32 ( ( ^ [P2: nat > $o] :
% 5.01/5.32 ? [X6: nat] : ( P2 @ X6 ) )
% 5.01/5.32 = ( ^ [P3: nat > $o] :
% 5.01/5.32 ? [N4: nat] :
% 5.01/5.32 ( ( P3 @ N4 )
% 5.01/5.32 & ! [M3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ M3 @ N4 )
% 5.01/5.32 => ~ ( P3 @ M3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % exists_least_iff
% 5.01/5.32 thf(fact_8559_linorder__less__wlog,axiom,
% 5.01/5.32 ! [P: real > real > $o,A: real,B: real] :
% 5.01/5.32 ( ! [A3: real,B2: real] :
% 5.01/5.32 ( ( ord_less_real @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: real] : ( P @ A3 @ A3 )
% 5.01/5.32 => ( ! [A3: real,B2: real] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_wlog
% 5.01/5.32 thf(fact_8560_linorder__less__wlog,axiom,
% 5.01/5.32 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.01/5.32 ( ! [A3: rat,B2: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: rat] : ( P @ A3 @ A3 )
% 5.01/5.32 => ( ! [A3: rat,B2: rat] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_wlog
% 5.01/5.32 thf(fact_8561_linorder__less__wlog,axiom,
% 5.01/5.32 ! [P: num > num > $o,A: num,B: num] :
% 5.01/5.32 ( ! [A3: num,B2: num] :
% 5.01/5.32 ( ( ord_less_num @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: num] : ( P @ A3 @ A3 )
% 5.01/5.32 => ( ! [A3: num,B2: num] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_wlog
% 5.01/5.32 thf(fact_8562_linorder__less__wlog,axiom,
% 5.01/5.32 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.01/5.32 ( ! [A3: nat,B2: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 5.01/5.32 => ( ! [A3: nat,B2: nat] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_wlog
% 5.01/5.32 thf(fact_8563_linorder__less__wlog,axiom,
% 5.01/5.32 ! [P: int > int > $o,A: int,B: int] :
% 5.01/5.32 ( ! [A3: int,B2: int] :
% 5.01/5.32 ( ( ord_less_int @ A3 @ B2 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( ! [A3: int] : ( P @ A3 @ A3 )
% 5.01/5.32 => ( ! [A3: int,B2: int] :
% 5.01/5.32 ( ( P @ B2 @ A3 )
% 5.01/5.32 => ( P @ A3 @ B2 ) )
% 5.01/5.32 => ( P @ A @ B ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_wlog
% 5.01/5.32 thf(fact_8564_order_Ostrict__trans,axiom,
% 5.01/5.32 ! [A: real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans
% 5.01/5.32 thf(fact_8565_order_Ostrict__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans
% 5.01/5.32 thf(fact_8566_order_Ostrict__trans,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans
% 5.01/5.32 thf(fact_8567_order_Ostrict__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans
% 5.01/5.32 thf(fact_8568_order_Ostrict__trans,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans
% 5.01/5.32 thf(fact_8569_not__less__iff__gr__or__eq,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.01/5.32 = ( ( ord_less_real @ Y @ X2 )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_less_iff_gr_or_eq
% 5.01/5.32 thf(fact_8570_not__less__iff__gr__or__eq,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.01/5.32 = ( ( ord_less_rat @ Y @ X2 )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_less_iff_gr_or_eq
% 5.01/5.32 thf(fact_8571_not__less__iff__gr__or__eq,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.01/5.32 = ( ( ord_less_num @ Y @ X2 )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_less_iff_gr_or_eq
% 5.01/5.32 thf(fact_8572_not__less__iff__gr__or__eq,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.01/5.32 = ( ( ord_less_nat @ Y @ X2 )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_less_iff_gr_or_eq
% 5.01/5.32 thf(fact_8573_not__less__iff__gr__or__eq,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.01/5.32 = ( ( ord_less_int @ Y @ X2 )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_less_iff_gr_or_eq
% 5.01/5.32 thf(fact_8574_dual__order_Ostrict__trans,axiom,
% 5.01/5.32 ! [B: real,A: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ B @ A )
% 5.01/5.32 => ( ( ord_less_real @ C @ B )
% 5.01/5.32 => ( ord_less_real @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans
% 5.01/5.32 thf(fact_8575_dual__order_Ostrict__trans,axiom,
% 5.01/5.32 ! [B: rat,A: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B @ A )
% 5.01/5.32 => ( ( ord_less_rat @ C @ B )
% 5.01/5.32 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans
% 5.01/5.32 thf(fact_8576_dual__order_Ostrict__trans,axiom,
% 5.01/5.32 ! [B: num,A: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ B @ A )
% 5.01/5.32 => ( ( ord_less_num @ C @ B )
% 5.01/5.32 => ( ord_less_num @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans
% 5.01/5.32 thf(fact_8577_dual__order_Ostrict__trans,axiom,
% 5.01/5.32 ! [B: nat,A: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B @ A )
% 5.01/5.32 => ( ( ord_less_nat @ C @ B )
% 5.01/5.32 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans
% 5.01/5.32 thf(fact_8578_dual__order_Ostrict__trans,axiom,
% 5.01/5.32 ! [B: int,A: int,C: int] :
% 5.01/5.32 ( ( ord_less_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_int @ C @ B )
% 5.01/5.32 => ( ord_less_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans
% 5.01/5.32 thf(fact_8579_order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8580_order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8581_order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8582_order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8583_order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8584_dual__order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [B: real,A: real] :
% 5.01/5.32 ( ( ord_less_real @ B @ A )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8585_dual__order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [B: rat,A: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B @ A )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8586_dual__order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [B: num,A: num] :
% 5.01/5.32 ( ( ord_less_num @ B @ A )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8587_dual__order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [B: nat,A: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B @ A )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8588_dual__order_Ostrict__implies__not__eq,axiom,
% 5.01/5.32 ! [B: int,A: int] :
% 5.01/5.32 ( ( ord_less_int @ B @ A )
% 5.01/5.32 => ( A != B ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_not_eq
% 5.01/5.32 thf(fact_8589_linorder__neqE,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 => ( ~ ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neqE
% 5.01/5.32 thf(fact_8590_linorder__neqE,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 => ( ~ ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neqE
% 5.01/5.32 thf(fact_8591_linorder__neqE,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 => ( ~ ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neqE
% 5.01/5.32 thf(fact_8592_linorder__neqE,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 => ( ~ ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neqE
% 5.01/5.32 thf(fact_8593_linorder__neqE,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 => ( ~ ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neqE
% 5.01/5.32 thf(fact_8594_order__less__asym,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym
% 5.01/5.32 thf(fact_8595_order__less__asym,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym
% 5.01/5.32 thf(fact_8596_order__less__asym,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym
% 5.01/5.32 thf(fact_8597_order__less__asym,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym
% 5.01/5.32 thf(fact_8598_order__less__asym,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym
% 5.01/5.32 thf(fact_8599_linorder__neq__iff,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 = ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 | ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neq_iff
% 5.01/5.32 thf(fact_8600_linorder__neq__iff,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 = ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 | ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neq_iff
% 5.01/5.32 thf(fact_8601_linorder__neq__iff,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 = ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 | ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neq_iff
% 5.01/5.32 thf(fact_8602_linorder__neq__iff,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 = ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 | ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neq_iff
% 5.01/5.32 thf(fact_8603_linorder__neq__iff,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( X2 != Y )
% 5.01/5.32 = ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 | ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_neq_iff
% 5.01/5.32 thf(fact_8604_order__less__asym_H,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym'
% 5.01/5.32 thf(fact_8605_order__less__asym_H,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym'
% 5.01/5.32 thf(fact_8606_order__less__asym_H,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym'
% 5.01/5.32 thf(fact_8607_order__less__asym_H,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym'
% 5.01/5.32 thf(fact_8608_order__less__asym_H,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_asym'
% 5.01/5.32 thf(fact_8609_order__less__trans,axiom,
% 5.01/5.32 ! [X2: real,Y: real,Z: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_real @ Y @ Z )
% 5.01/5.32 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_trans
% 5.01/5.32 thf(fact_8610_order__less__trans,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_rat @ Y @ Z )
% 5.01/5.32 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_trans
% 5.01/5.32 thf(fact_8611_order__less__trans,axiom,
% 5.01/5.32 ! [X2: num,Y: num,Z: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_num @ Y @ Z )
% 5.01/5.32 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_trans
% 5.01/5.32 thf(fact_8612_order__less__trans,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,Z: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_nat @ Y @ Z )
% 5.01/5.32 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_trans
% 5.01/5.32 thf(fact_8613_order__less__trans,axiom,
% 5.01/5.32 ! [X2: int,Y: int,Z: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_trans
% 5.01/5.32 thf(fact_8614_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: real,F: real > real,B: real,C: real] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8615_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8616_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: num,F: real > num,B: real,C: real] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8617_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8618_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: int,F: real > int,B: real,C: real] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8619_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8620_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8621_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8622_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8623_ord__eq__less__subst,axiom,
% 5.01/5.32 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.01/5.32 ( ( A
% 5.01/5.32 = ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_eq_less_subst
% 5.01/5.32 thf(fact_8624_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8625_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8626_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > num,C: num] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8627_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8628_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > int,C: int] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8629_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8630_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8631_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8632_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8633_ord__less__eq__subst,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ( F @ B )
% 5.01/5.32 = C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ord_less_eq_subst
% 5.01/5.32 thf(fact_8634_order__less__irrefl,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ~ ( ord_less_real @ X2 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_irrefl
% 5.01/5.32 thf(fact_8635_order__less__irrefl,axiom,
% 5.01/5.32 ! [X2: rat] :
% 5.01/5.32 ~ ( ord_less_rat @ X2 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_irrefl
% 5.01/5.32 thf(fact_8636_order__less__irrefl,axiom,
% 5.01/5.32 ! [X2: num] :
% 5.01/5.32 ~ ( ord_less_num @ X2 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_irrefl
% 5.01/5.32 thf(fact_8637_order__less__irrefl,axiom,
% 5.01/5.32 ! [X2: nat] :
% 5.01/5.32 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_irrefl
% 5.01/5.32 thf(fact_8638_order__less__irrefl,axiom,
% 5.01/5.32 ! [X2: int] :
% 5.01/5.32 ~ ( ord_less_int @ X2 @ X2 ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_irrefl
% 5.01/5.32 thf(fact_8639_order__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: real > real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8640_order__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8641_order__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: num > real,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8642_order__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8643_order__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: int > real,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8644_order__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8645_order__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8646_order__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8647_order__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8648_order__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst1
% 5.01/5.32 thf(fact_8649_order__less__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8650_order__less__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8651_order__less__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > num,C: num] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8652_order__less__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8653_order__less__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > int,C: int] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8654_order__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8655_order__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8656_order__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8657_order__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8658_order__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_subst2
% 5.01/5.32 thf(fact_8659_order__less__not__sym,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_not_sym
% 5.01/5.32 thf(fact_8660_order__less__not__sym,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_not_sym
% 5.01/5.32 thf(fact_8661_order__less__not__sym,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_not_sym
% 5.01/5.32 thf(fact_8662_order__less__not__sym,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_not_sym
% 5.01/5.32 thf(fact_8663_order__less__not__sym,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_not_sym
% 5.01/5.32 thf(fact_8664_order__less__imp__triv,axiom,
% 5.01/5.32 ! [X2: real,Y: real,P: $o] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_real @ Y @ X2 )
% 5.01/5.32 => P ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_triv
% 5.01/5.32 thf(fact_8665_order__less__imp__triv,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,P: $o] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_rat @ Y @ X2 )
% 5.01/5.32 => P ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_triv
% 5.01/5.32 thf(fact_8666_order__less__imp__triv,axiom,
% 5.01/5.32 ! [X2: num,Y: num,P: $o] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_num @ Y @ X2 )
% 5.01/5.32 => P ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_triv
% 5.01/5.32 thf(fact_8667_order__less__imp__triv,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,P: $o] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_nat @ Y @ X2 )
% 5.01/5.32 => P ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_triv
% 5.01/5.32 thf(fact_8668_order__less__imp__triv,axiom,
% 5.01/5.32 ! [X2: int,Y: int,P: $o] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_int @ Y @ X2 )
% 5.01/5.32 => P ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_triv
% 5.01/5.32 thf(fact_8669_linorder__less__linear,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y )
% 5.01/5.32 | ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_linear
% 5.01/5.32 thf(fact_8670_linorder__less__linear,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y )
% 5.01/5.32 | ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_linear
% 5.01/5.32 thf(fact_8671_linorder__less__linear,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y )
% 5.01/5.32 | ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_linear
% 5.01/5.32 thf(fact_8672_linorder__less__linear,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y )
% 5.01/5.32 | ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_linear
% 5.01/5.32 thf(fact_8673_linorder__less__linear,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y )
% 5.01/5.32 | ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_less_linear
% 5.01/5.32 thf(fact_8674_order__less__imp__not__eq,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq
% 5.01/5.32 thf(fact_8675_order__less__imp__not__eq,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq
% 5.01/5.32 thf(fact_8676_order__less__imp__not__eq,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq
% 5.01/5.32 thf(fact_8677_order__less__imp__not__eq,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq
% 5.01/5.32 thf(fact_8678_order__less__imp__not__eq,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( X2 != Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq
% 5.01/5.32 thf(fact_8679_order__less__imp__not__eq2,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( Y != X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq2
% 5.01/5.32 thf(fact_8680_order__less__imp__not__eq2,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( Y != X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq2
% 5.01/5.32 thf(fact_8681_order__less__imp__not__eq2,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( Y != X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq2
% 5.01/5.32 thf(fact_8682_order__less__imp__not__eq2,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( Y != X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq2
% 5.01/5.32 thf(fact_8683_order__less__imp__not__eq2,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( Y != X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_eq2
% 5.01/5.32 thf(fact_8684_order__less__imp__not__less,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_less
% 5.01/5.32 thf(fact_8685_order__less__imp__not__less,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_less
% 5.01/5.32 thf(fact_8686_order__less__imp__not__less,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_less
% 5.01/5.32 thf(fact_8687_order__less__imp__not__less,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_less
% 5.01/5.32 thf(fact_8688_order__less__imp__not__less,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_not_less
% 5.01/5.32 thf(fact_8689_CauchyD,axiom,
% 5.01/5.32 ! [X8: nat > complex,E: real] :
% 5.01/5.32 ( ( topolo6517432010174082258omplex @ X8 )
% 5.01/5.32 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.32 => ? [M9: nat] :
% 5.01/5.32 ! [M2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M9 @ M2 )
% 5.01/5.32 => ! [N6: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.01/5.32 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % CauchyD
% 5.01/5.32 thf(fact_8690_CauchyD,axiom,
% 5.01/5.32 ! [X8: nat > real,E: real] :
% 5.01/5.32 ( ( topolo4055970368930404560y_real @ X8 )
% 5.01/5.32 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.01/5.32 => ? [M9: nat] :
% 5.01/5.32 ! [M2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M9 @ M2 )
% 5.01/5.32 => ! [N6: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.01/5.32 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % CauchyD
% 5.01/5.32 thf(fact_8691_CauchyI,axiom,
% 5.01/5.32 ! [X8: nat > complex] :
% 5.01/5.32 ( ! [E2: real] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.32 => ? [M10: nat] :
% 5.01/5.32 ! [M4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.01/5.32 => ! [N3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M10 @ N3 )
% 5.01/5.32 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) ) @ E2 ) ) ) )
% 5.01/5.32 => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 5.01/5.32
% 5.01/5.32 % CauchyI
% 5.01/5.32 thf(fact_8692_CauchyI,axiom,
% 5.01/5.32 ! [X8: nat > real] :
% 5.01/5.32 ( ! [E2: real] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.32 => ? [M10: nat] :
% 5.01/5.32 ! [M4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.01/5.32 => ! [N3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M10 @ N3 )
% 5.01/5.32 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) ) @ E2 ) ) ) )
% 5.01/5.32 => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 5.01/5.32
% 5.01/5.32 % CauchyI
% 5.01/5.32 thf(fact_8693_Cauchy__iff,axiom,
% 5.01/5.32 ( topolo6517432010174082258omplex
% 5.01/5.32 = ( ^ [X5: nat > complex] :
% 5.01/5.32 ! [E3: real] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.01/5.32 => ? [M8: nat] :
% 5.01/5.32 ! [M3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.01/5.32 => ! [N4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M8 @ N4 )
% 5.01/5.32 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X5 @ M3 ) @ ( X5 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Cauchy_iff
% 5.01/5.32 thf(fact_8694_Cauchy__iff,axiom,
% 5.01/5.32 ( topolo4055970368930404560y_real
% 5.01/5.32 = ( ^ [X5: nat > real] :
% 5.01/5.32 ! [E3: real] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.01/5.32 => ? [M8: nat] :
% 5.01/5.32 ! [M3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.01/5.32 => ! [N4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ M8 @ N4 )
% 5.01/5.32 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X5 @ M3 ) @ ( X5 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Cauchy_iff
% 5.01/5.32 thf(fact_8695_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8696_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_set_int @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8697_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8698_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8699_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8700_order__le__imp__less__or__eq,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 | ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_imp_less_or_eq
% 5.01/5.32 thf(fact_8701_linorder__le__less__linear,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.32 | ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_le_less_linear
% 5.01/5.32 thf(fact_8702_linorder__le__less__linear,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 | ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_le_less_linear
% 5.01/5.32 thf(fact_8703_linorder__le__less__linear,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 | ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_le_less_linear
% 5.01/5.32 thf(fact_8704_linorder__le__less__linear,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 | ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_le_less_linear
% 5.01/5.32 thf(fact_8705_linorder__le__less__linear,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 | ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_le_less_linear
% 5.01/5.32 thf(fact_8706_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8707_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8708_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > real,C: real] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8709_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8710_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: int,B: int,F: int > real,C: real] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8711_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8712_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8713_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8714_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8715_order__less__le__subst2,axiom,
% 5.01/5.32 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst2
% 5.01/5.32 thf(fact_8716_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8717_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8718_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8719_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8720_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8721_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: real,F: num > real,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8722_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8723_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: num,F: num > num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8724_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8725_order__less__le__subst1,axiom,
% 5.01/5.32 ! [A: int,F: num > int,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_subst1
% 5.01/5.32 thf(fact_8726_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8727_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8728_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8729_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8730_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8731_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8732_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8733_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8734_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8735_order__le__less__subst2,axiom,
% 5.01/5.32 ! [A: num,B: num,F: num > int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst2
% 5.01/5.32 thf(fact_8736_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: real > real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8737_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8738_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: num > real,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8739_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8740_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: real,F: int > real,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8741_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ! [X4: real,Y3: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8742_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ! [X4: rat,Y3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8743_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ! [X4: num,Y3: num] :
% 5.01/5.32 ( ( ord_less_num @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8744_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ! [X4: nat,Y3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8745_order__le__less__subst1,axiom,
% 5.01/5.32 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ! [X4: int,Y3: int] :
% 5.01/5.32 ( ( ord_less_int @ X4 @ Y3 )
% 5.01/5.32 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.01/5.32 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_subst1
% 5.01/5.32 thf(fact_8746_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: real,Y: real,Z: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_real @ Y @ Z )
% 5.01/5.32 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8747_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int,Z: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8748_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.01/5.32 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8749_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: num,Y: num,Z: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_num @ Y @ Z )
% 5.01/5.32 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8750_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,Z: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.01/5.32 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8751_order__less__le__trans,axiom,
% 5.01/5.32 ! [X2: int,Y: int,Z: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le_trans
% 5.01/5.32 thf(fact_8752_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: real,Y: real,Z: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_real @ Y @ Z )
% 5.01/5.32 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8753_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int,Z: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_set_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_set_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8754_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_rat @ Y @ Z )
% 5.01/5.32 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8755_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: num,Y: num,Z: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_num @ Y @ Z )
% 5.01/5.32 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8756_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat,Z: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_nat @ Y @ Z )
% 5.01/5.32 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8757_order__le__less__trans,axiom,
% 5.01/5.32 ! [X2: int,Y: int,Z: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_int @ Y @ Z )
% 5.01/5.32 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less_trans
% 5.01/5.32 thf(fact_8758_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_real @ A @ B )
% 5.01/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8759_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8760_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8761_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ord_less_num @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8762_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8763_order__neq__le__trans,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( A != B )
% 5.01/5.32 => ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_neq_le_trans
% 5.01/5.32 thf(fact_8764_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_real @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8765_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8766_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8767_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_num @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8768_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8769_order__le__neq__trans,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ( A != B )
% 5.01/5.32 => ( ord_less_int @ A @ B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_neq_trans
% 5.01/5.32 thf(fact_8770_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8771_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_set_int @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8772_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8773_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8774_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8775_order__less__imp__le,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_imp_le
% 5.01/5.32 thf(fact_8776_linorder__not__less,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_eq_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_less
% 5.01/5.32 thf(fact_8777_linorder__not__less,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_less
% 5.01/5.32 thf(fact_8778_linorder__not__less,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_less
% 5.01/5.32 thf(fact_8779_linorder__not__less,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_less
% 5.01/5.32 thf(fact_8780_linorder__not__less,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_less
% 5.01/5.32 thf(fact_8781_linorder__not__le,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_real @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_le
% 5.01/5.32 thf(fact_8782_linorder__not__le,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_rat @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_le
% 5.01/5.32 thf(fact_8783_linorder__not__le,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_num @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_le
% 5.01/5.32 thf(fact_8784_linorder__not__le,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_nat @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_le
% 5.01/5.32 thf(fact_8785_linorder__not__le,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ~ ( ord_less_eq_int @ X2 @ Y ) )
% 5.01/5.32 = ( ord_less_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % linorder_not_le
% 5.01/5.32 thf(fact_8786_order__less__le,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [X3: real,Y2: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8787_order__less__le,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [X3: set_int,Y2: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8788_order__less__le,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [X3: rat,Y2: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8789_order__less__le,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [X3: num,Y2: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8790_order__less__le,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [X3: nat,Y2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8791_order__less__le,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [X3: int,Y2: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X3 @ Y2 )
% 5.01/5.32 & ( X3 != Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_less_le
% 5.01/5.32 thf(fact_8792_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_real
% 5.01/5.32 = ( ^ [X3: real,Y2: real] :
% 5.01/5.32 ( ( ord_less_real @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8793_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_set_int
% 5.01/5.32 = ( ^ [X3: set_int,Y2: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8794_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_rat
% 5.01/5.32 = ( ^ [X3: rat,Y2: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8795_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_num
% 5.01/5.32 = ( ^ [X3: num,Y2: num] :
% 5.01/5.32 ( ( ord_less_num @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8796_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_nat
% 5.01/5.32 = ( ^ [X3: nat,Y2: nat] :
% 5.01/5.32 ( ( ord_less_nat @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8797_order__le__less,axiom,
% 5.01/5.32 ( ord_less_eq_int
% 5.01/5.32 = ( ^ [X3: int,Y2: int] :
% 5.01/5.32 ( ( ord_less_int @ X3 @ Y2 )
% 5.01/5.32 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order_le_less
% 5.01/5.32 thf(fact_8798_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: real,A: real] :
% 5.01/5.32 ( ( ord_less_real @ B @ A )
% 5.01/5.32 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8799_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: set_int,A: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ B @ A )
% 5.01/5.32 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8800_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: rat,A: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B @ A )
% 5.01/5.32 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8801_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: num,A: num] :
% 5.01/5.32 ( ( ord_less_num @ B @ A )
% 5.01/5.32 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8802_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: nat,A: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B @ A )
% 5.01/5.32 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8803_dual__order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [B: int,A: int] :
% 5.01/5.32 ( ( ord_less_int @ B @ A )
% 5.01/5.32 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_implies_order
% 5.01/5.32 thf(fact_8804_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8805_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ A @ B )
% 5.01/5.32 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8806_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8807_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8808_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8809_order_Ostrict__implies__order,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_implies_order
% 5.01/5.32 thf(fact_8810_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [B3: real,A4: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_real @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8811_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [B3: set_int,A4: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_set_int @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8812_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [B3: rat,A4: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_rat @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8813_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [B3: num,A4: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_num @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8814_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [B3: nat,A4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_nat @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8815_dual__order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [B3: int,A4: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.01/5.32 & ~ ( ord_less_eq_int @ A4 @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_not
% 5.01/5.32 thf(fact_8816_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: real,A: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_real @ C @ B )
% 5.01/5.32 => ( ord_less_real @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8817_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: set_int,A: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ C @ B )
% 5.01/5.32 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8818_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: rat,A: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_rat @ C @ B )
% 5.01/5.32 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8819_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: num,A: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_num @ C @ B )
% 5.01/5.32 => ( ord_less_num @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8820_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: nat,A: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_nat @ C @ B )
% 5.01/5.32 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8821_dual__order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [B: int,A: int,C: int] :
% 5.01/5.32 ( ( ord_less_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_eq_int @ C @ B )
% 5.01/5.32 => ( ord_less_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans2
% 5.01/5.32 thf(fact_8822_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: real,A: real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ B @ A )
% 5.01/5.32 => ( ( ord_less_real @ C @ B )
% 5.01/5.32 => ( ord_less_real @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8823_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: set_int,A: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_set_int @ C @ B )
% 5.01/5.32 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8824_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: rat,A: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B @ A )
% 5.01/5.32 => ( ( ord_less_rat @ C @ B )
% 5.01/5.32 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8825_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: num,A: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B @ A )
% 5.01/5.32 => ( ( ord_less_num @ C @ B )
% 5.01/5.32 => ( ord_less_num @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8826_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: nat,A: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B @ A )
% 5.01/5.32 => ( ( ord_less_nat @ C @ B )
% 5.01/5.32 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8827_dual__order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [B: int,A: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B @ A )
% 5.01/5.32 => ( ( ord_less_int @ C @ B )
% 5.01/5.32 => ( ord_less_int @ C @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_trans1
% 5.01/5.32 thf(fact_8828_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [B3: real,A4: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8829_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [B3: set_int,A4: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8830_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [B3: rat,A4: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8831_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [B3: num,A4: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8832_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [B3: nat,A4: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8833_dual__order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [B3: int,A4: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ B3 @ A4 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.strict_iff_order
% 5.01/5.32 thf(fact_8834_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_real
% 5.01/5.32 = ( ^ [B3: real,A4: real] :
% 5.01/5.32 ( ( ord_less_real @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8835_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_set_int
% 5.01/5.32 = ( ^ [B3: set_int,A4: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8836_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_rat
% 5.01/5.32 = ( ^ [B3: rat,A4: rat] :
% 5.01/5.32 ( ( ord_less_rat @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8837_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_num
% 5.01/5.32 = ( ^ [B3: num,A4: num] :
% 5.01/5.32 ( ( ord_less_num @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8838_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_nat
% 5.01/5.32 = ( ^ [B3: nat,A4: nat] :
% 5.01/5.32 ( ( ord_less_nat @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8839_dual__order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_int
% 5.01/5.32 = ( ^ [B3: int,A4: int] :
% 5.01/5.32 ( ( ord_less_int @ B3 @ A4 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dual_order.order_iff_strict
% 5.01/5.32 thf(fact_8840_dense__le__bounded,axiom,
% 5.01/5.32 ! [X2: real,Y: real,Z: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ! [W3: real] :
% 5.01/5.32 ( ( ord_less_real @ X2 @ W3 )
% 5.01/5.32 => ( ( ord_less_real @ W3 @ Y )
% 5.01/5.32 => ( ord_less_eq_real @ W3 @ Z ) ) )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_le_bounded
% 5.01/5.32 thf(fact_8841_dense__le__bounded,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat,Z: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ! [W3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X2 @ W3 )
% 5.01/5.32 => ( ( ord_less_rat @ W3 @ Y )
% 5.01/5.32 => ( ord_less_eq_rat @ W3 @ Z ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_le_bounded
% 5.01/5.32 thf(fact_8842_dense__ge__bounded,axiom,
% 5.01/5.32 ! [Z: real,X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_real @ Z @ X2 )
% 5.01/5.32 => ( ! [W3: real] :
% 5.01/5.32 ( ( ord_less_real @ Z @ W3 )
% 5.01/5.32 => ( ( ord_less_real @ W3 @ X2 )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ W3 ) ) )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_ge_bounded
% 5.01/5.32 thf(fact_8843_dense__ge__bounded,axiom,
% 5.01/5.32 ! [Z: rat,X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_rat @ Z @ X2 )
% 5.01/5.32 => ( ! [W3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ Z @ W3 )
% 5.01/5.32 => ( ( ord_less_rat @ W3 @ X2 )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ W3 ) ) )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_ge_bounded
% 5.01/5.32 thf(fact_8844_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [A4: real,B3: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_real @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8845_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [A4: set_int,B3: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_set_int @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8846_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_rat @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8847_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [A4: num,B3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_num @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8848_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_nat @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8849_order_Ostrict__iff__not,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [A4: int,B3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.01/5.32 & ~ ( ord_less_eq_int @ B3 @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_not
% 5.01/5.32 thf(fact_8850_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_real @ B @ C )
% 5.01/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8851_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ B @ C )
% 5.01/5.32 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8852_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_rat @ B @ C )
% 5.01/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8853_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_num @ B @ C )
% 5.01/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8854_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_nat @ B @ C )
% 5.01/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8855_order_Ostrict__trans2,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_eq_int @ B @ C )
% 5.01/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans2
% 5.01/5.32 thf(fact_8856_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: real,B: real,C: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.32 => ( ( ord_less_real @ B @ C )
% 5.01/5.32 => ( ord_less_real @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8857_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int,C: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_set_int @ B @ C )
% 5.01/5.32 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8858_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: rat,B: rat,C: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 => ( ( ord_less_rat @ B @ C )
% 5.01/5.32 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8859_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: num,B: num,C: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A @ B )
% 5.01/5.32 => ( ( ord_less_num @ B @ C )
% 5.01/5.32 => ( ord_less_num @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8860_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: nat,B: nat,C: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 => ( ( ord_less_nat @ B @ C )
% 5.01/5.32 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8861_order_Ostrict__trans1,axiom,
% 5.01/5.32 ! [A: int,B: int,C: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A @ B )
% 5.01/5.32 => ( ( ord_less_int @ B @ C )
% 5.01/5.32 => ( ord_less_int @ A @ C ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_trans1
% 5.01/5.32 thf(fact_8862_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [A4: real,B3: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8863_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [A4: set_int,B3: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8864_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8865_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [A4: num,B3: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8866_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8867_order_Ostrict__iff__order,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [A4: int,B3: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.01/5.32 & ( A4 != B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.strict_iff_order
% 5.01/5.32 thf(fact_8868_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_real
% 5.01/5.32 = ( ^ [A4: real,B3: real] :
% 5.01/5.32 ( ( ord_less_real @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8869_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_set_int
% 5.01/5.32 = ( ^ [A4: set_int,B3: set_int] :
% 5.01/5.32 ( ( ord_less_set_int @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8870_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_rat
% 5.01/5.32 = ( ^ [A4: rat,B3: rat] :
% 5.01/5.32 ( ( ord_less_rat @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8871_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_num
% 5.01/5.32 = ( ^ [A4: num,B3: num] :
% 5.01/5.32 ( ( ord_less_num @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8872_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8873_order_Oorder__iff__strict,axiom,
% 5.01/5.32 ( ord_less_eq_int
% 5.01/5.32 = ( ^ [A4: int,B3: int] :
% 5.01/5.32 ( ( ord_less_int @ A4 @ B3 )
% 5.01/5.32 | ( A4 = B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % order.order_iff_strict
% 5.01/5.32 thf(fact_8874_not__le__imp__less,axiom,
% 5.01/5.32 ! [Y: real,X2: real] :
% 5.01/5.32 ( ~ ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.32 => ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_le_imp_less
% 5.01/5.32 thf(fact_8875_not__le__imp__less,axiom,
% 5.01/5.32 ! [Y: rat,X2: rat] :
% 5.01/5.32 ( ~ ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.32 => ( ord_less_rat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_le_imp_less
% 5.01/5.32 thf(fact_8876_not__le__imp__less,axiom,
% 5.01/5.32 ! [Y: num,X2: num] :
% 5.01/5.32 ( ~ ( ord_less_eq_num @ Y @ X2 )
% 5.01/5.32 => ( ord_less_num @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_le_imp_less
% 5.01/5.32 thf(fact_8877_not__le__imp__less,axiom,
% 5.01/5.32 ! [Y: nat,X2: nat] :
% 5.01/5.32 ( ~ ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.32 => ( ord_less_nat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_le_imp_less
% 5.01/5.32 thf(fact_8878_not__le__imp__less,axiom,
% 5.01/5.32 ! [Y: int,X2: int] :
% 5.01/5.32 ( ~ ( ord_less_eq_int @ Y @ X2 )
% 5.01/5.32 => ( ord_less_int @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % not_le_imp_less
% 5.01/5.32 thf(fact_8879_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_real
% 5.01/5.32 = ( ^ [X3: real,Y2: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_real @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8880_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_set_int
% 5.01/5.32 = ( ^ [X3: set_int,Y2: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_set_int @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8881_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_rat
% 5.01/5.32 = ( ^ [X3: rat,Y2: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_rat @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8882_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_num
% 5.01/5.32 = ( ^ [X3: num,Y2: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_num @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8883_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [X3: nat,Y2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8884_less__le__not__le,axiom,
% 5.01/5.32 ( ord_less_int
% 5.01/5.32 = ( ^ [X3: int,Y2: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X3 @ Y2 )
% 5.01/5.32 & ~ ( ord_less_eq_int @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_le_not_le
% 5.01/5.32 thf(fact_8885_dense__le,axiom,
% 5.01/5.32 ! [Y: real,Z: real] :
% 5.01/5.32 ( ! [X4: real] :
% 5.01/5.32 ( ( ord_less_real @ X4 @ Y )
% 5.01/5.32 => ( ord_less_eq_real @ X4 @ Z ) )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_le
% 5.01/5.32 thf(fact_8886_dense__le,axiom,
% 5.01/5.32 ! [Y: rat,Z: rat] :
% 5.01/5.32 ( ! [X4: rat] :
% 5.01/5.32 ( ( ord_less_rat @ X4 @ Y )
% 5.01/5.32 => ( ord_less_eq_rat @ X4 @ Z ) )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_le
% 5.01/5.32 thf(fact_8887_dense__ge,axiom,
% 5.01/5.32 ! [Z: real,Y: real] :
% 5.01/5.32 ( ! [X4: real] :
% 5.01/5.32 ( ( ord_less_real @ Z @ X4 )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ X4 ) )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_ge
% 5.01/5.32 thf(fact_8888_dense__ge,axiom,
% 5.01/5.32 ! [Z: rat,Y: rat] :
% 5.01/5.32 ( ! [X4: rat] :
% 5.01/5.32 ( ( ord_less_rat @ Z @ X4 )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ X4 ) )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.01/5.32
% 5.01/5.32 % dense_ge
% 5.01/5.32 thf(fact_8889_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8890_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_set_int @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8891_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8892_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8893_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8894_antisym__conv2,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv2
% 5.01/5.32 thf(fact_8895_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ~ ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8896_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: set_int,Y: set_int] :
% 5.01/5.32 ( ~ ( ord_less_set_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_set_int @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8897_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8898_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ~ ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_num @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8899_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_nat @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8900_antisym__conv1,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ~ ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ( ord_less_eq_int @ X2 @ Y )
% 5.01/5.32 = ( X2 = Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % antisym_conv1
% 5.01/5.32 thf(fact_8901_nless__le,axiom,
% 5.01/5.32 ! [A: real,B: real] :
% 5.01/5.32 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8902_nless__le,axiom,
% 5.01/5.32 ! [A: set_int,B: set_int] :
% 5.01/5.32 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8903_nless__le,axiom,
% 5.01/5.32 ! [A: rat,B: rat] :
% 5.01/5.32 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8904_nless__le,axiom,
% 5.01/5.32 ! [A: num,B: num] :
% 5.01/5.32 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8905_nless__le,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8906_nless__le,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.01/5.32 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.01/5.32 | ( A = B ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nless_le
% 5.01/5.32 thf(fact_8907_leI,axiom,
% 5.01/5.32 ! [X2: real,Y: real] :
% 5.01/5.32 ( ~ ( ord_less_real @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % leI
% 5.01/5.32 thf(fact_8908_leI,axiom,
% 5.01/5.32 ! [X2: rat,Y: rat] :
% 5.01/5.32 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % leI
% 5.01/5.32 thf(fact_8909_leI,axiom,
% 5.01/5.32 ! [X2: num,Y: num] :
% 5.01/5.32 ( ~ ( ord_less_num @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % leI
% 5.01/5.32 thf(fact_8910_leI,axiom,
% 5.01/5.32 ! [X2: nat,Y: nat] :
% 5.01/5.32 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % leI
% 5.01/5.32 thf(fact_8911_leI,axiom,
% 5.01/5.32 ! [X2: int,Y: int] :
% 5.01/5.32 ( ~ ( ord_less_int @ X2 @ Y )
% 5.01/5.32 => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % leI
% 5.01/5.32 thf(fact_8912_leD,axiom,
% 5.01/5.32 ! [Y: real,X2: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_real @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8913_leD,axiom,
% 5.01/5.32 ! [Y: set_int,X2: set_int] :
% 5.01/5.32 ( ( ord_less_eq_set_int @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_set_int @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8914_leD,axiom,
% 5.01/5.32 ! [Y: rat,X2: rat] :
% 5.01/5.32 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_rat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8915_leD,axiom,
% 5.01/5.32 ! [Y: num,X2: num] :
% 5.01/5.32 ( ( ord_less_eq_num @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_num @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8916_leD,axiom,
% 5.01/5.32 ! [Y: nat,X2: nat] :
% 5.01/5.32 ( ( ord_less_eq_nat @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_nat @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8917_leD,axiom,
% 5.01/5.32 ! [Y: int,X2: int] :
% 5.01/5.32 ( ( ord_less_eq_int @ Y @ X2 )
% 5.01/5.32 => ~ ( ord_less_int @ X2 @ Y ) ) ).
% 5.01/5.32
% 5.01/5.32 % leD
% 5.01/5.32 thf(fact_8918_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.32 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.32 => ( ! [Uu: $o,Uv: $o] :
% 5.01/5.32 ( X2
% 5.01/5.32 != ( vEBT_Leaf @ Uu @ Uv ) )
% 5.01/5.32 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat] :
% 5.01/5.32 ( ? [Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.32 => ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 ) ) )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vc: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.32 => ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 )
% 5.01/5.32 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.01/5.32 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vd: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.32 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.membermima.elims(3)
% 5.01/5.32 thf(fact_8919_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.01/5.32 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.32 = Y )
% 5.01/5.32 => ( ( ? [Uu: $o,Uv: $o] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.01/5.32 => Y )
% 5.01/5.32 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.01/5.32 => Y )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat] :
% 5.01/5.32 ( ? [Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.32 => ( Y
% 5.01/5.32 = ( ~ ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 ) ) ) ) )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vc: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.32 => ( Y
% 5.01/5.32 = ( ~ ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 )
% 5.01/5.32 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.01/5.32 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vd: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.32 => ( Y
% 5.01/5.32 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.membermima.elims(1)
% 5.01/5.32 thf(fact_8920_length__subseqs,axiom,
% 5.01/5.32 ! [Xs: list_VEBT_VEBT] :
% 5.01/5.32 ( ( size_s8217280938318005548T_VEBT @ ( subseqs_VEBT_VEBT @ Xs ) )
% 5.01/5.32 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_subseqs
% 5.01/5.32 thf(fact_8921_length__subseqs,axiom,
% 5.01/5.32 ! [Xs: list_o] :
% 5.01/5.32 ( ( size_s2710708370519433104list_o @ ( subseqs_o @ Xs ) )
% 5.01/5.32 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_subseqs
% 5.01/5.32 thf(fact_8922_length__subseqs,axiom,
% 5.01/5.32 ! [Xs: list_nat] :
% 5.01/5.32 ( ( size_s3023201423986296836st_nat @ ( subseqs_nat @ Xs ) )
% 5.01/5.32 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_subseqs
% 5.01/5.32 thf(fact_8923_length__subseqs,axiom,
% 5.01/5.32 ! [Xs: list_int] :
% 5.01/5.32 ( ( size_s533118279054570080st_int @ ( subseqs_int @ Xs ) )
% 5.01/5.32 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_subseqs
% 5.01/5.32 thf(fact_8924_csqrt_Osimps_I1_J,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( re @ ( csqrt @ Z ) )
% 5.01/5.32 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt.simps(1)
% 5.01/5.32 thf(fact_8925_complex__Re__of__nat,axiom,
% 5.01/5.32 ! [N: nat] :
% 5.01/5.32 ( ( re @ ( semiri8010041392384452111omplex @ N ) )
% 5.01/5.32 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Re_of_nat
% 5.01/5.32 thf(fact_8926_complex__Re__numeral,axiom,
% 5.01/5.32 ! [V: num] :
% 5.01/5.32 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.01/5.32 = ( numeral_numeral_real @ V ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Re_numeral
% 5.01/5.32 thf(fact_8927_Re__divide__of__nat,axiom,
% 5.01/5.32 ! [Z: complex,N: nat] :
% 5.01/5.32 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_divide_of_nat
% 5.01/5.32 thf(fact_8928_Re__divide__of__real,axiom,
% 5.01/5.32 ! [Z: complex,R: real] :
% 5.01/5.32 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( re @ Z ) @ R ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_divide_of_real
% 5.01/5.32 thf(fact_8929_Re__sgn,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.01/5.32 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_sgn
% 5.01/5.32 thf(fact_8930_Re__divide__numeral,axiom,
% 5.01/5.32 ! [Z: complex,W: num] :
% 5.01/5.32 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_divide_numeral
% 5.01/5.32 thf(fact_8931_cos__Arg__i__mult__zero,axiom,
% 5.01/5.32 ! [Y: complex] :
% 5.01/5.32 ( ( Y != zero_zero_complex )
% 5.01/5.32 => ( ( ( re @ Y )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( cos_real @ ( arg @ Y ) )
% 5.01/5.32 = zero_zero_real ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cos_Arg_i_mult_zero
% 5.01/5.32 thf(fact_8932_minus__set__def,axiom,
% 5.01/5.32 ( minus_minus_set_real
% 5.01/5.32 = ( ^ [A6: set_real,B7: set_real] :
% 5.01/5.32 ( collect_real
% 5.01/5.32 @ ( minus_minus_real_o
% 5.01/5.32 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: real] : ( member_real @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8933_minus__set__def,axiom,
% 5.01/5.32 ( minus_811609699411566653omplex
% 5.01/5.32 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.01/5.32 ( collect_complex
% 5.01/5.32 @ ( minus_8727706125548526216plex_o
% 5.01/5.32 @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: complex] : ( member_complex @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8934_minus__set__def,axiom,
% 5.01/5.32 ( minus_7954133019191499631st_nat
% 5.01/5.32 = ( ^ [A6: set_list_nat,B7: set_list_nat] :
% 5.01/5.32 ( collect_list_nat
% 5.01/5.32 @ ( minus_1139252259498527702_nat_o
% 5.01/5.32 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8935_minus__set__def,axiom,
% 5.01/5.32 ( minus_2163939370556025621et_nat
% 5.01/5.32 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.01/5.32 ( collect_set_nat
% 5.01/5.32 @ ( minus_6910147592129066416_nat_o
% 5.01/5.32 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8936_minus__set__def,axiom,
% 5.01/5.32 ( minus_minus_set_int
% 5.01/5.32 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.32 ( collect_int
% 5.01/5.32 @ ( minus_minus_int_o
% 5.01/5.32 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: int] : ( member_int @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8937_minus__set__def,axiom,
% 5.01/5.32 ( minus_minus_set_nat
% 5.01/5.32 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.01/5.32 ( collect_nat
% 5.01/5.32 @ ( minus_minus_nat_o
% 5.01/5.32 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: nat] : ( member_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_set_def
% 5.01/5.32 thf(fact_8938_set__diff__eq,axiom,
% 5.01/5.32 ( minus_minus_set_real
% 5.01/5.32 = ( ^ [A6: set_real,B7: set_real] :
% 5.01/5.32 ( collect_real
% 5.01/5.32 @ ^ [X3: real] :
% 5.01/5.32 ( ( member_real @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_real @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8939_set__diff__eq,axiom,
% 5.01/5.32 ( minus_811609699411566653omplex
% 5.01/5.32 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.01/5.32 ( collect_complex
% 5.01/5.32 @ ^ [X3: complex] :
% 5.01/5.32 ( ( member_complex @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_complex @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8940_set__diff__eq,axiom,
% 5.01/5.32 ( minus_7954133019191499631st_nat
% 5.01/5.32 = ( ^ [A6: set_list_nat,B7: set_list_nat] :
% 5.01/5.32 ( collect_list_nat
% 5.01/5.32 @ ^ [X3: list_nat] :
% 5.01/5.32 ( ( member_list_nat @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_list_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8941_set__diff__eq,axiom,
% 5.01/5.32 ( minus_2163939370556025621et_nat
% 5.01/5.32 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.01/5.32 ( collect_set_nat
% 5.01/5.32 @ ^ [X3: set_nat] :
% 5.01/5.32 ( ( member_set_nat @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_set_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8942_set__diff__eq,axiom,
% 5.01/5.32 ( minus_minus_set_int
% 5.01/5.32 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.32 ( collect_int
% 5.01/5.32 @ ^ [X3: int] :
% 5.01/5.32 ( ( member_int @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_int @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8943_set__diff__eq,axiom,
% 5.01/5.32 ( minus_minus_set_nat
% 5.01/5.32 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.01/5.32 ( collect_nat
% 5.01/5.32 @ ^ [X3: nat] :
% 5.01/5.32 ( ( member_nat @ X3 @ A6 )
% 5.01/5.32 & ~ ( member_nat @ X3 @ B7 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_diff_eq
% 5.01/5.32 thf(fact_8944_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_real,P: real > $o] :
% 5.01/5.32 ( ord_less_eq_set_real
% 5.01/5.32 @ ( collect_real
% 5.01/5.32 @ ^ [X3: real] :
% 5.01/5.32 ( ( member_real @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8945_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_complex,P: complex > $o] :
% 5.01/5.32 ( ord_le211207098394363844omplex
% 5.01/5.32 @ ( collect_complex
% 5.01/5.32 @ ^ [X3: complex] :
% 5.01/5.32 ( ( member_complex @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8946_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_list_nat,P: list_nat > $o] :
% 5.01/5.32 ( ord_le6045566169113846134st_nat
% 5.01/5.32 @ ( collect_list_nat
% 5.01/5.32 @ ^ [X3: list_nat] :
% 5.01/5.32 ( ( member_list_nat @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8947_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_set_nat,P: set_nat > $o] :
% 5.01/5.32 ( ord_le6893508408891458716et_nat
% 5.01/5.32 @ ( collect_set_nat
% 5.01/5.32 @ ^ [X3: set_nat] :
% 5.01/5.32 ( ( member_set_nat @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8948_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_nat,P: nat > $o] :
% 5.01/5.32 ( ord_less_eq_set_nat
% 5.01/5.32 @ ( collect_nat
% 5.01/5.32 @ ^ [X3: nat] :
% 5.01/5.32 ( ( member_nat @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8949_Collect__subset,axiom,
% 5.01/5.32 ! [A2: set_int,P: int > $o] :
% 5.01/5.32 ( ord_less_eq_set_int
% 5.01/5.32 @ ( collect_int
% 5.01/5.32 @ ^ [X3: int] :
% 5.01/5.32 ( ( member_int @ X3 @ A2 )
% 5.01/5.32 & ( P @ X3 ) ) )
% 5.01/5.32 @ A2 ) ).
% 5.01/5.32
% 5.01/5.32 % Collect_subset
% 5.01/5.32 thf(fact_8950_less__eq__set__def,axiom,
% 5.01/5.32 ( ord_less_eq_set_real
% 5.01/5.32 = ( ^ [A6: set_real,B7: set_real] :
% 5.01/5.32 ( ord_less_eq_real_o
% 5.01/5.32 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: real] : ( member_real @ X3 @ B7 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_eq_set_def
% 5.01/5.32 thf(fact_8951_less__eq__set__def,axiom,
% 5.01/5.32 ( ord_less_eq_set_nat
% 5.01/5.32 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.01/5.32 ( ord_less_eq_nat_o
% 5.01/5.32 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: nat] : ( member_nat @ X3 @ B7 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_eq_set_def
% 5.01/5.32 thf(fact_8952_less__eq__set__def,axiom,
% 5.01/5.32 ( ord_le211207098394363844omplex
% 5.01/5.32 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.01/5.32 ( ord_le4573692005234683329plex_o
% 5.01/5.32 @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: complex] : ( member_complex @ X3 @ B7 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_eq_set_def
% 5.01/5.32 thf(fact_8953_less__eq__set__def,axiom,
% 5.01/5.32 ( ord_le6893508408891458716et_nat
% 5.01/5.32 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.01/5.32 ( ord_le3964352015994296041_nat_o
% 5.01/5.32 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B7 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_eq_set_def
% 5.01/5.32 thf(fact_8954_less__eq__set__def,axiom,
% 5.01/5.32 ( ord_less_eq_set_int
% 5.01/5.32 = ( ^ [A6: set_int,B7: set_int] :
% 5.01/5.32 ( ord_less_eq_int_o
% 5.01/5.32 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.01/5.32 @ ^ [X3: int] : ( member_int @ X3 @ B7 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % less_eq_set_def
% 5.01/5.32 thf(fact_8955_numeral__code_I2_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.01/5.32 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(2)
% 5.01/5.32 thf(fact_8956_numeral__code_I2_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.01/5.32 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(2)
% 5.01/5.32 thf(fact_8957_numeral__code_I2_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.01/5.32 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(2)
% 5.01/5.32 thf(fact_8958_numeral__code_I2_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.01/5.32 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(2)
% 5.01/5.32 thf(fact_8959_numeral__code_I2_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.01/5.32 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(2)
% 5.01/5.32 thf(fact_8960_lambda__zero,axiom,
% 5.01/5.32 ( ( ^ [H2: real] : zero_zero_real )
% 5.01/5.32 = ( times_times_real @ zero_zero_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_zero
% 5.01/5.32 thf(fact_8961_lambda__zero,axiom,
% 5.01/5.32 ( ( ^ [H2: rat] : zero_zero_rat )
% 5.01/5.32 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_zero
% 5.01/5.32 thf(fact_8962_lambda__zero,axiom,
% 5.01/5.32 ( ( ^ [H2: nat] : zero_zero_nat )
% 5.01/5.32 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_zero
% 5.01/5.32 thf(fact_8963_lambda__zero,axiom,
% 5.01/5.32 ( ( ^ [H2: int] : zero_zero_int )
% 5.01/5.32 = ( times_times_int @ zero_zero_int ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_zero
% 5.01/5.32 thf(fact_8964_lambda__zero,axiom,
% 5.01/5.32 ( ( ^ [H2: complex] : zero_zero_complex )
% 5.01/5.32 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_zero
% 5.01/5.32 thf(fact_8965_mult__commute__abs,axiom,
% 5.01/5.32 ! [C: real] :
% 5.01/5.32 ( ( ^ [X3: real] : ( times_times_real @ X3 @ C ) )
% 5.01/5.32 = ( times_times_real @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % mult_commute_abs
% 5.01/5.32 thf(fact_8966_mult__commute__abs,axiom,
% 5.01/5.32 ! [C: rat] :
% 5.01/5.32 ( ( ^ [X3: rat] : ( times_times_rat @ X3 @ C ) )
% 5.01/5.32 = ( times_times_rat @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % mult_commute_abs
% 5.01/5.32 thf(fact_8967_mult__commute__abs,axiom,
% 5.01/5.32 ! [C: nat] :
% 5.01/5.32 ( ( ^ [X3: nat] : ( times_times_nat @ X3 @ C ) )
% 5.01/5.32 = ( times_times_nat @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % mult_commute_abs
% 5.01/5.32 thf(fact_8968_mult__commute__abs,axiom,
% 5.01/5.32 ! [C: int] :
% 5.01/5.32 ( ( ^ [X3: int] : ( times_times_int @ X3 @ C ) )
% 5.01/5.32 = ( times_times_int @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % mult_commute_abs
% 5.01/5.32 thf(fact_8969_mult__commute__abs,axiom,
% 5.01/5.32 ! [C: complex] :
% 5.01/5.32 ( ( ^ [X3: complex] : ( times_times_complex @ X3 @ C ) )
% 5.01/5.32 = ( times_times_complex @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % mult_commute_abs
% 5.01/5.32 thf(fact_8970_lambda__one,axiom,
% 5.01/5.32 ( ( ^ [X3: real] : X3 )
% 5.01/5.32 = ( times_times_real @ one_one_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_one
% 5.01/5.32 thf(fact_8971_lambda__one,axiom,
% 5.01/5.32 ( ( ^ [X3: rat] : X3 )
% 5.01/5.32 = ( times_times_rat @ one_one_rat ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_one
% 5.01/5.32 thf(fact_8972_lambda__one,axiom,
% 5.01/5.32 ( ( ^ [X3: nat] : X3 )
% 5.01/5.32 = ( times_times_nat @ one_one_nat ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_one
% 5.01/5.32 thf(fact_8973_lambda__one,axiom,
% 5.01/5.32 ( ( ^ [X3: int] : X3 )
% 5.01/5.32 = ( times_times_int @ one_one_int ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_one
% 5.01/5.32 thf(fact_8974_lambda__one,axiom,
% 5.01/5.32 ( ( ^ [X3: complex] : X3 )
% 5.01/5.32 = ( times_times_complex @ one_one_complex ) ) ).
% 5.01/5.32
% 5.01/5.32 % lambda_one
% 5.01/5.32 thf(fact_8975_subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: complex,B: complex] :
% 5.01/5.32 ( ( ord_le211207098394363844omplex
% 5.01/5.32 @ ( collect_complex
% 5.01/5.32 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.01/5.32 @ ( collect_complex
% 5.01/5.32 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.01/5.32 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % subset_divisors_dvd
% 5.01/5.32 thf(fact_8976_subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_eq_set_nat
% 5.01/5.32 @ ( collect_nat
% 5.01/5.32 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.01/5.32 @ ( collect_nat
% 5.01/5.32 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.01/5.32 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % subset_divisors_dvd
% 5.01/5.32 thf(fact_8977_subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: code_integer,B: code_integer] :
% 5.01/5.32 ( ( ord_le7084787975880047091nteger
% 5.01/5.32 @ ( collect_Code_integer
% 5.01/5.32 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.01/5.32 @ ( collect_Code_integer
% 5.01/5.32 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.01/5.32 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % subset_divisors_dvd
% 5.01/5.32 thf(fact_8978_subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_eq_set_int
% 5.01/5.32 @ ( collect_int
% 5.01/5.32 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.01/5.32 @ ( collect_int
% 5.01/5.32 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.01/5.32 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.01/5.32
% 5.01/5.32 % subset_divisors_dvd
% 5.01/5.32 thf(fact_8979_nat__leq__as__int,axiom,
% 5.01/5.32 ( ord_less_eq_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_leq_as_int
% 5.01/5.32 thf(fact_8980_nat__less__as__int,axiom,
% 5.01/5.32 ( ord_less_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_less_as_int
% 5.01/5.32 thf(fact_8981_strict__subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: complex,B: complex] :
% 5.01/5.32 ( ( ord_less_set_complex
% 5.01/5.32 @ ( collect_complex
% 5.01/5.32 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.01/5.32 @ ( collect_complex
% 5.01/5.32 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.01/5.32 = ( ( dvd_dvd_complex @ A @ B )
% 5.01/5.32 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % strict_subset_divisors_dvd
% 5.01/5.32 thf(fact_8982_strict__subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: int,B: int] :
% 5.01/5.32 ( ( ord_less_set_int
% 5.01/5.32 @ ( collect_int
% 5.01/5.32 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.01/5.32 @ ( collect_int
% 5.01/5.32 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.01/5.32 = ( ( dvd_dvd_int @ A @ B )
% 5.01/5.32 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % strict_subset_divisors_dvd
% 5.01/5.32 thf(fact_8983_strict__subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: nat,B: nat] :
% 5.01/5.32 ( ( ord_less_set_nat
% 5.01/5.32 @ ( collect_nat
% 5.01/5.32 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.01/5.32 @ ( collect_nat
% 5.01/5.32 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.01/5.32 = ( ( dvd_dvd_nat @ A @ B )
% 5.01/5.32 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % strict_subset_divisors_dvd
% 5.01/5.32 thf(fact_8984_strict__subset__divisors__dvd,axiom,
% 5.01/5.32 ! [A: code_integer,B: code_integer] :
% 5.01/5.32 ( ( ord_le1307284697595431911nteger
% 5.01/5.32 @ ( collect_Code_integer
% 5.01/5.32 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.01/5.32 @ ( collect_Code_integer
% 5.01/5.32 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.01/5.32 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.01/5.32 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % strict_subset_divisors_dvd
% 5.01/5.32 thf(fact_8985_numeral__code_I3_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.01/5.32 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(3)
% 5.01/5.32 thf(fact_8986_numeral__code_I3_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.01/5.32 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(3)
% 5.01/5.32 thf(fact_8987_numeral__code_I3_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.01/5.32 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(3)
% 5.01/5.32 thf(fact_8988_numeral__code_I3_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.01/5.32 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(3)
% 5.01/5.32 thf(fact_8989_numeral__code_I3_J,axiom,
% 5.01/5.32 ! [N: num] :
% 5.01/5.32 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.01/5.32 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.01/5.32
% 5.01/5.32 % numeral_code(3)
% 5.01/5.32 thf(fact_8990_power__numeral__even,axiom,
% 5.01/5.32 ! [Z: real,W: num] :
% 5.01/5.32 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.01/5.32 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_even
% 5.01/5.32 thf(fact_8991_power__numeral__even,axiom,
% 5.01/5.32 ! [Z: rat,W: num] :
% 5.01/5.32 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.01/5.32 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_even
% 5.01/5.32 thf(fact_8992_power__numeral__even,axiom,
% 5.01/5.32 ! [Z: nat,W: num] :
% 5.01/5.32 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.01/5.32 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_even
% 5.01/5.32 thf(fact_8993_power__numeral__even,axiom,
% 5.01/5.32 ! [Z: int,W: num] :
% 5.01/5.32 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.01/5.32 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_even
% 5.01/5.32 thf(fact_8994_power__numeral__even,axiom,
% 5.01/5.32 ! [Z: complex,W: num] :
% 5.01/5.32 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.01/5.32 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_even
% 5.01/5.32 thf(fact_8995_power__numeral__odd,axiom,
% 5.01/5.32 ! [Z: real,W: num] :
% 5.01/5.32 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.01/5.32 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_odd
% 5.01/5.32 thf(fact_8996_power__numeral__odd,axiom,
% 5.01/5.32 ! [Z: rat,W: num] :
% 5.01/5.32 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.01/5.32 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_odd
% 5.01/5.32 thf(fact_8997_power__numeral__odd,axiom,
% 5.01/5.32 ! [Z: nat,W: num] :
% 5.01/5.32 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.01/5.32 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_odd
% 5.01/5.32 thf(fact_8998_power__numeral__odd,axiom,
% 5.01/5.32 ! [Z: int,W: num] :
% 5.01/5.32 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.01/5.32 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_odd
% 5.01/5.32 thf(fact_8999_power__numeral__odd,axiom,
% 5.01/5.32 ! [Z: complex,W: num] :
% 5.01/5.32 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.01/5.32 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % power_numeral_odd
% 5.01/5.32 thf(fact_9000_nat__plus__as__int,axiom,
% 5.01/5.32 ( plus_plus_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_plus_as_int
% 5.01/5.32 thf(fact_9001_nat__times__as__int,axiom,
% 5.01/5.32 ( times_times_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_times_as_int
% 5.01/5.32 thf(fact_9002_nat__minus__as__int,axiom,
% 5.01/5.32 ( minus_minus_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_minus_as_int
% 5.01/5.32 thf(fact_9003_nat__div__as__int,axiom,
% 5.01/5.32 ( divide_divide_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_div_as_int
% 5.01/5.32 thf(fact_9004_nat__mod__as__int,axiom,
% 5.01/5.32 ( modulo_modulo_nat
% 5.01/5.32 = ( ^ [A4: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A4 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % nat_mod_as_int
% 5.01/5.32 thf(fact_9005_imaginary__unit_Osimps_I1_J,axiom,
% 5.01/5.32 ( ( re @ imaginary_unit )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % imaginary_unit.simps(1)
% 5.01/5.32 thf(fact_9006_complex__Re__le__cmod,axiom,
% 5.01/5.32 ! [X2: complex] : ( ord_less_eq_real @ ( re @ X2 ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Re_le_cmod
% 5.01/5.32 thf(fact_9007_zero__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ( ( re @ zero_zero_complex )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % zero_complex.simps(1)
% 5.01/5.32 thf(fact_9008_one__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ( ( re @ one_one_complex )
% 5.01/5.32 = one_one_real ) ).
% 5.01/5.32
% 5.01/5.32 % one_complex.simps(1)
% 5.01/5.32 thf(fact_9009_uminus__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( re @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.32 = ( uminus_uminus_real @ ( re @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % uminus_complex.simps(1)
% 5.01/5.32 thf(fact_9010_plus__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( re @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.32 = ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % plus_complex.simps(1)
% 5.01/5.32 thf(fact_9011_minus__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( re @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.32 = ( minus_minus_real @ ( re @ X2 ) @ ( re @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_complex.simps(1)
% 5.01/5.32 thf(fact_9012_diff__nat__eq__if,axiom,
% 5.01/5.32 ! [Z6: int,Z: int] :
% 5.01/5.32 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.01/5.32 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.01/5.32 = ( nat2 @ Z ) ) )
% 5.01/5.32 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.01/5.32 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.01/5.32 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % diff_nat_eq_if
% 5.01/5.32 thf(fact_9013_abs__Re__le__cmod,axiom,
% 5.01/5.32 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % abs_Re_le_cmod
% 5.01/5.32 thf(fact_9014_Re__csqrt,axiom,
% 5.01/5.32 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_csqrt
% 5.01/5.32 thf(fact_9015_set__decode__def,axiom,
% 5.01/5.32 ( nat_set_decode
% 5.01/5.32 = ( ^ [X3: nat] :
% 5.01/5.32 ( collect_nat
% 5.01/5.32 @ ^ [N4: nat] :
% 5.01/5.32 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % set_decode_def
% 5.01/5.32 thf(fact_9016_signed__take__bit__code,axiom,
% 5.01/5.32 ( bit_ri6519982836138164636nteger
% 5.01/5.32 = ( ^ [N4: nat,A4: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A4 ) @ N4 ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A4 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N4 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N4 ) @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % signed_take_bit_code
% 5.01/5.32 thf(fact_9017_signed__take__bit__code,axiom,
% 5.01/5.32 ( bit_ri631733984087533419it_int
% 5.01/5.32 = ( ^ [N4: nat,A4: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A4 ) @ N4 ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A4 ) @ ( bit_se545348938243370406it_int @ ( suc @ N4 ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ A4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % signed_take_bit_code
% 5.01/5.32 thf(fact_9018_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s4028243227959126397er_rat
% 5.01/5.32 = ( ^ [A4: rat,N4: nat] :
% 5.01/5.32 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 5.01/5.32 @ ( set_fo1949268297981939178at_rat
% 5.01/5.32 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A4 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_rat ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9019_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s7457072308508201937r_real
% 5.01/5.32 = ( ^ [A4: real,N4: nat] :
% 5.01/5.32 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 5.01/5.32 @ ( set_fo3111899725591712190t_real
% 5.01/5.32 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A4 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_real ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9020_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s4660882817536571857er_int
% 5.01/5.32 = ( ^ [A4: int,N4: nat] :
% 5.01/5.32 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 5.01/5.32 @ ( set_fo2581907887559384638at_int
% 5.01/5.32 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A4 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_int ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9021_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s2602460028002588243omplex
% 5.01/5.32 = ( ^ [A4: complex,N4: nat] :
% 5.01/5.32 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 5.01/5.32 @ ( set_fo1517530859248394432omplex
% 5.01/5.32 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A4 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_complex ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9022_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s8582702949713902594nteger
% 5.01/5.32 = ( ^ [A4: code_integer,N4: nat] :
% 5.01/5.32 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 5.01/5.32 @ ( set_fo1084959871951514735nteger
% 5.01/5.32 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A4 @ ( semiri4939895301339042750nteger @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9023_pochhammer__code,axiom,
% 5.01/5.32 ( comm_s4663373288045622133er_nat
% 5.01/5.32 = ( ^ [A4: nat,N4: nat] :
% 5.01/5.32 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 5.01/5.32 @ ( set_fo2584398358068434914at_nat
% 5.01/5.32 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A4 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 5.01/5.32 @ one_one_nat ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % pochhammer_code
% 5.01/5.32 thf(fact_9024_cmod__plus__Re__le__0__iff,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.01/5.32 = ( ( re @ Z )
% 5.01/5.32 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_plus_Re_le_0_iff
% 5.01/5.32 thf(fact_9025_gbinomial__code,axiom,
% 5.01/5.32 ( gbinomial_rat
% 5.01/5.32 = ( ^ [A4: rat,K2: nat] :
% 5.01/5.32 ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 5.01/5.32 @ ( divide_divide_rat
% 5.01/5.32 @ ( set_fo1949268297981939178at_rat
% 5.01/5.32 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A4 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.01/5.32 @ one_one_rat )
% 5.01/5.32 @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % gbinomial_code
% 5.01/5.32 thf(fact_9026_gbinomial__code,axiom,
% 5.01/5.32 ( gbinomial_real
% 5.01/5.32 = ( ^ [A4: real,K2: nat] :
% 5.01/5.32 ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 5.01/5.32 @ ( divide_divide_real
% 5.01/5.32 @ ( set_fo3111899725591712190t_real
% 5.01/5.32 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A4 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.01/5.32 @ one_one_real )
% 5.01/5.32 @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % gbinomial_code
% 5.01/5.32 thf(fact_9027_gbinomial__code,axiom,
% 5.01/5.32 ( gbinomial_complex
% 5.01/5.32 = ( ^ [A4: complex,K2: nat] :
% 5.01/5.32 ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 5.01/5.32 @ ( divide1717551699836669952omplex
% 5.01/5.32 @ ( set_fo1517530859248394432omplex
% 5.01/5.32 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A4 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.01/5.32 @ zero_zero_nat
% 5.01/5.32 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.01/5.32 @ one_one_complex )
% 5.01/5.32 @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % gbinomial_code
% 5.01/5.32 thf(fact_9028_cos__n__Re__cis__pow__n,axiom,
% 5.01/5.32 ! [N: nat,A: real] :
% 5.01/5.32 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.01/5.32 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cos_n_Re_cis_pow_n
% 5.01/5.32 thf(fact_9029_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.01/5.32 ! [Uy2: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.01/5.32 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V ) @ TreeList @ S2 ) @ X2 )
% 5.01/5.32 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.01/5.32 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.naive_member.simps(3)
% 5.01/5.32 thf(fact_9030_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.01/5.32 ! [V: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X2: nat] :
% 5.01/5.32 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd2 ) @ X2 )
% 5.01/5.32 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.membermima.simps(5)
% 5.01/5.32 thf(fact_9031_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.01/5.32 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X2: nat] :
% 5.01/5.32 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X2 )
% 5.01/5.32 = ( ( X2 = Mi )
% 5.01/5.32 | ( X2 = Ma )
% 5.01/5.32 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.membermima.simps(4)
% 5.01/5.32 thf(fact_9032_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.32 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.32 => ( ! [A3: $o,B2: $o] :
% 5.01/5.32 ( ( X2
% 5.01/5.32 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.32 => ( ( ( Xa = zero_zero_nat )
% 5.01/5.32 => A3 )
% 5.01/5.32 & ( ( Xa != zero_zero_nat )
% 5.01/5.32 => ( ( ( Xa = one_one_nat )
% 5.01/5.32 => B2 )
% 5.01/5.32 & ( Xa = one_one_nat ) ) ) ) )
% 5.01/5.32 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.01/5.32 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [S3: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.32 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.naive_member.elims(3)
% 5.01/5.32 thf(fact_9033_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.32 ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.32 => ( ! [A3: $o,B2: $o] :
% 5.01/5.32 ( ( X2
% 5.01/5.32 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.32 => ~ ( ( ( Xa = zero_zero_nat )
% 5.01/5.32 => A3 )
% 5.01/5.32 & ( ( Xa != zero_zero_nat )
% 5.01/5.32 => ( ( ( Xa = one_one_nat )
% 5.01/5.32 => B2 )
% 5.01/5.32 & ( Xa = one_one_nat ) ) ) ) )
% 5.01/5.32 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [S3: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.32 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.naive_member.elims(2)
% 5.01/5.32 thf(fact_9034_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.01/5.32 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.32 = Y )
% 5.01/5.32 => ( ! [A3: $o,B2: $o] :
% 5.01/5.32 ( ( X2
% 5.01/5.32 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.32 => ( Y
% 5.01/5.32 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.01/5.32 => A3 )
% 5.01/5.32 & ( ( Xa != zero_zero_nat )
% 5.01/5.32 => ( ( ( Xa = one_one_nat )
% 5.01/5.32 => B2 )
% 5.01/5.32 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.01/5.32 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.01/5.32 => Y )
% 5.01/5.32 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [S3: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.32 => ( Y
% 5.01/5.32 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.naive_member.elims(1)
% 5.01/5.32 thf(fact_9035_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.01/5.32 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.32 ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat] :
% 5.01/5.32 ( ? [Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.32 => ~ ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 ) ) )
% 5.01/5.32 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vc: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.32 => ~ ( ( Xa = Mi3 )
% 5.01/5.32 | ( Xa = Ma3 )
% 5.01/5.32 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.01/5.32 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.01/5.32 ( ? [Vd: vEBT_VEBT] :
% 5.01/5.32 ( X2
% 5.01/5.32 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.32 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.32 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.32 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % VEBT_internal.membermima.elims(2)
% 5.01/5.32 thf(fact_9036_of__int__code__if,axiom,
% 5.01/5.32 ( ring_1_of_int_real
% 5.01/5.32 = ( ^ [K2: int] :
% 5.01/5.32 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.01/5.32 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.32 @ ( if_real
% 5.01/5.32 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.32 = zero_zero_int )
% 5.01/5.32 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.32 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % of_int_code_if
% 5.01/5.32 thf(fact_9037_of__int__code__if,axiom,
% 5.01/5.32 ( ring_1_of_int_int
% 5.01/5.32 = ( ^ [K2: int] :
% 5.01/5.32 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.01/5.32 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.32 @ ( if_int
% 5.01/5.32 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.32 = zero_zero_int )
% 5.01/5.32 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.32 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % of_int_code_if
% 5.01/5.32 thf(fact_9038_of__int__code__if,axiom,
% 5.01/5.32 ( ring_17405671764205052669omplex
% 5.01/5.32 = ( ^ [K2: int] :
% 5.01/5.32 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.01/5.32 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.32 @ ( if_complex
% 5.01/5.32 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.32 = zero_zero_int )
% 5.01/5.32 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.32 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % of_int_code_if
% 5.01/5.32 thf(fact_9039_of__int__code__if,axiom,
% 5.01/5.32 ( ring_18347121197199848620nteger
% 5.01/5.32 = ( ^ [K2: int] :
% 5.01/5.32 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.01/5.32 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.32 @ ( if_Code_integer
% 5.01/5.32 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.32 = zero_zero_int )
% 5.01/5.32 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.32 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % of_int_code_if
% 5.01/5.32 thf(fact_9040_of__int__code__if,axiom,
% 5.01/5.32 ( ring_1_of_int_rat
% 5.01/5.32 = ( ^ [K2: int] :
% 5.01/5.32 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.01/5.32 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.32 @ ( if_rat
% 5.01/5.32 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.32 = zero_zero_int )
% 5.01/5.32 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.32 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % of_int_code_if
% 5.01/5.32 thf(fact_9041_foldr__zero,axiom,
% 5.01/5.32 ! [Xs: list_nat,D: nat] :
% 5.01/5.32 ( ! [I3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.01/5.32 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs @ I3 ) ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ D ) @ D ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr_zero
% 5.01/5.32 thf(fact_9042_monoseq__arctan__series,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.32 => ( topolo6980174941875973593q_real
% 5.01/5.32 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % monoseq_arctan_series
% 5.01/5.32 thf(fact_9043_csqrt_Ocode,axiom,
% 5.01/5.32 ( csqrt
% 5.01/5.32 = ( ^ [Z5: complex] :
% 5.01/5.32 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.32 @ ( times_times_real
% 5.01/5.32 @ ( if_real
% 5.01/5.32 @ ( ( im @ Z5 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 @ one_one_real
% 5.01/5.32 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.01/5.32 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt.code
% 5.01/5.32 thf(fact_9044_foldr__one,axiom,
% 5.01/5.32 ! [D: nat,Ys: list_nat] : ( ord_less_eq_nat @ D @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr_one
% 5.01/5.32 thf(fact_9045_foldr__mono,axiom,
% 5.01/5.32 ! [Xs: list_nat,Ys: list_nat,C: nat,D: nat] :
% 5.01/5.32 ( ( ( size_size_list_nat @ Xs )
% 5.01/5.32 = ( size_size_list_nat @ Ys ) )
% 5.01/5.32 => ( ! [I3: nat] :
% 5.01/5.32 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.01/5.32 => ( ord_less_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Ys @ I3 ) ) )
% 5.01/5.32 => ( ( ord_less_eq_nat @ C @ D )
% 5.01/5.32 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ C ) @ ( size_size_list_nat @ Ys ) ) @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr_mono
% 5.01/5.32 thf(fact_9046_complex__Im__fact,axiom,
% 5.01/5.32 ! [N: nat] :
% 5.01/5.32 ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Im_fact
% 5.01/5.32 thf(fact_9047_complex__Im__of__int,axiom,
% 5.01/5.32 ! [Z: int] :
% 5.01/5.32 ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Im_of_int
% 5.01/5.32 thf(fact_9048_Im__complex__of__real,axiom,
% 5.01/5.32 ! [Z: real] :
% 5.01/5.32 ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % Im_complex_of_real
% 5.01/5.32 thf(fact_9049_Im__power__real,axiom,
% 5.01/5.32 ! [X2: complex,N: nat] :
% 5.01/5.32 ( ( ( im @ X2 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( im @ ( power_power_complex @ X2 @ N ) )
% 5.01/5.32 = zero_zero_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_power_real
% 5.01/5.32 thf(fact_9050_complex__Im__numeral,axiom,
% 5.01/5.32 ! [V: num] :
% 5.01/5.32 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Im_numeral
% 5.01/5.32 thf(fact_9051_complex__Im__of__nat,axiom,
% 5.01/5.32 ! [N: nat] :
% 5.01/5.32 ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % complex_Im_of_nat
% 5.01/5.32 thf(fact_9052_Im__divide__of__real,axiom,
% 5.01/5.32 ! [Z: complex,R: real] :
% 5.01/5.32 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( im @ Z ) @ R ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_divide_of_real
% 5.01/5.32 thf(fact_9053_Im__sgn,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.01/5.32 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_sgn
% 5.01/5.32 thf(fact_9054_Re__power__real,axiom,
% 5.01/5.32 ! [X2: complex,N: nat] :
% 5.01/5.32 ( ( ( im @ X2 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( re @ ( power_power_complex @ X2 @ N ) )
% 5.01/5.32 = ( power_power_real @ ( re @ X2 ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_power_real
% 5.01/5.32 thf(fact_9055_Re__i__times,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.01/5.32 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_i_times
% 5.01/5.32 thf(fact_9056_Im__divide__numeral,axiom,
% 5.01/5.32 ! [Z: complex,W: num] :
% 5.01/5.32 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_divide_numeral
% 5.01/5.32 thf(fact_9057_Im__divide__of__nat,axiom,
% 5.01/5.32 ! [Z: complex,N: nat] :
% 5.01/5.32 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.01/5.32 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_divide_of_nat
% 5.01/5.32 thf(fact_9058_csqrt__of__real__nonneg,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( ( im @ X2 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) )
% 5.01/5.32 => ( ( csqrt @ X2 )
% 5.01/5.32 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X2 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_of_real_nonneg
% 5.01/5.32 thf(fact_9059_csqrt__minus,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.01/5.32 | ( ( ( im @ X2 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.01/5.32 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.32 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_minus
% 5.01/5.32 thf(fact_9060_csqrt__of__real__nonpos,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( ( im @ X2 )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( re @ X2 ) @ zero_zero_real )
% 5.01/5.32 => ( ( csqrt @ X2 )
% 5.01/5.32 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_of_real_nonpos
% 5.01/5.32 thf(fact_9061_foldr__cong,axiom,
% 5.01/5.32 ! [A: real,B: real,L: list_real,K: list_real,F: real > real > real,G: real > real > real] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( L = K )
% 5.01/5.32 => ( ! [A3: real,X4: real] :
% 5.01/5.32 ( ( member_real @ X4 @ ( set_real2 @ L ) )
% 5.01/5.32 => ( ( F @ X4 @ A3 )
% 5.01/5.32 = ( G @ X4 @ A3 ) ) )
% 5.01/5.32 => ( ( foldr_real_real @ F @ L @ A )
% 5.01/5.32 = ( foldr_real_real @ G @ K @ B ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr_cong
% 5.01/5.32 thf(fact_9062_foldr__cong,axiom,
% 5.01/5.32 ! [A: nat,B: nat,L: list_nat,K: list_nat,F: nat > nat > nat,G: nat > nat > nat] :
% 5.01/5.32 ( ( A = B )
% 5.01/5.32 => ( ( L = K )
% 5.01/5.32 => ( ! [A3: nat,X4: nat] :
% 5.01/5.32 ( ( member_nat @ X4 @ ( set_nat2 @ L ) )
% 5.01/5.32 => ( ( F @ X4 @ A3 )
% 5.01/5.32 = ( G @ X4 @ A3 ) ) )
% 5.01/5.32 => ( ( foldr_nat_nat @ F @ L @ A )
% 5.01/5.32 = ( foldr_nat_nat @ G @ K @ B ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr_cong
% 5.01/5.32 thf(fact_9063_imaginary__unit_Osimps_I2_J,axiom,
% 5.01/5.32 ( ( im @ imaginary_unit )
% 5.01/5.32 = one_one_real ) ).
% 5.01/5.32
% 5.01/5.32 % imaginary_unit.simps(2)
% 5.01/5.32 thf(fact_9064_zero__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ( ( im @ zero_zero_complex )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % zero_complex.simps(2)
% 5.01/5.32 thf(fact_9065_one__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ( ( im @ one_one_complex )
% 5.01/5.32 = zero_zero_real ) ).
% 5.01/5.32
% 5.01/5.32 % one_complex.simps(2)
% 5.01/5.32 thf(fact_9066_uminus__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( im @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.01/5.32 = ( uminus_uminus_real @ ( im @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % uminus_complex.simps(2)
% 5.01/5.32 thf(fact_9067_plus__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( im @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.32 = ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % plus_complex.simps(2)
% 5.01/5.32 thf(fact_9068_minus__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( im @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.32 = ( minus_minus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_complex.simps(2)
% 5.01/5.32 thf(fact_9069_complex__is__Int__iff,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( member_complex @ Z @ ring_1_Ints_complex )
% 5.01/5.32 = ( ( ( im @ Z )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 & ? [I4: int] :
% 5.01/5.32 ( ( re @ Z )
% 5.01/5.32 = ( ring_1_of_int_real @ I4 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_is_Int_iff
% 5.01/5.32 thf(fact_9070_abs__Im__le__cmod,axiom,
% 5.01/5.32 ! [X2: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( real_V1022390504157884413omplex @ X2 ) ) ).
% 5.01/5.32
% 5.01/5.32 % abs_Im_le_cmod
% 5.01/5.32 thf(fact_9071_times__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( im @ ( times_times_complex @ X2 @ Y ) )
% 5.01/5.32 = ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % times_complex.simps(2)
% 5.01/5.32 thf(fact_9072_cmod__eq__Re,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( ( im @ Z )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( real_V1022390504157884413omplex @ Z )
% 5.01/5.32 = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_eq_Re
% 5.01/5.32 thf(fact_9073_cmod__eq__Im,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( ( re @ Z )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 => ( ( real_V1022390504157884413omplex @ Z )
% 5.01/5.32 = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_eq_Im
% 5.01/5.32 thf(fact_9074_Im__eq__0,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( ( abs_abs_real @ ( re @ Z ) )
% 5.01/5.32 = ( real_V1022390504157884413omplex @ Z ) )
% 5.01/5.32 => ( ( im @ Z )
% 5.01/5.32 = zero_zero_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_eq_0
% 5.01/5.32 thf(fact_9075_cmod__Re__le__iff,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( ( im @ X2 )
% 5.01/5.32 = ( im @ Y ) )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.01/5.32 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X2 ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_Re_le_iff
% 5.01/5.32 thf(fact_9076_cmod__Im__le__iff,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( ( re @ X2 )
% 5.01/5.32 = ( re @ Y ) )
% 5.01/5.32 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.01/5.32 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X2 ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_Im_le_iff
% 5.01/5.32 thf(fact_9077_times__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( re @ ( times_times_complex @ X2 @ Y ) )
% 5.01/5.32 = ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % times_complex.simps(1)
% 5.01/5.32 thf(fact_9078_uminus__complex_Ocode,axiom,
% 5.01/5.32 ( uminus1482373934393186551omplex
% 5.01/5.32 = ( ^ [X3: complex] : ( complex2 @ ( uminus_uminus_real @ ( re @ X3 ) ) @ ( uminus_uminus_real @ ( im @ X3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % uminus_complex.code
% 5.01/5.32 thf(fact_9079_plus__complex_Ocode,axiom,
% 5.01/5.32 ( plus_plus_complex
% 5.01/5.32 = ( ^ [X3: complex,Y2: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X3 ) @ ( re @ Y2 ) ) @ ( plus_plus_real @ ( im @ X3 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % plus_complex.code
% 5.01/5.32 thf(fact_9080_minus__complex_Ocode,axiom,
% 5.01/5.32 ( minus_minus_complex
% 5.01/5.32 = ( ^ [X3: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X3 ) @ ( re @ Y2 ) ) @ ( minus_minus_real @ ( im @ X3 ) @ ( im @ Y2 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % minus_complex.code
% 5.01/5.32 thf(fact_9081_csqrt__principal,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.01/5.32 | ( ( ( re @ ( csqrt @ Z ) )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_principal
% 5.01/5.32 thf(fact_9082_cmod__le,axiom,
% 5.01/5.32 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_le
% 5.01/5.32 thf(fact_9083_sin__n__Im__cis__pow__n,axiom,
% 5.01/5.32 ! [N: nat,A: real] :
% 5.01/5.32 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.01/5.32 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % sin_n_Im_cis_pow_n
% 5.01/5.32 thf(fact_9084_Re__exp,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( re @ ( exp_complex @ Z ) )
% 5.01/5.32 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_exp
% 5.01/5.32 thf(fact_9085_Im__exp,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( im @ ( exp_complex @ Z ) )
% 5.01/5.32 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_exp
% 5.01/5.32 thf(fact_9086_complex__eq,axiom,
% 5.01/5.32 ! [A: complex] :
% 5.01/5.32 ( A
% 5.01/5.32 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_eq
% 5.01/5.32 thf(fact_9087_monoseq__realpow,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.32 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.32 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % monoseq_realpow
% 5.01/5.32 thf(fact_9088_times__complex_Ocode,axiom,
% 5.01/5.32 ( times_times_complex
% 5.01/5.32 = ( ^ [X3: complex,Y2: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y2 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y2 ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % times_complex.code
% 5.01/5.32 thf(fact_9089_cmod__power2,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.32 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % cmod_power2
% 5.01/5.32 thf(fact_9090_Im__power2,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( im @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.32 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X2 ) ) @ ( im @ X2 ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_power2
% 5.01/5.32 thf(fact_9091_Re__power2,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( re @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.32 = ( minus_minus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_power2
% 5.01/5.32 thf(fact_9092_complex__eq__0,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( Z = zero_zero_complex )
% 5.01/5.32 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.32 = zero_zero_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_eq_0
% 5.01/5.32 thf(fact_9093_norm__complex__def,axiom,
% 5.01/5.32 ( real_V1022390504157884413omplex
% 5.01/5.32 = ( ^ [Z5: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % norm_complex_def
% 5.01/5.32 thf(fact_9094_inverse__complex_Osimps_I1_J,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( re @ ( invers8013647133539491842omplex @ X2 ) )
% 5.01/5.32 = ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % inverse_complex.simps(1)
% 5.01/5.32 thf(fact_9095_complex__neq__0,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( Z != zero_zero_complex )
% 5.01/5.32 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_neq_0
% 5.01/5.32 thf(fact_9096_Re__divide,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( re @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 5.01/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Re_divide
% 5.01/5.32 thf(fact_9097_csqrt__square,axiom,
% 5.01/5.32 ! [B: complex] :
% 5.01/5.32 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.01/5.32 | ( ( ( re @ B )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.01/5.32 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.32 = B ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_square
% 5.01/5.32 thf(fact_9098_csqrt__unique,axiom,
% 5.01/5.32 ! [W: complex,Z: complex] :
% 5.01/5.32 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.32 = Z )
% 5.01/5.32 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.01/5.32 | ( ( ( re @ W )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.01/5.32 => ( ( csqrt @ Z )
% 5.01/5.32 = W ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt_unique
% 5.01/5.32 thf(fact_9099_inverse__complex_Osimps_I2_J,axiom,
% 5.01/5.32 ! [X2: complex] :
% 5.01/5.32 ( ( im @ ( invers8013647133539491842omplex @ X2 ) )
% 5.01/5.32 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % inverse_complex.simps(2)
% 5.01/5.32 thf(fact_9100_Im__divide,axiom,
% 5.01/5.32 ! [X2: complex,Y: complex] :
% 5.01/5.32 ( ( im @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 5.01/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Im_divide
% 5.01/5.32 thf(fact_9101_complex__abs__le__norm,axiom,
% 5.01/5.32 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_abs_le_norm
% 5.01/5.32 thf(fact_9102_complex__unit__circle,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( Z != zero_zero_complex )
% 5.01/5.32 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.32 = one_one_real ) ) ).
% 5.01/5.32
% 5.01/5.32 % complex_unit_circle
% 5.01/5.32 thf(fact_9103_inverse__complex_Ocode,axiom,
% 5.01/5.32 ( invers8013647133539491842omplex
% 5.01/5.32 = ( ^ [X3: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X3 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X3 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % inverse_complex.code
% 5.01/5.32 thf(fact_9104_Complex__divide,axiom,
% 5.01/5.32 ( divide1717551699836669952omplex
% 5.01/5.32 = ( ^ [X3: complex,Y2: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y2 ) ) @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y2 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % Complex_divide
% 5.01/5.32 thf(fact_9105_csqrt_Osimps_I2_J,axiom,
% 5.01/5.32 ! [Z: complex] :
% 5.01/5.32 ( ( im @ ( csqrt @ Z ) )
% 5.01/5.32 = ( times_times_real
% 5.01/5.32 @ ( if_real
% 5.01/5.32 @ ( ( im @ Z )
% 5.01/5.32 = zero_zero_real )
% 5.01/5.32 @ one_one_real
% 5.01/5.32 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.01/5.32 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % csqrt.simps(2)
% 5.01/5.32 thf(fact_9106_horner__sum__foldr,axiom,
% 5.01/5.32 ( groups1503878375050959669l_real
% 5.01/5.32 = ( ^ [F3: real > real,A4: real,Xs3: list_real] :
% 5.01/5.32 ( foldr_real_real
% 5.01/5.32 @ ^ [X3: real,B3: real] : ( plus_plus_real @ ( F3 @ X3 ) @ ( times_times_real @ A4 @ B3 ) )
% 5.01/5.32 @ Xs3
% 5.01/5.32 @ zero_zero_real ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % horner_sum_foldr
% 5.01/5.32 thf(fact_9107_horner__sum__foldr,axiom,
% 5.01/5.32 ( groups7488368174851004413at_nat
% 5.01/5.32 = ( ^ [F3: nat > nat,A4: nat,Xs3: list_nat] :
% 5.01/5.32 ( foldr_nat_nat
% 5.01/5.32 @ ^ [X3: nat,B3: nat] : ( plus_plus_nat @ ( F3 @ X3 ) @ ( times_times_nat @ A4 @ B3 ) )
% 5.01/5.32 @ Xs3
% 5.01/5.32 @ zero_zero_nat ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % horner_sum_foldr
% 5.01/5.32 thf(fact_9108_horner__sum__foldr,axiom,
% 5.01/5.32 ( groups9116527308978886569_o_int
% 5.01/5.32 = ( ^ [F3: $o > int,A4: int,Xs3: list_o] :
% 5.01/5.32 ( foldr_o_int
% 5.01/5.32 @ ^ [X3: $o,B3: int] : ( plus_plus_int @ ( F3 @ X3 ) @ ( times_times_int @ A4 @ B3 ) )
% 5.01/5.32 @ Xs3
% 5.01/5.32 @ zero_zero_int ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % horner_sum_foldr
% 5.01/5.32 thf(fact_9109_ln__series,axiom,
% 5.01/5.32 ! [X2: real] :
% 5.01/5.32 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.32 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.32 => ( ( ln_ln_real @ X2 )
% 5.01/5.32 = ( suminf_real
% 5.01/5.32 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % ln_series
% 5.01/5.32 thf(fact_9110_length__mul__elem,axiom,
% 5.01/5.32 ! [Xs: list_list_VEBT_VEBT,N: nat] :
% 5.01/5.32 ( ! [X4: list_VEBT_VEBT] :
% 5.01/5.32 ( ( member2936631157270082147T_VEBT @ X4 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 5.01/5.32 => ( ( size_s6755466524823107622T_VEBT @ X4 )
% 5.01/5.32 = N ) )
% 5.01/5.32 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 5.01/5.32 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_mul_elem
% 5.01/5.32 thf(fact_9111_length__mul__elem,axiom,
% 5.01/5.32 ! [Xs: list_list_o,N: nat] :
% 5.01/5.32 ( ! [X4: list_o] :
% 5.01/5.32 ( ( member_list_o @ X4 @ ( set_list_o2 @ Xs ) )
% 5.01/5.32 => ( ( size_size_list_o @ X4 )
% 5.01/5.32 = N ) )
% 5.01/5.32 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 5.01/5.32 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_mul_elem
% 5.01/5.32 thf(fact_9112_length__mul__elem,axiom,
% 5.01/5.32 ! [Xs: list_list_nat,N: nat] :
% 5.01/5.32 ( ! [X4: list_nat] :
% 5.01/5.32 ( ( member_list_nat @ X4 @ ( set_list_nat2 @ Xs ) )
% 5.01/5.32 => ( ( size_size_list_nat @ X4 )
% 5.01/5.32 = N ) )
% 5.01/5.32 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 5.01/5.32 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_mul_elem
% 5.01/5.32 thf(fact_9113_length__mul__elem,axiom,
% 5.01/5.32 ! [Xs: list_list_int,N: nat] :
% 5.01/5.32 ( ! [X4: list_int] :
% 5.01/5.32 ( ( member_list_int @ X4 @ ( set_list_int2 @ Xs ) )
% 5.01/5.32 => ( ( size_size_list_int @ X4 )
% 5.01/5.32 = N ) )
% 5.01/5.32 => ( ( size_size_list_int @ ( concat_int @ Xs ) )
% 5.01/5.32 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs ) @ N ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % length_mul_elem
% 5.01/5.32 thf(fact_9114_list__every__elemnt__bound__sum__bound,axiom,
% 5.01/5.32 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat,Bound: nat,I: nat] :
% 5.01/5.32 ( ! [X4: vEBT_VEBT] :
% 5.01/5.32 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % list_every_elemnt_bound_sum_bound
% 5.01/5.32 thf(fact_9115_list__every__elemnt__bound__sum__bound,axiom,
% 5.01/5.32 ! [Xs: list_o,F: $o > nat,Bound: nat,I: nat] :
% 5.01/5.32 ( ! [X4: $o] :
% 5.01/5.32 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_o_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % list_every_elemnt_bound_sum_bound
% 5.01/5.32 thf(fact_9116_list__every__elemnt__bound__sum__bound,axiom,
% 5.01/5.32 ! [Xs: list_nat,F: nat > nat,Bound: nat,I: nat] :
% 5.01/5.32 ( ! [X4: nat] :
% 5.01/5.32 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_nat_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % list_every_elemnt_bound_sum_bound
% 5.01/5.32 thf(fact_9117_list__every__elemnt__bound__sum__bound,axiom,
% 5.01/5.32 ! [Xs: list_int,F: int > nat,Bound: nat,I: nat] :
% 5.01/5.32 ( ! [X4: int] :
% 5.01/5.32 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( F @ X4 ) @ Bound ) )
% 5.01/5.32 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_int_nat @ F @ Xs ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ Bound ) @ I ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % list_every_elemnt_bound_sum_bound
% 5.01/5.32 thf(fact_9118_foldr0,axiom,
% 5.01/5.32 ! [Xs: list_real,C: real,D: real] :
% 5.01/5.32 ( ( foldr_real_real @ plus_plus_real @ Xs @ ( plus_plus_real @ C @ D ) )
% 5.01/5.32 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs @ D ) @ C ) ) ).
% 5.01/5.32
% 5.01/5.32 % foldr0
% 5.01/5.32 thf(fact_9119_map__ident,axiom,
% 5.01/5.32 ( ( map_nat_nat
% 5.01/5.32 @ ^ [X3: nat] : X3 )
% 5.01/5.32 = ( ^ [Xs3: list_nat] : Xs3 ) ) ).
% 5.01/5.32
% 5.01/5.32 % map_ident
% 5.01/5.32 thf(fact_9120_map__eq__conv,axiom,
% 5.01/5.32 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: vEBT_VEBT > real] :
% 5.01/5.32 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.32 = ( map_VEBT_VEBT_real @ G @ Xs ) )
% 5.01/5.32 = ( ! [X3: vEBT_VEBT] :
% 5.01/5.32 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.32 => ( ( F @ X3 )
% 5.01/5.32 = ( G @ X3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % map_eq_conv
% 5.01/5.32 thf(fact_9121_map__eq__conv,axiom,
% 5.01/5.32 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.01/5.32 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.32 = ( map_VEBT_VEBT_nat @ G @ Xs ) )
% 5.01/5.32 = ( ! [X3: vEBT_VEBT] :
% 5.01/5.32 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.32 => ( ( F @ X3 )
% 5.01/5.32 = ( G @ X3 ) ) ) ) ) ).
% 5.01/5.32
% 5.01/5.32 % map_eq_conv
% 5.01/5.32 thf(fact_9122_map__eq__conv,axiom,
% 5.01/5.32 ! [F: nat > nat,Xs: list_nat,G: nat > nat] :
% 5.01/5.33 ( ( ( map_nat_nat @ F @ Xs )
% 5.01/5.33 = ( map_nat_nat @ G @ Xs ) )
% 5.01/5.33 = ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X3 )
% 5.01/5.33 = ( G @ X3 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_conv
% 5.01/5.33 thf(fact_9123_length__map,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT] :
% 5.01/5.33 ( ( size_size_list_real @ ( map_VEBT_VEBT_real @ F @ Xs ) )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9124_length__map,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.01/5.33 ( ( size_s6755466524823107622T_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs ) )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9125_length__map,axiom,
% 5.01/5.33 ! [F: $o > vEBT_VEBT,Xs: list_o] :
% 5.01/5.33 ( ( size_s6755466524823107622T_VEBT @ ( map_o_VEBT_VEBT @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_o @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9126_length__map,axiom,
% 5.01/5.33 ! [F: nat > vEBT_VEBT,Xs: list_nat] :
% 5.01/5.33 ( ( size_s6755466524823107622T_VEBT @ ( map_nat_VEBT_VEBT @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_nat @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9127_length__map,axiom,
% 5.01/5.33 ! [F: int > vEBT_VEBT,Xs: list_int] :
% 5.01/5.33 ( ( size_s6755466524823107622T_VEBT @ ( map_int_VEBT_VEBT @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_int @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9128_length__map,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.01/5.33 ( ( size_size_list_o @ ( map_VEBT_VEBT_o @ F @ Xs ) )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9129_length__map,axiom,
% 5.01/5.33 ! [F: $o > $o,Xs: list_o] :
% 5.01/5.33 ( ( size_size_list_o @ ( map_o_o @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_o @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9130_length__map,axiom,
% 5.01/5.33 ! [F: nat > $o,Xs: list_nat] :
% 5.01/5.33 ( ( size_size_list_o @ ( map_nat_o @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_nat @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9131_length__map,axiom,
% 5.01/5.33 ! [F: int > $o,Xs: list_int] :
% 5.01/5.33 ( ( size_size_list_o @ ( map_int_o @ F @ Xs ) )
% 5.01/5.33 = ( size_size_list_int @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9132_length__map,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT] :
% 5.01/5.33 ( ( size_size_list_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_map
% 5.01/5.33 thf(fact_9133_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.01/5.33 => ( ( nth_VEBT_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9134_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > int] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.01/5.33 => ( ( nth_int @ ( map_VEBT_VEBT_int @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9135_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > real] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.01/5.33 => ( ( nth_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9136_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.01/5.33 => ( ( nth_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9137_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_o,F: $o > vEBT_VEBT] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.01/5.33 => ( ( nth_VEBT_VEBT @ ( map_o_VEBT_VEBT @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9138_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_o,F: $o > nat] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.01/5.33 => ( ( nth_nat @ ( map_o_nat @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9139_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_o,F: $o > int] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.01/5.33 => ( ( nth_int @ ( map_o_int @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9140_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_nat,F: nat > vEBT_VEBT] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.01/5.33 => ( ( nth_VEBT_VEBT @ ( map_nat_VEBT_VEBT @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9141_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_nat,F: nat > int] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.01/5.33 => ( ( nth_int @ ( map_nat_int @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9142_nth__map,axiom,
% 5.01/5.33 ! [N: nat,Xs: list_nat,F: nat > nat] :
% 5.01/5.33 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.01/5.33 => ( ( nth_nat @ ( map_nat_nat @ F @ Xs ) @ N )
% 5.01/5.33 = ( F @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_map
% 5.01/5.33 thf(fact_9143_powser__zero,axiom,
% 5.01/5.33 ! [F: nat > real] :
% 5.01/5.33 ( ( suminf_real
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) ) )
% 5.01/5.33 = ( F @ zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % powser_zero
% 5.01/5.33 thf(fact_9144_powser__zero,axiom,
% 5.01/5.33 ! [F: nat > complex] :
% 5.01/5.33 ( ( suminf_complex
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_complex @ ( F @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) ) )
% 5.01/5.33 = ( F @ zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % powser_zero
% 5.01/5.33 thf(fact_9145_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: vEBT_VEBT > real,Ys: list_VEBT_VEBT] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9146_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: vEBT_VEBT > nat,Ys: list_VEBT_VEBT] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9147_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: $o > real,Ys: list_o] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_o_real @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_o @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9148_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: $o > nat,Ys: list_o] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_o_nat @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_o @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9149_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: nat > real,Ys: list_nat] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_nat_real @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9150_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: nat > nat,Ys: list_nat] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_nat_nat @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_nat @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9151_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_VEBT_VEBT,G: int > real,Ys: list_int] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_int_real @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_int @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9152_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,G: int > nat,Ys: list_int] :
% 5.01/5.33 ( ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_int_nat @ G @ Ys ) )
% 5.01/5.33 => ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.01/5.33 = ( size_size_list_int @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9153_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: $o > real,Xs: list_o,G: vEBT_VEBT > real,Ys: list_VEBT_VEBT] :
% 5.01/5.33 ( ( ( map_o_real @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ Ys ) )
% 5.01/5.33 => ( ( size_size_list_o @ Xs )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9154_map__eq__imp__length__eq,axiom,
% 5.01/5.33 ! [F: $o > nat,Xs: list_o,G: vEBT_VEBT > nat,Ys: list_VEBT_VEBT] :
% 5.01/5.33 ( ( ( map_o_nat @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ Ys ) )
% 5.01/5.33 => ( ( size_size_list_o @ Xs )
% 5.01/5.33 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_eq_imp_length_eq
% 5.01/5.33 thf(fact_9155_ex__map__conv,axiom,
% 5.01/5.33 ! [Ys: list_real,F: vEBT_VEBT > real] :
% 5.01/5.33 ( ( ? [Xs3: list_VEBT_VEBT] :
% 5.01/5.33 ( Ys
% 5.01/5.33 = ( map_VEBT_VEBT_real @ F @ Xs3 ) ) )
% 5.01/5.33 = ( ! [X3: real] :
% 5.01/5.33 ( ( member_real @ X3 @ ( set_real2 @ Ys ) )
% 5.01/5.33 => ? [Y2: vEBT_VEBT] :
% 5.01/5.33 ( X3
% 5.01/5.33 = ( F @ Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ex_map_conv
% 5.01/5.33 thf(fact_9156_ex__map__conv,axiom,
% 5.01/5.33 ! [Ys: list_nat,F: vEBT_VEBT > nat] :
% 5.01/5.33 ( ( ? [Xs3: list_VEBT_VEBT] :
% 5.01/5.33 ( Ys
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ F @ Xs3 ) ) )
% 5.01/5.33 = ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 5.01/5.33 => ? [Y2: vEBT_VEBT] :
% 5.01/5.33 ( X3
% 5.01/5.33 = ( F @ Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ex_map_conv
% 5.01/5.33 thf(fact_9157_ex__map__conv,axiom,
% 5.01/5.33 ! [Ys: list_nat,F: nat > nat] :
% 5.01/5.33 ( ( ? [Xs3: list_nat] :
% 5.01/5.33 ( Ys
% 5.01/5.33 = ( map_nat_nat @ F @ Xs3 ) ) )
% 5.01/5.33 = ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 5.01/5.33 => ? [Y2: nat] :
% 5.01/5.33 ( X3
% 5.01/5.33 = ( F @ Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ex_map_conv
% 5.01/5.33 thf(fact_9158_map__cong,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.01/5.33 ( ( Xs = Ys )
% 5.01/5.33 => ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ Ys ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_cong
% 5.01/5.33 thf(fact_9159_map__cong,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.01/5.33 ( ( Xs = Ys )
% 5.01/5.33 => ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Ys ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ Ys ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_cong
% 5.01/5.33 thf(fact_9160_map__cong,axiom,
% 5.01/5.33 ! [Xs: list_nat,Ys: list_nat,F: nat > nat,G: nat > nat] :
% 5.01/5.33 ( ( Xs = Ys )
% 5.01/5.33 => ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ ( set_nat2 @ Ys ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_nat_nat @ F @ Xs )
% 5.01/5.33 = ( map_nat_nat @ G @ Ys ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_cong
% 5.01/5.33 thf(fact_9161_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_real,F: real > real] :
% 5.01/5.33 ( ! [X4: real] :
% 5.01/5.33 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_real_real @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9162_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_complex,F: complex > complex] :
% 5.01/5.33 ( ! [X4: complex] :
% 5.01/5.33 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_complex_complex @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9163_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_set_nat,F: set_nat > set_nat] :
% 5.01/5.33 ( ! [X4: set_nat] :
% 5.01/5.33 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_set_nat_set_nat @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9164_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 5.01/5.33 ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_VE8901447254227204932T_VEBT @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9165_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_nat,F: nat > nat] :
% 5.01/5.33 ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_nat_nat @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9166_map__idI,axiom,
% 5.01/5.33 ! [Xs: list_int,F: int > int] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = X4 ) )
% 5.01/5.33 => ( ( map_int_int @ F @ Xs )
% 5.01/5.33 = Xs ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_idI
% 5.01/5.33 thf(fact_9167_map__ext,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.01/5.33 ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_real @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_ext
% 5.01/5.33 thf(fact_9168_map__ext,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.01/5.33 ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_nat @ F @ Xs )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_ext
% 5.01/5.33 thf(fact_9169_map__ext,axiom,
% 5.01/5.33 ! [Xs: list_nat,F: nat > nat,G: nat > nat] :
% 5.01/5.33 ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.01/5.33 => ( ( F @ X4 )
% 5.01/5.33 = ( G @ X4 ) ) )
% 5.01/5.33 => ( ( map_nat_nat @ F @ Xs )
% 5.01/5.33 = ( map_nat_nat @ G @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_ext
% 5.01/5.33 thf(fact_9170_list_Oinj__map__strong,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,Xa: list_VEBT_VEBT,F: vEBT_VEBT > real,Fa: vEBT_VEBT > real] :
% 5.01/5.33 ( ! [Z3: vEBT_VEBT,Za: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.01/5.33 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa ) )
% 5.01/5.33 => ( ( ( F @ Z3 )
% 5.01/5.33 = ( Fa @ Za ) )
% 5.01/5.33 => ( Z3 = Za ) ) ) )
% 5.01/5.33 => ( ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ Fa @ Xa ) )
% 5.01/5.33 => ( X2 = Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.inj_map_strong
% 5.01/5.33 thf(fact_9171_list_Oinj__map__strong,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,Xa: list_VEBT_VEBT,F: vEBT_VEBT > nat,Fa: vEBT_VEBT > nat] :
% 5.01/5.33 ( ! [Z3: vEBT_VEBT,Za: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.01/5.33 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa ) )
% 5.01/5.33 => ( ( ( F @ Z3 )
% 5.01/5.33 = ( Fa @ Za ) )
% 5.01/5.33 => ( Z3 = Za ) ) ) )
% 5.01/5.33 => ( ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ Fa @ Xa ) )
% 5.01/5.33 => ( X2 = Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.inj_map_strong
% 5.01/5.33 thf(fact_9172_list_Oinj__map__strong,axiom,
% 5.01/5.33 ! [X2: list_nat,Xa: list_nat,F: nat > nat,Fa: nat > nat] :
% 5.01/5.33 ( ! [Z3: nat,Za: nat] :
% 5.01/5.33 ( ( member_nat @ Z3 @ ( set_nat2 @ X2 ) )
% 5.01/5.33 => ( ( member_nat @ Za @ ( set_nat2 @ Xa ) )
% 5.01/5.33 => ( ( ( F @ Z3 )
% 5.01/5.33 = ( Fa @ Za ) )
% 5.01/5.33 => ( Z3 = Za ) ) ) )
% 5.01/5.33 => ( ( ( map_nat_nat @ F @ X2 )
% 5.01/5.33 = ( map_nat_nat @ Fa @ Xa ) )
% 5.01/5.33 => ( X2 = Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.inj_map_strong
% 5.01/5.33 thf(fact_9173_list_Omap__cong0,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.01/5.33 ( ! [Z3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong0
% 5.01/5.33 thf(fact_9174_list_Omap__cong0,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.01/5.33 ( ! [Z3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X2 ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong0
% 5.01/5.33 thf(fact_9175_list_Omap__cong0,axiom,
% 5.01/5.33 ! [X2: list_nat,F: nat > nat,G: nat > nat] :
% 5.01/5.33 ( ! [Z3: nat] :
% 5.01/5.33 ( ( member_nat @ Z3 @ ( set_nat2 @ X2 ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_nat_nat @ F @ X2 )
% 5.01/5.33 = ( map_nat_nat @ G @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong0
% 5.01/5.33 thf(fact_9176_list_Omap__cong,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 5.01/5.33 ( ( X2 = Ya )
% 5.01/5.33 => ( ! [Z3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ Ya ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_real @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_real @ G @ Ya ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong
% 5.01/5.33 thf(fact_9177_list_Omap__cong,axiom,
% 5.01/5.33 ! [X2: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 5.01/5.33 ( ( X2 = Ya )
% 5.01/5.33 => ( ! [Z3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ Ya ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_VEBT_VEBT_nat @ F @ X2 )
% 5.01/5.33 = ( map_VEBT_VEBT_nat @ G @ Ya ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong
% 5.01/5.33 thf(fact_9178_list_Omap__cong,axiom,
% 5.01/5.33 ! [X2: list_nat,Ya: list_nat,F: nat > nat,G: nat > nat] :
% 5.01/5.33 ( ( X2 = Ya )
% 5.01/5.33 => ( ! [Z3: nat] :
% 5.01/5.33 ( ( member_nat @ Z3 @ ( set_nat2 @ Ya ) )
% 5.01/5.33 => ( ( F @ Z3 )
% 5.01/5.33 = ( G @ Z3 ) ) )
% 5.01/5.33 => ( ( map_nat_nat @ F @ X2 )
% 5.01/5.33 = ( map_nat_nat @ G @ Ya ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_cong
% 5.01/5.33 thf(fact_9179_map__concat,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,Xs: list_list_VEBT_VEBT] :
% 5.01/5.33 ( ( map_VEBT_VEBT_real @ F @ ( concat_VEBT_VEBT @ Xs ) )
% 5.01/5.33 = ( concat_real @ ( map_li2470829856544091186t_real @ ( map_VEBT_VEBT_real @ F ) @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_concat
% 5.01/5.33 thf(fact_9180_map__concat,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_list_VEBT_VEBT] :
% 5.01/5.33 ( ( map_VEBT_VEBT_nat @ F @ ( concat_VEBT_VEBT @ Xs ) )
% 5.01/5.33 = ( concat_nat @ ( map_li576258494306137302st_nat @ ( map_VEBT_VEBT_nat @ F ) @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_concat
% 5.01/5.33 thf(fact_9181_map__concat,axiom,
% 5.01/5.33 ! [F: nat > nat,Xs: list_list_nat] :
% 5.01/5.33 ( ( map_nat_nat @ F @ ( concat_nat @ Xs ) )
% 5.01/5.33 = ( concat_nat @ ( map_li7225945977422193158st_nat @ ( map_nat_nat @ F ) @ Xs ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_concat
% 5.01/5.33 thf(fact_9182_list_Omap__ident,axiom,
% 5.01/5.33 ! [T: list_nat] :
% 5.01/5.33 ( ( map_nat_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ T )
% 5.01/5.33 = T ) ).
% 5.01/5.33
% 5.01/5.33 % list.map_ident
% 5.01/5.33 thf(fact_9183_pi__series,axiom,
% 5.01/5.33 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.33 = ( suminf_real
% 5.01/5.33 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % pi_series
% 5.01/5.33 thf(fact_9184_arctan__series,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.33 => ( ( arctan @ X2 )
% 5.01/5.33 = ( suminf_real
% 5.01/5.33 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % arctan_series
% 5.01/5.33 thf(fact_9185__092_060open_062foldr_A_I_L_J_A_Imap_Acnt_AtreeList_J_A0_A_092_060le_062_A2_A_094_An_A_K_A2_A_K_A_I2_A_094_An_A_N_Ac_J_092_060close_062,axiom,
% 5.01/5.33 ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ treeList ) @ zero_zero_real ) @ ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ na ) @ c ) ) ).
% 5.01/5.33
% 5.01/5.33 % \<open>foldr (+) (map cnt treeList) 0 \<le> 2 ^ n * 2 * (2 ^ n - c)\<close>
% 5.01/5.33 thf(fact_9186_suminf__geometric,axiom,
% 5.01/5.33 ! [C: real] :
% 5.01/5.33 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.01/5.33 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.01/5.33 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_geometric
% 5.01/5.33 thf(fact_9187_suminf__geometric,axiom,
% 5.01/5.33 ! [C: complex] :
% 5.01/5.33 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.01/5.33 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.01/5.33 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_geometric
% 5.01/5.33 thf(fact_9188_suminf__zero,axiom,
% 5.01/5.33 ( ( suminf_complex
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_complex )
% 5.01/5.33 = zero_zero_complex ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_zero
% 5.01/5.33 thf(fact_9189_suminf__zero,axiom,
% 5.01/5.33 ( ( suminf_real
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_real )
% 5.01/5.33 = zero_zero_real ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_zero
% 5.01/5.33 thf(fact_9190_suminf__zero,axiom,
% 5.01/5.33 ( ( suminf_nat
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_nat )
% 5.01/5.33 = zero_zero_nat ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_zero
% 5.01/5.33 thf(fact_9191_suminf__zero,axiom,
% 5.01/5.33 ( ( suminf_int
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_int )
% 5.01/5.33 = zero_zero_int ) ).
% 5.01/5.33
% 5.01/5.33 % suminf_zero
% 5.01/5.33 thf(fact_9192_VEBT__internal_Ospace_Oelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: nat] :
% 5.01/5.33 ( ( ( vEBT_VEBT_space @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ? [A3: $o,B2: $o] :
% 5.01/5.33 ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary3 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList3 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space.elims
% 5.01/5.33 thf(fact_9193_f__g__map__foldr__bound,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,C: real,G: vEBT_VEBT > real,D: real] :
% 5.01/5.33 ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C @ ( G @ X4 ) ) ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ D ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ G @ Xs ) @ zero_zero_real ) ) @ D ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % f_g_map_foldr_bound
% 5.01/5.33 thf(fact_9194_f__g__map__foldr__bound,axiom,
% 5.01/5.33 ! [Xs: list_nat,F: nat > real,C: real,G: nat > real,D: real] :
% 5.01/5.33 ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C @ ( G @ X4 ) ) ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ D ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ G @ Xs ) @ zero_zero_real ) ) @ D ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % f_g_map_foldr_bound
% 5.01/5.33 thf(fact_9195_f__g__map__foldr__bound,axiom,
% 5.01/5.33 ! [Xs: list_int,F: int > real,C: real,G: int > real,D: real] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ ( times_times_real @ C @ ( G @ X4 ) ) ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs ) @ D ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ G @ Xs ) @ zero_zero_real ) ) @ D ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % f_g_map_foldr_bound
% 5.01/5.33 thf(fact_9196_real__nat__list,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,Xs: list_VEBT_VEBT,C: nat] :
% 5.01/5.33 ( ( semiri5074537144036343181t_real @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs ) @ C ) )
% 5.01/5.33 = ( foldr_real_real @ plus_plus_real
% 5.01/5.33 @ ( map_VEBT_VEBT_real
% 5.01/5.33 @ ^ [X3: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( F @ X3 ) )
% 5.01/5.33 @ Xs )
% 5.01/5.33 @ ( semiri5074537144036343181t_real @ C ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_nat_list
% 5.01/5.33 thf(fact_9197_real__nat__list,axiom,
% 5.01/5.33 ! [F: nat > nat,Xs: list_nat,C: nat] :
% 5.01/5.33 ( ( semiri5074537144036343181t_real @ ( foldr_nat_nat @ plus_plus_nat @ ( map_nat_nat @ F @ Xs ) @ C ) )
% 5.01/5.33 = ( foldr_real_real @ plus_plus_real
% 5.01/5.33 @ ( map_nat_real
% 5.01/5.33 @ ^ [X3: nat] : ( semiri5074537144036343181t_real @ ( F @ X3 ) )
% 5.01/5.33 @ Xs )
% 5.01/5.33 @ ( semiri5074537144036343181t_real @ C ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_nat_list
% 5.01/5.33 thf(fact_9198_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.01/5.33 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,Bound: real,I: real] :
% 5.01/5.33 ( ! [X4: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list_every_elemnt_bound_sum_bound_real
% 5.01/5.33 thf(fact_9199_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.01/5.33 ! [Xs: list_o,F: $o > real,Bound: real,I: real] :
% 5.01/5.33 ( ! [X4: $o] :
% 5.01/5.33 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_o_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_o @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list_every_elemnt_bound_sum_bound_real
% 5.01/5.33 thf(fact_9200_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.01/5.33 ! [Xs: list_nat,F: nat > real,Bound: real,I: real] :
% 5.01/5.33 ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_nat @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list_every_elemnt_bound_sum_bound_real
% 5.01/5.33 thf(fact_9201_list__every__elemnt__bound__sum__bound__real,axiom,
% 5.01/5.33 ! [Xs: list_int,F: int > real,Bound: real,I: real] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( F @ X4 ) @ Bound ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_int @ Xs ) ) @ Bound ) @ I ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % list_every_elemnt_bound_sum_bound_real
% 5.01/5.33 thf(fact_9202_space__space_H,axiom,
% 5.01/5.33 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 5.01/5.33
% 5.01/5.33 % space_space'
% 5.01/5.33 thf(fact_9203_product__concat__map,axiom,
% 5.01/5.33 ( product_int_int
% 5.01/5.33 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 5.01/5.33 ( concat4512918505337516154nt_int
% 5.01/5.33 @ ( map_in7266296235447420877nt_int
% 5.01/5.33 @ ^ [X3: int] : ( map_in7157766398909135175nt_int @ ( product_Pair_int_int @ X3 ) @ Ys3 )
% 5.01/5.33 @ Xs3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % product_concat_map
% 5.01/5.33 thf(fact_9204_product__concat__map,axiom,
% 5.01/5.33 ( produc4846348955484107138nteger
% 5.01/5.33 = ( ^ [Xs3: list_C878401137130745250e_term,Ys3: list_P5578671422887162913nteger] :
% 5.01/5.33 ( concat5449216342283422845nteger
% 5.01/5.33 @ ( map_Co3516991824712006758nteger
% 5.01/5.33 @ ^ [X3: code_integer > option6357759511663192854e_term] : ( map_Pr6982716525268357333nteger @ ( produc6137756002093451184nteger @ X3 ) @ Ys3 )
% 5.01/5.33 @ Xs3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % product_concat_map
% 5.01/5.33 thf(fact_9205_product__concat__map,axiom,
% 5.01/5.33 ( produc2929234284598166170nteger
% 5.01/5.33 = ( ^ [Xs3: list_P1316552470764441098e_term,Ys3: list_P5578671422887162913nteger] :
% 5.01/5.33 ( concat1359917873574114197nteger
% 5.01/5.33 @ ( map_Pr1383036205076807398nteger
% 5.01/5.33 @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term] : ( map_Pr4561634935768196077nteger @ ( produc8603105652947943368nteger @ X3 ) @ Ys3 )
% 5.01/5.33 @ Xs3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % product_concat_map
% 5.01/5.33 thf(fact_9206_product__concat__map,axiom,
% 5.01/5.33 ( produc8640348060098379399nt_int
% 5.01/5.33 = ( ^ [Xs3: list_P1743416141875011707e_term,Ys3: list_P5707943133018811711nt_int] :
% 5.01/5.33 ( concat27718206033014914nt_int
% 5.01/5.33 @ ( map_Pr6227401909088194244nt_int
% 5.01/5.33 @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term] : ( map_Pr1898935522916328184nt_int @ ( produc5700946648718959541nt_int @ X3 ) @ Ys3 )
% 5.01/5.33 @ Xs3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % product_concat_map
% 5.01/5.33 thf(fact_9207_product__concat__map,axiom,
% 5.01/5.33 ( produc5707002291657922193nt_int
% 5.01/5.33 = ( ^ [Xs3: list_i8448526496819171953e_term,Ys3: list_P5707943133018811711nt_int] :
% 5.01/5.33 ( concat3620511419746071180nt_int
% 5.01/5.33 @ ( map_in2673801078721063236nt_int
% 5.01/5.33 @ ^ [X3: int > option6357759511663192854e_term] : ( map_Pr1306541819098601986nt_int @ ( produc4305682042979456191nt_int @ X3 ) @ Ys3 )
% 5.01/5.33 @ Xs3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % product_concat_map
% 5.01/5.33 thf(fact_9208_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 5.01/5.33 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.01/5.33 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.01/5.33 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList ) @ zero_zero_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.cnt.simps(2)
% 5.01/5.33 thf(fact_9209_VEBT__internal_Ocnt_Oelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: real] :
% 5.01/5.33 ( ( ( vEBT_VEBT_cnt @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ? [A3: $o,B2: $o] :
% 5.01/5.33 ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( Y != one_one_real ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary3 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList3 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.cnt.elims
% 5.01/5.33 thf(fact_9210_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 5.01/5.33 ! [A: $o,B: $o] :
% 5.01/5.33 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A @ B ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space.simps(1)
% 5.01/5.33 thf(fact_9211_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 5.01/5.33 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.01/5.33 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList ) @ zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space.simps(2)
% 5.01/5.33 thf(fact_9212_VEBT__internal_Ospace_H_Oelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: nat] :
% 5.01/5.33 ( ( ( vEBT_VEBT_space2 @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ? [A3: $o,B2: $o] :
% 5.01/5.33 ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary3 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList3 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space'.elims
% 5.01/5.33 thf(fact_9213_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 5.01/5.33 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.01/5.33 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space'.simps(2)
% 5.01/5.33 thf(fact_9214_summable__arctan__series,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.33 => ( summable_real
% 5.01/5.33 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_arctan_series
% 5.01/5.33 thf(fact_9215_vebt__buildup_Oelims,axiom,
% 5.01/5.33 ! [X2: nat,Y: vEBT_VEBT] :
% 5.01/5.33 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ( X2 = zero_zero_nat )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.01/5.33 => ( ( ( X2
% 5.01/5.33 = ( suc @ zero_zero_nat ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.01/5.33 => ~ ! [Va: nat] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % vebt_buildup.elims
% 5.01/5.33 thf(fact_9216_intind,axiom,
% 5.01/5.33 ! [I: nat,N: nat,P: nat > $o,X2: nat] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( P @ X2 )
% 5.01/5.33 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % intind
% 5.01/5.33 thf(fact_9217_intind,axiom,
% 5.01/5.33 ! [I: nat,N: nat,P: int > $o,X2: int] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( P @ X2 )
% 5.01/5.33 => ( P @ ( nth_int @ ( replicate_int @ N @ X2 ) @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % intind
% 5.01/5.33 thf(fact_9218_intind,axiom,
% 5.01/5.33 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( P @ X2 )
% 5.01/5.33 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % intind
% 5.01/5.33 thf(fact_9219_replicate__eq__replicate,axiom,
% 5.01/5.33 ! [M: nat,X2: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.01/5.33 ( ( ( replicate_VEBT_VEBT @ M @ X2 )
% 5.01/5.33 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.01/5.33 = ( ( M = N )
% 5.01/5.33 & ( ( M != zero_zero_nat )
% 5.01/5.33 => ( X2 = Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % replicate_eq_replicate
% 5.01/5.33 thf(fact_9220_length__replicate,axiom,
% 5.01/5.33 ! [N: nat,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % length_replicate
% 5.01/5.33 thf(fact_9221_length__replicate,axiom,
% 5.01/5.33 ! [N: nat,X2: $o] :
% 5.01/5.33 ( ( size_size_list_o @ ( replicate_o @ N @ X2 ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % length_replicate
% 5.01/5.33 thf(fact_9222_length__replicate,axiom,
% 5.01/5.33 ! [N: nat,X2: nat] :
% 5.01/5.33 ( ( size_size_list_nat @ ( replicate_nat @ N @ X2 ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % length_replicate
% 5.01/5.33 thf(fact_9223_length__replicate,axiom,
% 5.01/5.33 ! [N: nat,X2: int] :
% 5.01/5.33 ( ( size_size_list_int @ ( replicate_int @ N @ X2 ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % length_replicate
% 5.01/5.33 thf(fact_9224_map__replicate,axiom,
% 5.01/5.33 ! [F: nat > nat,N: nat,X2: nat] :
% 5.01/5.33 ( ( map_nat_nat @ F @ ( replicate_nat @ N @ X2 ) )
% 5.01/5.33 = ( replicate_nat @ N @ ( F @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_replicate
% 5.01/5.33 thf(fact_9225_map__replicate,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > real,N: nat,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( map_VEBT_VEBT_real @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.01/5.33 = ( replicate_real @ N @ ( F @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_replicate
% 5.01/5.33 thf(fact_9226_map__replicate,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > nat,N: nat,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( map_VEBT_VEBT_nat @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.01/5.33 = ( replicate_nat @ N @ ( F @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_replicate
% 5.01/5.33 thf(fact_9227_map__replicate,axiom,
% 5.01/5.33 ! [F: vEBT_VEBT > vEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( map_VE8901447254227204932T_VEBT @ F @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.01/5.33 = ( replicate_VEBT_VEBT @ N @ ( F @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_replicate
% 5.01/5.33 thf(fact_9228_summable__zero,axiom,
% 5.01/5.33 ( summable_complex
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_complex ) ).
% 5.01/5.33
% 5.01/5.33 % summable_zero
% 5.01/5.33 thf(fact_9229_summable__zero,axiom,
% 5.01/5.33 ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_real ) ).
% 5.01/5.33
% 5.01/5.33 % summable_zero
% 5.01/5.33 thf(fact_9230_summable__zero,axiom,
% 5.01/5.33 ( summable_nat
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_nat ) ).
% 5.01/5.33
% 5.01/5.33 % summable_zero
% 5.01/5.33 thf(fact_9231_summable__zero,axiom,
% 5.01/5.33 ( summable_int
% 5.01/5.33 @ ^ [N4: nat] : zero_zero_int ) ).
% 5.01/5.33
% 5.01/5.33 % summable_zero
% 5.01/5.33 thf(fact_9232_summable__single,axiom,
% 5.01/5.33 ! [I: nat,F: nat > complex] :
% 5.01/5.33 ( summable_complex
% 5.01/5.33 @ ^ [R5: nat] : ( if_complex @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_single
% 5.01/5.33 thf(fact_9233_summable__single,axiom,
% 5.01/5.33 ! [I: nat,F: nat > real] :
% 5.01/5.33 ( summable_real
% 5.01/5.33 @ ^ [R5: nat] : ( if_real @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_single
% 5.01/5.33 thf(fact_9234_summable__single,axiom,
% 5.01/5.33 ! [I: nat,F: nat > nat] :
% 5.01/5.33 ( summable_nat
% 5.01/5.33 @ ^ [R5: nat] : ( if_nat @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_single
% 5.01/5.33 thf(fact_9235_summable__single,axiom,
% 5.01/5.33 ! [I: nat,F: nat > int] :
% 5.01/5.33 ( summable_int
% 5.01/5.33 @ ^ [R5: nat] : ( if_int @ ( R5 = I ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_single
% 5.01/5.33 thf(fact_9236_summable__iff__shift,axiom,
% 5.01/5.33 ! [F: nat > real,K: nat] :
% 5.01/5.33 ( ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : ( F @ ( plus_plus_nat @ N4 @ K ) ) )
% 5.01/5.33 = ( summable_real @ F ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_iff_shift
% 5.01/5.33 thf(fact_9237_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: real,N: nat,Y: real] :
% 5.01/5.33 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9238_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: complex,N: nat,Y: complex] :
% 5.01/5.33 ( ( member_complex @ X2 @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9239_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: set_nat,N: nat,Y: set_nat] :
% 5.01/5.33 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9240_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: nat,N: nat,Y: nat] :
% 5.01/5.33 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9241_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: int,N: nat,Y: int] :
% 5.01/5.33 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9242_in__set__replicate,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 5.01/5.33 = ( ( X2 = Y )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % in_set_replicate
% 5.01/5.33 thf(fact_9243_Bex__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: nat,P: nat > $o] :
% 5.01/5.33 ( ( ? [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.01/5.33 & ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Bex_set_replicate
% 5.01/5.33 thf(fact_9244_Bex__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: int,P: int > $o] :
% 5.01/5.33 ( ( ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.01/5.33 & ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Bex_set_replicate
% 5.01/5.33 thf(fact_9245_Bex__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.01/5.33 ( ( ? [X3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.01/5.33 & ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 & ( N != zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Bex_set_replicate
% 5.01/5.33 thf(fact_9246_Ball__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: nat,P: nat > $o] :
% 5.01/5.33 ( ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.01/5.33 => ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Ball_set_replicate
% 5.01/5.33 thf(fact_9247_Ball__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: int,P: int > $o] :
% 5.01/5.33 ( ( ! [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.01/5.33 => ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Ball_set_replicate
% 5.01/5.33 thf(fact_9248_Ball__set__replicate,axiom,
% 5.01/5.33 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.01/5.33 ( ( ! [X3: vEBT_VEBT] :
% 5.01/5.33 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.01/5.33 => ( P @ X3 ) ) )
% 5.01/5.33 = ( ( P @ A )
% 5.01/5.33 | ( N = zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Ball_set_replicate
% 5.01/5.33 thf(fact_9249_nth__replicate,axiom,
% 5.01/5.33 ! [I: nat,N: nat,X2: nat] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_replicate
% 5.01/5.33 thf(fact_9250_nth__replicate,axiom,
% 5.01/5.33 ! [I: nat,N: nat,X2: int] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( nth_int @ ( replicate_int @ N @ X2 ) @ I )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_replicate
% 5.01/5.33 thf(fact_9251_nth__replicate,axiom,
% 5.01/5.33 ! [I: nat,N: nat,X2: vEBT_VEBT] :
% 5.01/5.33 ( ( ord_less_nat @ I @ N )
% 5.01/5.33 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_replicate
% 5.01/5.33 thf(fact_9252_summable__cmult__iff,axiom,
% 5.01/5.33 ! [C: real,F: nat > real] :
% 5.01/5.33 ( ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_real @ C @ ( F @ N4 ) ) )
% 5.01/5.33 = ( ( C = zero_zero_real )
% 5.01/5.33 | ( summable_real @ F ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_cmult_iff
% 5.01/5.33 thf(fact_9253_summable__cmult__iff,axiom,
% 5.01/5.33 ! [C: complex,F: nat > complex] :
% 5.01/5.33 ( ( summable_complex
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_complex @ C @ ( F @ N4 ) ) )
% 5.01/5.33 = ( ( C = zero_zero_complex )
% 5.01/5.33 | ( summable_complex @ F ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_cmult_iff
% 5.01/5.33 thf(fact_9254_summable__divide__iff,axiom,
% 5.01/5.33 ! [F: nat > complex,C: complex] :
% 5.01/5.33 ( ( summable_complex
% 5.01/5.33 @ ^ [N4: nat] : ( divide1717551699836669952omplex @ ( F @ N4 ) @ C ) )
% 5.01/5.33 = ( ( C = zero_zero_complex )
% 5.01/5.33 | ( summable_complex @ F ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_divide_iff
% 5.01/5.33 thf(fact_9255_summable__divide__iff,axiom,
% 5.01/5.33 ! [F: nat > real,C: real] :
% 5.01/5.33 ( ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : ( divide_divide_real @ ( F @ N4 ) @ C ) )
% 5.01/5.33 = ( ( C = zero_zero_real )
% 5.01/5.33 | ( summable_real @ F ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_divide_iff
% 5.01/5.33 thf(fact_9256_summable__geometric__iff,axiom,
% 5.01/5.33 ! [C: real] :
% 5.01/5.33 ( ( summable_real @ ( power_power_real @ C ) )
% 5.01/5.33 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_geometric_iff
% 5.01/5.33 thf(fact_9257_summable__geometric__iff,axiom,
% 5.01/5.33 ! [C: complex] :
% 5.01/5.33 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.01/5.33 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_geometric_iff
% 5.01/5.33 thf(fact_9258_summable__minus__iff,axiom,
% 5.01/5.33 ! [F: nat > complex] :
% 5.01/5.33 ( ( summable_complex
% 5.01/5.33 @ ^ [N4: nat] : ( uminus1482373934393186551omplex @ ( F @ N4 ) ) )
% 5.01/5.33 = ( summable_complex @ F ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_minus_iff
% 5.01/5.33 thf(fact_9259_summable__rabs__comparison__test,axiom,
% 5.01/5.33 ! [F: nat > real,G: nat > real] :
% 5.01/5.33 ( ? [N7: nat] :
% 5.01/5.33 ! [N3: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.01/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.01/5.33 => ( ( summable_real @ G )
% 5.01/5.33 => ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_rabs_comparison_test
% 5.01/5.33 thf(fact_9260_summable__rabs,axiom,
% 5.01/5.33 ! [F: nat > real] :
% 5.01/5.33 ( ( summable_real
% 5.01/5.33 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) )
% 5.01/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.01/5.33 @ ( suminf_real
% 5.01/5.33 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_rabs
% 5.01/5.33 thf(fact_9261_summable__power__series,axiom,
% 5.01/5.33 ! [F: nat > real,Z: real] :
% 5.01/5.33 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.01/5.33 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.01/5.33 => ( ( ord_less_real @ Z @ one_one_real )
% 5.01/5.33 => ( summable_real
% 5.01/5.33 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % summable_power_series
% 5.01/5.33 thf(fact_9262_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 5.01/5.33 ! [A: $o,B: $o] :
% 5.01/5.33 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A @ B ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space'.simps(1)
% 5.01/5.33 thf(fact_9263_vebt__buildup_Osimps_I3_J,axiom,
% 5.01/5.33 ! [Va3: nat] :
% 5.01/5.33 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.01/5.33 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 5.01/5.33 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % vebt_buildup.simps(3)
% 5.01/5.33 thf(fact_9264_Im__Reals__divide,axiom,
% 5.01/5.33 ! [R: complex,Z: complex] :
% 5.01/5.33 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.01/5.33 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_Reals_divide
% 5.01/5.33 thf(fact_9265_sin__paired,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( sums_real
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.01/5.33 @ ( sin_real @ X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % sin_paired
% 5.01/5.33 thf(fact_9266_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.33 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [Uu: $o,Uv: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) )
% 5.01/5.33 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa ) ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) @ Xa ) )
% 5.01/5.33 => ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 ) ) ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 5.01/5.33 => ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 )
% 5.01/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.01/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 5.01/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.membermima.pelims(3)
% 5.01/5.33 thf(fact_9267_Re__divide__Reals,axiom,
% 5.01/5.33 ! [R: complex,Z: complex] :
% 5.01/5.33 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.01/5.33 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_divide_Reals
% 5.01/5.33 thf(fact_9268_imaginary__eq__real__iff,axiom,
% 5.01/5.33 ! [Y: complex,X2: complex] :
% 5.01/5.33 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.01/5.33 = X2 )
% 5.01/5.33 = ( ( X2 = zero_zero_complex )
% 5.01/5.33 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % imaginary_eq_real_iff
% 5.01/5.33 thf(fact_9269_real__eq__imaginary__iff,axiom,
% 5.01/5.33 ! [Y: complex,X2: complex] :
% 5.01/5.33 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( X2
% 5.01/5.33 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.01/5.33 = ( ( X2 = zero_zero_complex )
% 5.01/5.33 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_eq_imaginary_iff
% 5.01/5.33 thf(fact_9270_Im__divide__Reals,axiom,
% 5.01/5.33 ! [R: complex,Z: complex] :
% 5.01/5.33 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R ) )
% 5.01/5.33 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_divide_Reals
% 5.01/5.33 thf(fact_9271_complex__is__Real__iff,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 5.01/5.33 = ( ( im @ Z )
% 5.01/5.33 = zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_is_Real_iff
% 5.01/5.33 thf(fact_9272_Complex__in__Reals,axiom,
% 5.01/5.33 ! [X2: real] : ( member_complex @ ( complex2 @ X2 @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 5.01/5.33
% 5.01/5.33 % Complex_in_Reals
% 5.01/5.33 thf(fact_9273_power__half__series,axiom,
% 5.01/5.33 ( sums_real
% 5.01/5.33 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 5.01/5.33 @ one_one_real ) ).
% 5.01/5.33
% 5.01/5.33 % power_half_series
% 5.01/5.33 thf(fact_9274_sums__if_H,axiom,
% 5.01/5.33 ! [G: nat > real,X2: real] :
% 5.01/5.33 ( ( sums_real @ G @ X2 )
% 5.01/5.33 => ( sums_real
% 5.01/5.33 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.33 @ X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % sums_if'
% 5.01/5.33 thf(fact_9275_sums__if,axiom,
% 5.01/5.33 ! [G: nat > real,X2: real,F: nat > real,Y: real] :
% 5.01/5.33 ( ( sums_real @ G @ X2 )
% 5.01/5.33 => ( ( sums_real @ F @ Y )
% 5.01/5.33 => ( sums_real
% 5.01/5.33 @ ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( F @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.01/5.33 @ ( plus_plus_real @ X2 @ Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sums_if
% 5.01/5.33 thf(fact_9276_Re__Reals__divide,axiom,
% 5.01/5.33 ! [R: complex,Z: complex] :
% 5.01/5.33 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.01/5.33 => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.01/5.33 = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_Reals_divide
% 5.01/5.33 thf(fact_9277_cos__paired,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( sums_real
% 5.01/5.33 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.33 @ ( cos_real @ X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % cos_paired
% 5.01/5.33 thf(fact_9278_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.33 ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) @ Xa ) )
% 5.01/5.33 => ~ ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 ) ) ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 5.01/5.33 => ~ ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 )
% 5.01/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.01/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 5.01/5.33 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.membermima.pelims(2)
% 5.01/5.33 thf(fact_9279_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.01/5.33 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [Uu: $o,Uv: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.01/5.33 => ( ~ Y
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa ) ) ) )
% 5.01/5.33 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 5.01/5.33 => ( ~ Y
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa ) ) ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 ) ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va2 @ Vb ) @ Xa ) ) ) )
% 5.01/5.33 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( ( Xa = Mi3 )
% 5.01/5.33 | ( Xa = Ma3 )
% 5.01/5.33 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) ) ) )
% 5.01/5.33 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.membermima.pelims(1)
% 5.01/5.33 thf(fact_9280_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.33 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa ) )
% 5.01/5.33 => ( ( ( Xa = zero_zero_nat )
% 5.01/5.33 => A3 )
% 5.01/5.33 & ( ( Xa != zero_zero_nat )
% 5.01/5.33 => ( ( ( Xa = one_one_nat )
% 5.01/5.33 => B2 )
% 5.01/5.33 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.01/5.33 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) )
% 5.01/5.33 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.01/5.33 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.naive_member.pelims(3)
% 5.01/5.33 thf(fact_9281_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat] :
% 5.01/5.33 ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa ) )
% 5.01/5.33 => ~ ( ( ( Xa = zero_zero_nat )
% 5.01/5.33 => A3 )
% 5.01/5.33 & ( ( Xa != zero_zero_nat )
% 5.01/5.33 => ( ( ( Xa = one_one_nat )
% 5.01/5.33 => B2 )
% 5.01/5.33 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.01/5.33 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.01/5.33 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.naive_member.pelims(2)
% 5.01/5.33 thf(fact_9282_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.01/5.33 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa ) )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( ( ( Xa = zero_zero_nat )
% 5.01/5.33 => A3 )
% 5.01/5.33 & ( ( Xa != zero_zero_nat )
% 5.01/5.33 => ( ( ( Xa = one_one_nat )
% 5.01/5.33 => B2 )
% 5.01/5.33 & ( Xa = one_one_nat ) ) ) ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B2 ) @ Xa ) ) ) )
% 5.01/5.33 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.01/5.33 => ( ~ Y
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa ) ) ) )
% 5.01/5.33 => ~ ! [Uy: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.01/5.33 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.33 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.01/5.33 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.naive_member.pelims(1)
% 5.01/5.33 thf(fact_9283_diffs__cos__coeff,axiom,
% 5.01/5.33 ( ( diffs_real @ cos_coeff )
% 5.01/5.33 = ( ^ [N4: nat] : ( uminus_uminus_real @ ( sin_coeff @ N4 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % diffs_cos_coeff
% 5.01/5.33 thf(fact_9284_real__scaleR__def,axiom,
% 5.01/5.33 real_V1485227260804924795R_real = times_times_real ).
% 5.01/5.33
% 5.01/5.33 % real_scaleR_def
% 5.01/5.33 thf(fact_9285_scaleR__complex_Osimps_I1_J,axiom,
% 5.01/5.33 ! [R: real,X2: complex] :
% 5.01/5.33 ( ( re @ ( real_V2046097035970521341omplex @ R @ X2 ) )
% 5.01/5.33 = ( times_times_real @ R @ ( re @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % scaleR_complex.simps(1)
% 5.01/5.33 thf(fact_9286_scaleR__complex_Osimps_I2_J,axiom,
% 5.01/5.33 ! [R: real,X2: complex] :
% 5.01/5.33 ( ( im @ ( real_V2046097035970521341omplex @ R @ X2 ) )
% 5.01/5.33 = ( times_times_real @ R @ ( im @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % scaleR_complex.simps(2)
% 5.01/5.33 thf(fact_9287_complex__scaleR,axiom,
% 5.01/5.33 ! [R: real,A: real,B: real] :
% 5.01/5.33 ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 5.01/5.33 = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_scaleR
% 5.01/5.33 thf(fact_9288_scaleR__complex_Ocode,axiom,
% 5.01/5.33 ( real_V2046097035970521341omplex
% 5.01/5.33 = ( ^ [R5: real,X3: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X3 ) ) @ ( times_times_real @ R5 @ ( im @ X3 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % scaleR_complex.code
% 5.01/5.33 thf(fact_9289_Arg__def,axiom,
% 5.01/5.33 ( arg
% 5.01/5.33 = ( ^ [Z5: complex] :
% 5.01/5.33 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.01/5.33 @ ( fChoice_real
% 5.01/5.33 @ ^ [A4: real] :
% 5.01/5.33 ( ( ( sgn_sgn_complex @ Z5 )
% 5.01/5.33 = ( cis @ A4 ) )
% 5.01/5.33 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A4 )
% 5.01/5.33 & ( ord_less_eq_real @ A4 @ pi ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Arg_def
% 5.01/5.33 thf(fact_9290_set__vebt__def,axiom,
% 5.01/5.33 ( vEBT_set_vebt
% 5.01/5.33 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_vebt_def
% 5.01/5.33 thf(fact_9291_VEBT__internal_Ospace_Opelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: nat] :
% 5.01/5.33 ( ( ( vEBT_VEBT_space @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X2 )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary3 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList3 ) @ zero_zero_nat ) ) )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space.pelims
% 5.01/5.33 thf(fact_9292_VEBT__internal_Ospace_H_Opelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: nat] :
% 5.01/5.33 ( ( ( vEBT_VEBT_space2 @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X2 )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary3 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList3 ) @ zero_zero_nat ) ) )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.space'.pelims
% 5.01/5.33 thf(fact_9293_VEBT__internal_Ocnt_Opelims,axiom,
% 5.01/5.33 ! [X2: vEBT_VEBT,Y: real] :
% 5.01/5.33 ( ( ( vEBT_VEBT_cnt @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X2 )
% 5.01/5.33 => ( ! [A3: $o,B2: $o] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.01/5.33 => ( ( Y = one_one_real )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A3 @ B2 ) ) ) )
% 5.01/5.33 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary3 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList3 ) @ zero_zero_real ) ) )
% 5.01/5.33 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList3 @ Summary3 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT_internal.cnt.pelims
% 5.01/5.33 thf(fact_9294_sum__choose__upper,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.33 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_choose_upper
% 5.01/5.33 thf(fact_9295_sum__choose__lower,axiom,
% 5.01/5.33 ! [R: nat,N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.33 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_choose_lower
% 5.01/5.33 thf(fact_9296_choose__rising__sum_I2_J,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.01/5.33 @ ( set_ord_atMost_nat @ M ) )
% 5.01/5.33 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % choose_rising_sum(2)
% 5.01/5.33 thf(fact_9297_choose__rising__sum_I1_J,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.01/5.33 @ ( set_ord_atMost_nat @ M ) )
% 5.01/5.33 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % choose_rising_sum(1)
% 5.01/5.33 thf(fact_9298_sum__choose__diagonal,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ M ) )
% 5.01/5.33 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_choose_diagonal
% 5.01/5.33 thf(fact_9299_vandermonde,axiom,
% 5.01/5.33 ! [M: nat,N: nat,R: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ R ) )
% 5.01/5.33 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 5.01/5.33
% 5.01/5.33 % vandermonde
% 5.01/5.33 thf(fact_9300_choose__row__sum,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % choose_row_sum
% 5.01/5.33 thf(fact_9301_binomial,axiom,
% 5.01/5.33 ! [A: nat,B: nat,N: nat] :
% 5.01/5.33 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.01/5.33 = ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % binomial
% 5.01/5.33 thf(fact_9302_polynomial__product__nat,axiom,
% 5.01/5.33 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X2: nat] :
% 5.01/5.33 ( ! [I3: nat] :
% 5.01/5.33 ( ( ord_less_nat @ M @ I3 )
% 5.01/5.33 => ( ( A @ I3 )
% 5.01/5.33 = zero_zero_nat ) )
% 5.01/5.33 => ( ! [J2: nat] :
% 5.01/5.33 ( ( ord_less_nat @ N @ J2 )
% 5.01/5.33 => ( ( B @ J2 )
% 5.01/5.33 = zero_zero_nat ) )
% 5.01/5.33 => ( ( times_times_nat
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ M ) )
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) ) )
% 5.01/5.33 = ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [R5: nat] :
% 5.01/5.33 ( times_times_nat
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ R5 ) )
% 5.01/5.33 @ ( power_power_nat @ X2 @ R5 ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % polynomial_product_nat
% 5.01/5.33 thf(fact_9303_choose__square__sum,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.33 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % choose_square_sum
% 5.01/5.33 thf(fact_9304_binomial__r__part__sum,axiom,
% 5.01/5.33 ! [M: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.01/5.33 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % binomial_r_part_sum
% 5.01/5.33 thf(fact_9305_choose__linear__sum,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.01/5.33 @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.33 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % choose_linear_sum
% 5.01/5.33 thf(fact_9306_mask__eq__sum__exp__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.33 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % mask_eq_sum_exp_nat
% 5.01/5.33 thf(fact_9307_of__nat__id,axiom,
% 5.01/5.33 ( semiri1316708129612266289at_nat
% 5.01/5.33 = ( ^ [N4: nat] : N4 ) ) ).
% 5.01/5.33
% 5.01/5.33 % of_nat_id
% 5.01/5.33 thf(fact_9308_sum__nth__roots,axiom,
% 5.01/5.33 ! [N: nat,C: complex] :
% 5.01/5.33 ( ( ord_less_nat @ one_one_nat @ N )
% 5.01/5.33 => ( ( groups7754918857620584856omplex
% 5.01/5.33 @ ^ [X3: complex] : X3
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = C ) ) )
% 5.01/5.33 = zero_zero_complex ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_nth_roots
% 5.01/5.33 thf(fact_9309_sum__roots__unity,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_less_nat @ one_one_nat @ N )
% 5.01/5.33 => ( ( groups7754918857620584856omplex
% 5.01/5.33 @ ^ [X3: complex] : X3
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = one_one_complex ) ) )
% 5.01/5.33 = zero_zero_complex ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_roots_unity
% 5.01/5.33 thf(fact_9310_Maclaurin__minus__cos__expansion,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.33 => ? [T3: real] :
% 5.01/5.33 ( ( ord_less_real @ X2 @ T3 )
% 5.01/5.33 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.01/5.33 & ( ( cos_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_minus_cos_expansion
% 5.01/5.33 thf(fact_9311_Maclaurin__cos__expansion2,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ? [T3: real] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.01/5.33 & ( ord_less_real @ T3 @ X2 )
% 5.01/5.33 & ( ( cos_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_cos_expansion2
% 5.01/5.33 thf(fact_9312_Maclaurin__sin__expansion3,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ? [T3: real] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.01/5.33 & ( ord_less_real @ T3 @ X2 )
% 5.01/5.33 & ( ( sin_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_sin_expansion3
% 5.01/5.33 thf(fact_9313_Maclaurin__sin__expansion4,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ? [T3: real] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.01/5.33 & ( ord_less_eq_real @ T3 @ X2 )
% 5.01/5.33 & ( ( sin_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_sin_expansion4
% 5.01/5.33 thf(fact_9314_sumr__cos__zero__one,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.01/5.33 = one_one_real ) ).
% 5.01/5.33
% 5.01/5.33 % sumr_cos_zero_one
% 5.01/5.33 thf(fact_9315_lessThan__Suc__atMost,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.01/5.33 = ( set_ord_atMost_nat @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_Suc_atMost
% 5.01/5.33 thf(fact_9316_Maclaurin__lemma,axiom,
% 5.01/5.33 ! [H: real,F: real > real,J: nat > real,N: nat] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ H )
% 5.01/5.33 => ? [B8: real] :
% 5.01/5.33 ( ( F @ H )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_lemma
% 5.01/5.33 thf(fact_9317_sum__split__even__odd,axiom,
% 5.01/5.33 ! [F: nat > real,G: nat > real,N: nat] :
% 5.01/5.33 ( ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_split_even_odd
% 5.01/5.33 thf(fact_9318_Maclaurin__exp__le,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ? [T3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.33 & ( ( exp_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_exp_le
% 5.01/5.33 thf(fact_9319_Maclaurin__sin__bound,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ( ord_less_eq_real
% 5.01/5.33 @ ( abs_abs_real
% 5.01/5.33 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.01/5.33 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_sin_bound
% 5.01/5.33 thf(fact_9320_sum__pos__lt__pair,axiom,
% 5.01/5.33 ! [F: nat > real,K: nat] :
% 5.01/5.33 ( ( summable_real @ F )
% 5.01/5.33 => ( ! [D2: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) @ one_one_nat ) ) ) ) )
% 5.01/5.33 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_pos_lt_pair
% 5.01/5.33 thf(fact_9321_Maclaurin__exp__lt,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ( ( X2 != zero_zero_real )
% 5.01/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ? [T3: real] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.01/5.33 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.33 & ( ( exp_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_exp_lt
% 5.01/5.33 thf(fact_9322_Maclaurin__sin__expansion,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ? [T3: real] :
% 5.01/5.33 ( ( sin_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_sin_expansion
% 5.01/5.33 thf(fact_9323_Maclaurin__sin__expansion2,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ? [T3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.33 & ( ( sin_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_sin_expansion2
% 5.01/5.33 thf(fact_9324_Maclaurin__cos__expansion,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ? [T3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.33 & ( ( cos_real @ X2 )
% 5.01/5.33 = ( plus_plus_real
% 5.01/5.33 @ ( groups6591440286371151544t_real
% 5.01/5.33 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.33 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T3 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Maclaurin_cos_expansion
% 5.01/5.33 thf(fact_9325_bij__betw__roots__unity,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( bij_betw_nat_complex
% 5.01/5.33 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.01/5.33 @ ( set_ord_lessThan_nat @ N )
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = one_one_complex ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bij_betw_roots_unity
% 5.01/5.33 thf(fact_9326_ex__nat__less,axiom,
% 5.01/5.33 ! [N: nat,P: nat > $o] :
% 5.01/5.33 ( ( ? [M3: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M3 @ N )
% 5.01/5.33 & ( P @ M3 ) ) )
% 5.01/5.33 = ( ? [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 & ( P @ X3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ex_nat_less
% 5.01/5.33 thf(fact_9327_all__nat__less,axiom,
% 5.01/5.33 ! [N: nat,P: nat > $o] :
% 5.01/5.33 ( ( ! [M3: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M3 @ N )
% 5.01/5.33 => ( P @ M3 ) ) )
% 5.01/5.33 = ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 => ( P @ X3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % all_nat_less
% 5.01/5.33 thf(fact_9328_atMost__atLeast0,axiom,
% 5.01/5.33 ( set_ord_atMost_nat
% 5.01/5.33 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % atMost_atLeast0
% 5.01/5.33 thf(fact_9329_gauss__sum__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % gauss_sum_nat
% 5.01/5.33 thf(fact_9330_arith__series__nat,axiom,
% 5.01/5.33 ! [A: nat,D: nat,N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D ) )
% 5.01/5.33 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % arith_series_nat
% 5.01/5.33 thf(fact_9331_Sum__Icc__nat,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.01/5.33 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Sum_Icc_nat
% 5.01/5.33 thf(fact_9332_vebt__buildup_Opelims,axiom,
% 5.01/5.33 ! [X2: nat,Y: vEBT_VEBT] :
% 5.01/5.33 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.01/5.33 => ( ( ( X2 = zero_zero_nat )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( vEBT_Leaf @ $false @ $false ) )
% 5.01/5.33 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.01/5.33 => ( ( ( X2
% 5.01/5.33 = ( suc @ zero_zero_nat ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( vEBT_Leaf @ $false @ $false ) )
% 5.01/5.33 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.01/5.33 => ~ ! [Va: nat] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.01/5.33 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % vebt_buildup.pelims
% 5.01/5.33 thf(fact_9333_bset_I1_J,axiom,
% 5.01/5.33 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ B4 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ B4 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( Q @ X4 )
% 5.01/5.33 => ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ( P @ X )
% 5.01/5.33 & ( Q @ X ) )
% 5.01/5.33 => ( ( P @ ( minus_minus_int @ X @ D4 ) )
% 5.01/5.33 & ( Q @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(1)
% 5.01/5.33 thf(fact_9334_bset_I2_J,axiom,
% 5.01/5.33 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ B4 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ B4 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( Q @ X4 )
% 5.01/5.33 => ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ( P @ X )
% 5.01/5.33 | ( Q @ X ) )
% 5.01/5.33 => ( ( P @ ( minus_minus_int @ X @ D4 ) )
% 5.01/5.33 | ( Q @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(2)
% 5.01/5.33 thf(fact_9335_aset_I1_J,axiom,
% 5.01/5.33 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ A2 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ A2 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( Q @ X4 )
% 5.01/5.33 => ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ( P @ X )
% 5.01/5.33 & ( Q @ X ) )
% 5.01/5.33 => ( ( P @ ( plus_plus_int @ X @ D4 ) )
% 5.01/5.33 & ( Q @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(1)
% 5.01/5.33 thf(fact_9336_aset_I2_J,axiom,
% 5.01/5.33 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.01/5.33 ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ A2 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ A2 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( Q @ X4 )
% 5.01/5.33 => ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ( P @ X )
% 5.01/5.33 | ( Q @ X ) )
% 5.01/5.33 => ( ( P @ ( plus_plus_int @ X @ D4 ) )
% 5.01/5.33 | ( Q @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(2)
% 5.01/5.33 thf(fact_9337_aset_I10_J,axiom,
% 5.01/5.33 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.01/5.33 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.01/5.33 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(10)
% 5.01/5.33 thf(fact_9338_aset_I9_J,axiom,
% 5.01/5.33 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.01/5.33 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.01/5.33 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(9)
% 5.01/5.33 thf(fact_9339_bset_I10_J,axiom,
% 5.01/5.33 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.01/5.33 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.01/5.33 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(10)
% 5.01/5.33 thf(fact_9340_bset_I9_J,axiom,
% 5.01/5.33 ! [D: int,D4: int,B4: set_int,T: int] :
% 5.01/5.33 ( ( dvd_dvd_int @ D @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X @ T ) )
% 5.01/5.33 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(9)
% 5.01/5.33 thf(fact_9341_periodic__finite__ex,axiom,
% 5.01/5.33 ! [D: int,P: int > $o] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D )
% 5.01/5.33 => ( ! [X4: int,K3: int] :
% 5.01/5.33 ( ( P @ X4 )
% 5.01/5.33 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.01/5.33 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.01/5.33 = ( ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.01/5.33 & ( P @ X3 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % periodic_finite_ex
% 5.01/5.33 thf(fact_9342_aset_I7_J,axiom,
% 5.01/5.33 ! [D4: int,A2: set_int,T: int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_int @ T @ X )
% 5.01/5.33 => ( ord_less_int @ T @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(7)
% 5.01/5.33 thf(fact_9343_aset_I5_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,A2: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ T @ A2 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_int @ X @ T )
% 5.01/5.33 => ( ord_less_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(5)
% 5.01/5.33 thf(fact_9344_aset_I4_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,A2: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ T @ A2 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( X != T )
% 5.01/5.33 => ( ( plus_plus_int @ X @ D4 )
% 5.01/5.33 != T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(4)
% 5.01/5.33 thf(fact_9345_aset_I3_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,A2: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( X = T )
% 5.01/5.33 => ( ( plus_plus_int @ X @ D4 )
% 5.01/5.33 = T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(3)
% 5.01/5.33 thf(fact_9346_bset_I7_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,B4: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ T @ B4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_int @ T @ X )
% 5.01/5.33 => ( ord_less_int @ T @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(7)
% 5.01/5.33 thf(fact_9347_bset_I5_J,axiom,
% 5.01/5.33 ! [D4: int,B4: set_int,T: int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_int @ X @ T )
% 5.01/5.33 => ( ord_less_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(5)
% 5.01/5.33 thf(fact_9348_bset_I4_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,B4: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ T @ B4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( X != T )
% 5.01/5.33 => ( ( minus_minus_int @ X @ D4 )
% 5.01/5.33 != T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(4)
% 5.01/5.33 thf(fact_9349_bset_I3_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,B4: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( X = T )
% 5.01/5.33 => ( ( minus_minus_int @ X @ D4 )
% 5.01/5.33 = T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(3)
% 5.01/5.33 thf(fact_9350_fact__eq__fact__times,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.33 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.01/5.33 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.01/5.33 @ ( groups708209901874060359at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % fact_eq_fact_times
% 5.01/5.33 thf(fact_9351_aset_I8_J,axiom,
% 5.01/5.33 ! [D4: int,A2: set_int,T: int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_eq_int @ T @ X )
% 5.01/5.33 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X @ D4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(8)
% 5.01/5.33 thf(fact_9352_aset_I6_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,A2: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ A2 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_eq_int @ X @ T )
% 5.01/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ X @ D4 ) @ T ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % aset(6)
% 5.01/5.33 thf(fact_9353_bset_I8_J,axiom,
% 5.01/5.33 ! [D4: int,T: int,B4: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_eq_int @ T @ X )
% 5.01/5.33 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X @ D4 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(8)
% 5.01/5.33 thf(fact_9354_bset_I6_J,axiom,
% 5.01/5.33 ! [D4: int,B4: set_int,T: int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ! [X: int] :
% 5.01/5.33 ( ! [Xa3: int] :
% 5.01/5.33 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb3: int] :
% 5.01/5.33 ( ( member_int @ Xb3 @ B4 )
% 5.01/5.33 => ( X
% 5.01/5.33 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.01/5.33 => ( ( ord_less_eq_int @ X @ T )
% 5.01/5.33 => ( ord_less_eq_int @ ( minus_minus_int @ X @ D4 ) @ T ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bset(6)
% 5.01/5.33 thf(fact_9355_cpmi,axiom,
% 5.01/5.33 ! [D4: int,P: int > $o,P6: int > $o,B4: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ? [Z2: int] :
% 5.01/5.33 ! [X4: int] :
% 5.01/5.33 ( ( ord_less_int @ X4 @ Z2 )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 = ( P6 @ X4 ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ B4 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int,K3: int] :
% 5.01/5.33 ( ( P6 @ X4 )
% 5.01/5.33 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.33 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.01/5.33 = ( ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 & ( P6 @ X3 ) )
% 5.01/5.33 | ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 & ? [Y2: int] :
% 5.01/5.33 ( ( member_int @ Y2 @ B4 )
% 5.01/5.33 & ( P @ ( plus_plus_int @ Y2 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cpmi
% 5.01/5.33 thf(fact_9356_cppi,axiom,
% 5.01/5.33 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.01/5.33 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.01/5.33 => ( ? [Z2: int] :
% 5.01/5.33 ! [X4: int] :
% 5.01/5.33 ( ( ord_less_int @ Z2 @ X4 )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 = ( P6 @ X4 ) ) )
% 5.01/5.33 => ( ! [X4: int] :
% 5.01/5.33 ( ! [Xa2: int] :
% 5.01/5.33 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 => ! [Xb2: int] :
% 5.01/5.33 ( ( member_int @ Xb2 @ A2 )
% 5.01/5.33 => ( X4
% 5.01/5.33 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.01/5.33 => ( ( P @ X4 )
% 5.01/5.33 => ( P @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.01/5.33 => ( ! [X4: int,K3: int] :
% 5.01/5.33 ( ( P6 @ X4 )
% 5.01/5.33 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.01/5.33 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.01/5.33 = ( ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 & ( P6 @ X3 ) )
% 5.01/5.33 | ? [X3: int] :
% 5.01/5.33 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.01/5.33 & ? [Y2: int] :
% 5.01/5.33 ( ( member_int @ Y2 @ A2 )
% 5.01/5.33 & ( P @ ( minus_minus_int @ Y2 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cppi
% 5.01/5.33 thf(fact_9357_fact__div__fact,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.33 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.01/5.33 = ( groups708209901874060359at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % fact_div_fact
% 5.01/5.33 thf(fact_9358_divmod__step__nat__def,axiom,
% 5.01/5.33 ( unique5026877609467782581ep_nat
% 5.01/5.33 = ( ^ [L2: num] :
% 5.01/5.33 ( produc2626176000494625587at_nat
% 5.01/5.33 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_step_nat_def
% 5.01/5.33 thf(fact_9359_divmod__step__int__def,axiom,
% 5.01/5.33 ( unique5024387138958732305ep_int
% 5.01/5.33 = ( ^ [L2: num] :
% 5.01/5.33 ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_step_int_def
% 5.01/5.33 thf(fact_9360_Sum__Icc__int,axiom,
% 5.01/5.33 ! [M: int,N: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ M @ N )
% 5.01/5.33 => ( ( groups4538972089207619220nt_int
% 5.01/5.33 @ ^ [X3: int] : X3
% 5.01/5.33 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.01/5.33 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Sum_Icc_int
% 5.01/5.33 thf(fact_9361_divmod__nat__if,axiom,
% 5.01/5.33 ( divmod_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.33 ( if_Pro6206227464963214023at_nat
% 5.01/5.33 @ ( ( N4 = zero_zero_nat )
% 5.01/5.33 | ( ord_less_nat @ M3 @ N4 ) )
% 5.01/5.33 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 5.01/5.33 @ ( produc2626176000494625587at_nat
% 5.01/5.33 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.01/5.33 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_nat_if
% 5.01/5.33 thf(fact_9362_arctan__def,axiom,
% 5.01/5.33 ( arctan
% 5.01/5.33 = ( ^ [Y2: real] :
% 5.01/5.33 ( the_real
% 5.01/5.33 @ ^ [X3: real] :
% 5.01/5.33 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.01/5.33 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.33 & ( ( tan_real @ X3 )
% 5.01/5.33 = Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % arctan_def
% 5.01/5.33 thf(fact_9363_arcsin__def,axiom,
% 5.01/5.33 ( arcsin
% 5.01/5.33 = ( ^ [Y2: real] :
% 5.01/5.33 ( the_real
% 5.01/5.33 @ ^ [X3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.01/5.33 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.33 & ( ( sin_real @ X3 )
% 5.01/5.33 = Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % arcsin_def
% 5.01/5.33 thf(fact_9364_complex__diff__cnj,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.01/5.33 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_diff_cnj
% 5.01/5.33 thf(fact_9365_complex__cnj__zero,axiom,
% 5.01/5.33 ( ( cnj @ zero_zero_complex )
% 5.01/5.33 = zero_zero_complex ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj_zero
% 5.01/5.33 thf(fact_9366_complex__cnj__zero__iff,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( ( cnj @ Z )
% 5.01/5.33 = zero_zero_complex )
% 5.01/5.33 = ( Z = zero_zero_complex ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj_zero_iff
% 5.01/5.33 thf(fact_9367_complex__cnj__add,axiom,
% 5.01/5.33 ! [X2: complex,Y: complex] :
% 5.01/5.33 ( ( cnj @ ( plus_plus_complex @ X2 @ Y ) )
% 5.01/5.33 = ( plus_plus_complex @ ( cnj @ X2 ) @ ( cnj @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj_add
% 5.01/5.33 thf(fact_9368_complex__cnj__diff,axiom,
% 5.01/5.33 ! [X2: complex,Y: complex] :
% 5.01/5.33 ( ( cnj @ ( minus_minus_complex @ X2 @ Y ) )
% 5.01/5.33 = ( minus_minus_complex @ ( cnj @ X2 ) @ ( cnj @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj_diff
% 5.01/5.33 thf(fact_9369_complex__cnj__of__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( cnj @ ( semiri8010041392384452111omplex @ N ) )
% 5.01/5.33 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj_of_nat
% 5.01/5.33 thf(fact_9370_complex__In__mult__cnj__zero,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.01/5.33 = zero_zero_real ) ).
% 5.01/5.33
% 5.01/5.33 % complex_In_mult_cnj_zero
% 5.01/5.33 thf(fact_9371_cnj_Osimps_I2_J,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( im @ ( cnj @ Z ) )
% 5.01/5.33 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cnj.simps(2)
% 5.01/5.33 thf(fact_9372_complex__cnj,axiom,
% 5.01/5.33 ! [A: real,B: real] :
% 5.01/5.33 ( ( cnj @ ( complex2 @ A @ B ) )
% 5.01/5.33 = ( complex2 @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_cnj
% 5.01/5.33 thf(fact_9373_cis__cnj,axiom,
% 5.01/5.33 ! [T: real] :
% 5.01/5.33 ( ( cnj @ ( cis @ T ) )
% 5.01/5.33 = ( cis @ ( uminus_uminus_real @ T ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cis_cnj
% 5.01/5.33 thf(fact_9374_prod__int__eq,axiom,
% 5.01/5.33 ! [I: nat,J: nat] :
% 5.01/5.33 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.01/5.33 = ( groups1705073143266064639nt_int
% 5.01/5.33 @ ^ [X3: int] : X3
% 5.01/5.33 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_int_eq
% 5.01/5.33 thf(fact_9375_prod__int__plus__eq,axiom,
% 5.01/5.33 ! [I: nat,J: nat] :
% 5.01/5.33 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.01/5.33 = ( groups1705073143266064639nt_int
% 5.01/5.33 @ ^ [X3: int] : X3
% 5.01/5.33 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_int_plus_eq
% 5.01/5.33 thf(fact_9376_ln__neg__is__const,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.01/5.33 => ( ( ln_ln_real @ X2 )
% 5.01/5.33 = ( the_real
% 5.01/5.33 @ ^ [X3: real] : $false ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ln_neg_is_const
% 5.01/5.33 thf(fact_9377_cnj_Ocode,axiom,
% 5.01/5.33 ( cnj
% 5.01/5.33 = ( ^ [Z5: complex] : ( complex2 @ ( re @ Z5 ) @ ( uminus_uminus_real @ ( im @ Z5 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cnj.code
% 5.01/5.33 thf(fact_9378_Re__complex__div__eq__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.33 = zero_zero_real )
% 5.01/5.33 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.01/5.33 = zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_complex_div_eq_0
% 5.01/5.33 thf(fact_9379_Im__complex__div__eq__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.01/5.33 = zero_zero_real )
% 5.01/5.33 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.01/5.33 = zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_complex_div_eq_0
% 5.01/5.33 thf(fact_9380_Re__complex__div__lt__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_complex_div_lt_0
% 5.01/5.33 thf(fact_9381_Re__complex__div__gt__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_complex_div_gt_0
% 5.01/5.33 thf(fact_9382_Re__complex__div__ge__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_complex_div_ge_0
% 5.01/5.33 thf(fact_9383_Re__complex__div__le__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Re_complex_div_le_0
% 5.01/5.33 thf(fact_9384_Im__complex__div__lt__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_complex_div_lt_0
% 5.01/5.33 thf(fact_9385_Im__complex__div__gt__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_complex_div_gt_0
% 5.01/5.33 thf(fact_9386_Im__complex__div__ge__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_complex_div_ge_0
% 5.01/5.33 thf(fact_9387_Im__complex__div__le__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % Im_complex_div_le_0
% 5.01/5.33 thf(fact_9388_Divides_Oadjust__div__def,axiom,
% 5.01/5.33 ( adjust_div
% 5.01/5.33 = ( produc8211389475949308722nt_int
% 5.01/5.33 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Divides.adjust_div_def
% 5.01/5.33 thf(fact_9389_complex__mod__mult__cnj,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.01/5.33 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_mod_mult_cnj
% 5.01/5.33 thf(fact_9390_arccos__def,axiom,
% 5.01/5.33 ( arccos
% 5.01/5.33 = ( ^ [Y2: real] :
% 5.01/5.33 ( the_real
% 5.01/5.33 @ ^ [X3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.01/5.33 & ( ord_less_eq_real @ X3 @ pi )
% 5.01/5.33 & ( ( cos_real @ X3 )
% 5.01/5.33 = Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % arccos_def
% 5.01/5.33 thf(fact_9391_complex__div__gt__0,axiom,
% 5.01/5.33 ! [A: complex,B: complex] :
% 5.01/5.33 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.01/5.33 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.01/5.33 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_div_gt_0
% 5.01/5.33 thf(fact_9392_complex__norm__square,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.01/5.33 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_norm_square
% 5.01/5.33 thf(fact_9393_divmod__nat__def,axiom,
% 5.01/5.33 ( divmod_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N4 ) @ ( modulo_modulo_nat @ M3 @ N4 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_nat_def
% 5.01/5.33 thf(fact_9394_complex__add__cnj,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.01/5.33 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_add_cnj
% 5.01/5.33 thf(fact_9395_complex__div__cnj,axiom,
% 5.01/5.33 ( divide1717551699836669952omplex
% 5.01/5.33 = ( ^ [A4: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A4 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_div_cnj
% 5.01/5.33 thf(fact_9396_cnj__add__mult__eq__Re,axiom,
% 5.01/5.33 ! [Z: complex,W: complex] :
% 5.01/5.33 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.01/5.33 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % cnj_add_mult_eq_Re
% 5.01/5.33 thf(fact_9397_complex__mult__cnj,axiom,
% 5.01/5.33 ! [Z: complex] :
% 5.01/5.33 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.01/5.33 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % complex_mult_cnj
% 5.01/5.33 thf(fact_9398_pi__half,axiom,
% 5.01/5.33 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.33 = ( the_real
% 5.01/5.33 @ ^ [X3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.01/5.33 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.33 & ( ( cos_real @ X3 )
% 5.01/5.33 = zero_zero_real ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % pi_half
% 5.01/5.33 thf(fact_9399_pi__def,axiom,
% 5.01/5.33 ( pi
% 5.01/5.33 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.01/5.33 @ ( the_real
% 5.01/5.33 @ ^ [X3: real] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.01/5.33 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.01/5.33 & ( ( cos_real @ X3 )
% 5.01/5.33 = zero_zero_real ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % pi_def
% 5.01/5.33 thf(fact_9400_int__ge__less__than2__def,axiom,
% 5.01/5.33 ( int_ge_less_than2
% 5.01/5.33 = ( ^ [D3: int] :
% 5.01/5.33 ( collec213857154873943460nt_int
% 5.01/5.33 @ ( produc4947309494688390418_int_o
% 5.01/5.33 @ ^ [Z7: int,Z5: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ D3 @ Z5 )
% 5.01/5.33 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_ge_less_than2_def
% 5.01/5.33 thf(fact_9401_int__ge__less__than__def,axiom,
% 5.01/5.33 ( int_ge_less_than
% 5.01/5.33 = ( ^ [D3: int] :
% 5.01/5.33 ( collec213857154873943460nt_int
% 5.01/5.33 @ ( produc4947309494688390418_int_o
% 5.01/5.33 @ ^ [Z7: int,Z5: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ D3 @ Z7 )
% 5.01/5.33 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_ge_less_than_def
% 5.01/5.33 thf(fact_9402_set__encode__def,axiom,
% 5.01/5.33 ( nat_set_encode
% 5.01/5.33 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_def
% 5.01/5.33 thf(fact_9403_set__decode__inverse,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % set_decode_inverse
% 5.01/5.33 thf(fact_9404_length__upt,axiom,
% 5.01/5.33 ! [I: nat,J: nat] :
% 5.01/5.33 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.01/5.33 = ( minus_minus_nat @ J @ I ) ) ).
% 5.01/5.33
% 5.01/5.33 % length_upt
% 5.01/5.33 thf(fact_9405_nth__upt,axiom,
% 5.01/5.33 ! [I: nat,K: nat,J: nat] :
% 5.01/5.33 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.01/5.33 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.01/5.33 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nth_upt
% 5.01/5.33 thf(fact_9406_map__Suc__upt,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.01/5.33 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_Suc_upt
% 5.01/5.33 thf(fact_9407_atLeastAtMost__upt,axiom,
% 5.01/5.33 ( set_or1269000886237332187st_nat
% 5.01/5.33 = ( ^ [N4: nat,M3: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M3 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastAtMost_upt
% 5.01/5.33 thf(fact_9408_atLeast__upt,axiom,
% 5.01/5.33 ( set_ord_lessThan_nat
% 5.01/5.33 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeast_upt
% 5.01/5.33 thf(fact_9409_map__add__upt,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( map_nat_nat
% 5.01/5.33 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.01/5.33 @ ( upt @ zero_zero_nat @ M ) )
% 5.01/5.33 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_add_upt
% 5.01/5.33 thf(fact_9410_atMost__upto,axiom,
% 5.01/5.33 ( set_ord_atMost_nat
% 5.01/5.33 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atMost_upto
% 5.01/5.33 thf(fact_9411_map__decr__upt,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( map_nat_nat
% 5.01/5.33 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 5.01/5.33 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.01/5.33 = ( upt @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % map_decr_upt
% 5.01/5.33 thf(fact_9412_upto_Opinduct,axiom,
% 5.01/5.33 ! [A0: int,A12: int,P: int > int > $o] :
% 5.01/5.33 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.01/5.33 => ( ! [I3: int,J2: int] :
% 5.01/5.33 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.01/5.33 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.01/5.33 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.01/5.33 => ( P @ I3 @ J2 ) ) )
% 5.01/5.33 => ( P @ A0 @ A12 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % upto.pinduct
% 5.01/5.33 thf(fact_9413_VEBT_Osize_I3_J,axiom,
% 5.01/5.33 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.01/5.33 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT.size(3)
% 5.01/5.33 thf(fact_9414_VEBT_Osize__gen_I1_J,axiom,
% 5.01/5.33 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.01/5.33 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.01/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT.size_gen(1)
% 5.01/5.33 thf(fact_9415_Sum__Ico__nat,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.01/5.33 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Sum_Ico_nat
% 5.01/5.33 thf(fact_9416_sum__power2,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.01/5.33 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_power2
% 5.01/5.33 thf(fact_9417_all__nat__less__eq,axiom,
% 5.01/5.33 ! [N: nat,P: nat > $o] :
% 5.01/5.33 ( ( ! [M3: nat] :
% 5.01/5.33 ( ( ord_less_nat @ M3 @ N )
% 5.01/5.33 => ( P @ M3 ) ) )
% 5.01/5.33 = ( ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 => ( P @ X3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % all_nat_less_eq
% 5.01/5.33 thf(fact_9418_ex__nat__less__eq,axiom,
% 5.01/5.33 ! [N: nat,P: nat > $o] :
% 5.01/5.33 ( ( ? [M3: nat] :
% 5.01/5.33 ( ( ord_less_nat @ M3 @ N )
% 5.01/5.33 & ( P @ M3 ) ) )
% 5.01/5.33 = ( ? [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 & ( P @ X3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ex_nat_less_eq
% 5.01/5.33 thf(fact_9419_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.01/5.33 ! [L: nat,U: nat] :
% 5.01/5.33 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.01/5.33 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThanSuc_atLeastAtMost
% 5.01/5.33 thf(fact_9420_lessThan__atLeast0,axiom,
% 5.01/5.33 ( set_ord_lessThan_nat
% 5.01/5.33 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_atLeast0
% 5.01/5.33 thf(fact_9421_atLeastLessThan__upt,axiom,
% 5.01/5.33 ( set_or4665077453230672383an_nat
% 5.01/5.33 = ( ^ [I4: nat,J3: nat] : ( set_nat2 @ ( upt @ I4 @ J3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThan_upt
% 5.01/5.33 thf(fact_9422_prod__Suc__fact,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_Suc_fact
% 5.01/5.33 thf(fact_9423_prod__Suc__Suc__fact,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.01/5.33 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_Suc_Suc_fact
% 5.01/5.33 thf(fact_9424_VEBT_Osize__gen_I2_J,axiom,
% 5.01/5.33 ! [X21: $o,X222: $o] :
% 5.01/5.33 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.01/5.33 = zero_zero_nat ) ).
% 5.01/5.33
% 5.01/5.33 % VEBT.size_gen(2)
% 5.01/5.33 thf(fact_9425_Chebyshev__sum__upper__nat,axiom,
% 5.01/5.33 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.01/5.33 ( ! [I3: nat,J2: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.01/5.33 => ( ( ord_less_nat @ J2 @ N )
% 5.01/5.33 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.01/5.33 => ( ! [I3: nat,J2: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.01/5.33 => ( ( ord_less_nat @ J2 @ N )
% 5.01/5.33 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 5.01/5.33 => ( ord_less_eq_nat
% 5.01/5.33 @ ( times_times_nat @ N
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 5.01/5.33 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.01/5.33 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Chebyshev_sum_upper_nat
% 5.01/5.33 thf(fact_9426_int__of__nat__def,axiom,
% 5.01/5.33 code_T6385005292777649522of_nat = semiri1314217659103216013at_int ).
% 5.01/5.33
% 5.01/5.33 % int_of_nat_def
% 5.01/5.33 thf(fact_9427_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.01/5.33 ! [L: int,U: int] :
% 5.01/5.33 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.01/5.33 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.01/5.33 thf(fact_9428_Code__Target__Int_Opositive__def,axiom,
% 5.01/5.33 code_Target_positive = numeral_numeral_int ).
% 5.01/5.33
% 5.01/5.33 % Code_Target_Int.positive_def
% 5.01/5.33 thf(fact_9429_divmod__step__integer__def,axiom,
% 5.01/5.33 ( unique4921790084139445826nteger
% 5.01/5.33 = ( ^ [L2: num] :
% 5.01/5.33 ( produc6916734918728496179nteger
% 5.01/5.33 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_step_integer_def
% 5.01/5.33 thf(fact_9430_minus__integer__code_I1_J,axiom,
% 5.01/5.33 ! [K: code_integer] :
% 5.01/5.33 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.01/5.33 = K ) ).
% 5.01/5.33
% 5.01/5.33 % minus_integer_code(1)
% 5.01/5.33 thf(fact_9431_sgn__integer__code,axiom,
% 5.01/5.33 ( sgn_sgn_Code_integer
% 5.01/5.33 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sgn_integer_code
% 5.01/5.33 thf(fact_9432_minus__integer__code_I2_J,axiom,
% 5.01/5.33 ! [L: code_integer] :
% 5.01/5.33 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 5.01/5.33 = ( uminus1351360451143612070nteger @ L ) ) ).
% 5.01/5.33
% 5.01/5.33 % minus_integer_code(2)
% 5.01/5.33 thf(fact_9433_divmod__integer_H__def,axiom,
% 5.01/5.33 ( unique3479559517661332726nteger
% 5.01/5.33 = ( ^ [M3: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_integer'_def
% 5.01/5.33 thf(fact_9434_times__integer__code_I1_J,axiom,
% 5.01/5.33 ! [K: code_integer] :
% 5.01/5.33 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.01/5.33 = zero_z3403309356797280102nteger ) ).
% 5.01/5.33
% 5.01/5.33 % times_integer_code(1)
% 5.01/5.33 thf(fact_9435_times__integer__code_I2_J,axiom,
% 5.01/5.33 ! [L: code_integer] :
% 5.01/5.33 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.01/5.33 = zero_z3403309356797280102nteger ) ).
% 5.01/5.33
% 5.01/5.33 % times_integer_code(2)
% 5.01/5.33 thf(fact_9436_plus__integer__code_I2_J,axiom,
% 5.01/5.33 ! [L: code_integer] :
% 5.01/5.33 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 5.01/5.33 = L ) ).
% 5.01/5.33
% 5.01/5.33 % plus_integer_code(2)
% 5.01/5.33 thf(fact_9437_plus__integer__code_I1_J,axiom,
% 5.01/5.33 ! [K: code_integer] :
% 5.01/5.33 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.01/5.33 = K ) ).
% 5.01/5.33
% 5.01/5.33 % plus_integer_code(1)
% 5.01/5.33 thf(fact_9438_exhaustive__integer_H_Ocases,axiom,
% 5.01/5.33 ! [X2: produc8763457246119570046nteger] :
% 5.01/5.33 ~ ! [F2: code_integer > option6357759511663192854e_term,D2: code_integer,I3: code_integer] :
% 5.01/5.33 ( X2
% 5.01/5.33 != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D2 @ I3 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % exhaustive_integer'.cases
% 5.01/5.33 thf(fact_9439_full__exhaustive__integer_H_Ocases,axiom,
% 5.01/5.33 ! [X2: produc1908205239877642774nteger] :
% 5.01/5.33 ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D2: code_integer,I3: code_integer] :
% 5.01/5.33 ( X2
% 5.01/5.33 != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D2 @ I3 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % full_exhaustive_integer'.cases
% 5.01/5.33 thf(fact_9440_less__eq__integer__code_I1_J,axiom,
% 5.01/5.33 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.01/5.33
% 5.01/5.33 % less_eq_integer_code(1)
% 5.01/5.33 thf(fact_9441_nat_Odisc__eq__case_I2_J,axiom,
% 5.01/5.33 ! [Nat: nat] :
% 5.01/5.33 ( ( Nat != zero_zero_nat )
% 5.01/5.33 = ( case_nat_o @ $false
% 5.01/5.33 @ ^ [Uu3: nat] : $true
% 5.01/5.33 @ Nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat.disc_eq_case(2)
% 5.01/5.33 thf(fact_9442_nat_Odisc__eq__case_I1_J,axiom,
% 5.01/5.33 ! [Nat: nat] :
% 5.01/5.33 ( ( Nat = zero_zero_nat )
% 5.01/5.33 = ( case_nat_o @ $true
% 5.01/5.33 @ ^ [Uu3: nat] : $false
% 5.01/5.33 @ Nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat.disc_eq_case(1)
% 5.01/5.33 thf(fact_9443_zero__natural_Orsp,axiom,
% 5.01/5.33 zero_zero_nat = zero_zero_nat ).
% 5.01/5.33
% 5.01/5.33 % zero_natural.rsp
% 5.01/5.33 thf(fact_9444_zero__integer_Orsp,axiom,
% 5.01/5.33 zero_zero_int = zero_zero_int ).
% 5.01/5.33
% 5.01/5.33 % zero_integer.rsp
% 5.01/5.33 thf(fact_9445_one__integer_Orsp,axiom,
% 5.01/5.33 one_one_int = one_one_int ).
% 5.01/5.33
% 5.01/5.33 % one_integer.rsp
% 5.01/5.33 thf(fact_9446_one__natural_Orsp,axiom,
% 5.01/5.33 one_one_nat = one_one_nat ).
% 5.01/5.33
% 5.01/5.33 % one_natural.rsp
% 5.01/5.33 thf(fact_9447_less__eq__nat_Osimps_I2_J,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.01/5.33 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % less_eq_nat.simps(2)
% 5.01/5.33 thf(fact_9448_diff__Suc,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.01/5.33 = ( case_nat_nat @ zero_zero_nat
% 5.01/5.33 @ ^ [K2: nat] : K2
% 5.01/5.33 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % diff_Suc
% 5.01/5.33 thf(fact_9449_integer__of__int__code,axiom,
% 5.01/5.33 ( code_integer_of_int
% 5.01/5.33 = ( ^ [K2: int] :
% 5.01/5.33 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.01/5.33 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.01/5.33 @ ( if_Code_integer
% 5.01/5.33 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.01/5.33 = zero_zero_int )
% 5.01/5.33 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.33 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % integer_of_int_code
% 5.01/5.33 thf(fact_9450_integer__of__num_I3_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.01/5.33 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.01/5.33
% 5.01/5.33 % integer_of_num(3)
% 5.01/5.33 thf(fact_9451_less__integer__code_I1_J,axiom,
% 5.01/5.33 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.01/5.33
% 5.01/5.33 % less_integer_code(1)
% 5.01/5.33 thf(fact_9452_abs__integer__code,axiom,
% 5.01/5.33 ( abs_abs_Code_integer
% 5.01/5.33 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % abs_integer_code
% 5.01/5.33 thf(fact_9453_uminus__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [X2: int] :
% 5.01/5.33 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( code_integer_of_int @ ( uminus_uminus_int @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % uminus_integer.abs_eq
% 5.01/5.33 thf(fact_9454_uminus__integer__code_I1_J,axiom,
% 5.01/5.33 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.01/5.33 = zero_z3403309356797280102nteger ) ).
% 5.01/5.33
% 5.01/5.33 % uminus_integer_code(1)
% 5.01/5.33 thf(fact_9455_divide__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [Xa: int,X2: int] :
% 5.01/5.33 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divide_integer.abs_eq
% 5.01/5.33 thf(fact_9456_zero__integer__def,axiom,
% 5.01/5.33 ( zero_z3403309356797280102nteger
% 5.01/5.33 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % zero_integer_def
% 5.01/5.33 thf(fact_9457_modulo__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [Xa: int,X2: int] :
% 5.01/5.33 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % modulo_integer.abs_eq
% 5.01/5.33 thf(fact_9458_plus__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [Xa: int,X2: int] :
% 5.01/5.33 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( code_integer_of_int @ ( plus_plus_int @ Xa @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % plus_integer.abs_eq
% 5.01/5.33 thf(fact_9459_one__integer__def,axiom,
% 5.01/5.33 ( one_one_Code_integer
% 5.01/5.33 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % one_integer_def
% 5.01/5.33 thf(fact_9460_less__eq__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [Xa: int,X2: int] :
% 5.01/5.33 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( ord_less_eq_int @ Xa @ X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % less_eq_integer.abs_eq
% 5.01/5.33 thf(fact_9461_minus__integer_Oabs__eq,axiom,
% 5.01/5.33 ! [Xa: int,X2: int] :
% 5.01/5.33 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X2 ) )
% 5.01/5.33 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % minus_integer.abs_eq
% 5.01/5.33 thf(fact_9462_pred__def,axiom,
% 5.01/5.33 ( pred
% 5.01/5.33 = ( case_nat_nat @ zero_zero_nat
% 5.01/5.33 @ ^ [X24: nat] : X24 ) ) ).
% 5.01/5.33
% 5.01/5.33 % pred_def
% 5.01/5.33 thf(fact_9463_integer__of__num__triv_I1_J,axiom,
% 5.01/5.33 ( ( code_integer_of_num @ one )
% 5.01/5.33 = one_one_Code_integer ) ).
% 5.01/5.33
% 5.01/5.33 % integer_of_num_triv(1)
% 5.01/5.33 thf(fact_9464_integer__of__num_I2_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.01/5.33 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % integer_of_num(2)
% 5.01/5.33 thf(fact_9465_integer__of__num__triv_I2_J,axiom,
% 5.01/5.33 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.01/5.33 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % integer_of_num_triv(2)
% 5.01/5.33 thf(fact_9466_int__of__integer__code,axiom,
% 5.01/5.33 ( code_int_of_integer
% 5.01/5.33 = ( ^ [K2: code_integer] :
% 5.01/5.33 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.01/5.33 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.01/5.33 @ ( produc1553301316500091796er_int
% 5.01/5.33 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.01/5.33 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_of_integer_code
% 5.01/5.33 thf(fact_9467_bit__cut__integer__def,axiom,
% 5.01/5.33 ( code_bit_cut_integer
% 5.01/5.33 = ( ^ [K2: code_integer] :
% 5.01/5.33 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.01/5.33 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bit_cut_integer_def
% 5.01/5.33 thf(fact_9468_num__of__integer__code,axiom,
% 5.01/5.33 ( code_num_of_integer
% 5.01/5.33 = ( ^ [K2: code_integer] :
% 5.01/5.33 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.01/5.33 @ ( produc7336495610019696514er_num
% 5.01/5.33 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.01/5.33 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % num_of_integer_code
% 5.01/5.33 thf(fact_9469_int__of__integer__of__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.33 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_of_integer_of_nat
% 5.01/5.33 thf(fact_9470_zero__integer_Orep__eq,axiom,
% 5.01/5.33 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 5.01/5.33 = zero_zero_int ) ).
% 5.01/5.33
% 5.01/5.33 % zero_integer.rep_eq
% 5.01/5.33 thf(fact_9471_int__of__integer__numeral,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.01/5.33 = ( numeral_numeral_int @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_of_integer_numeral
% 5.01/5.33 thf(fact_9472_plus__integer_Orep__eq,axiom,
% 5.01/5.33 ! [X2: code_integer,Xa: code_integer] :
% 5.01/5.33 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X2 @ Xa ) )
% 5.01/5.33 = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % plus_integer.rep_eq
% 5.01/5.33 thf(fact_9473_uminus__integer_Orep__eq,axiom,
% 5.01/5.33 ! [X2: code_integer] :
% 5.01/5.33 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X2 ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( code_int_of_integer @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % uminus_integer.rep_eq
% 5.01/5.33 thf(fact_9474_one__integer_Orep__eq,axiom,
% 5.01/5.33 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.01/5.33 = one_one_int ) ).
% 5.01/5.33
% 5.01/5.33 % one_integer.rep_eq
% 5.01/5.33 thf(fact_9475_minus__integer_Orep__eq,axiom,
% 5.01/5.33 ! [X2: code_integer,Xa: code_integer] :
% 5.01/5.33 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X2 @ Xa ) )
% 5.01/5.33 = ( minus_minus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % minus_integer.rep_eq
% 5.01/5.33 thf(fact_9476_divide__integer_Orep__eq,axiom,
% 5.01/5.33 ! [X2: code_integer,Xa: code_integer] :
% 5.01/5.33 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa ) )
% 5.01/5.33 = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divide_integer.rep_eq
% 5.01/5.33 thf(fact_9477_modulo__integer_Orep__eq,axiom,
% 5.01/5.33 ! [X2: code_integer,Xa: code_integer] :
% 5.01/5.33 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X2 @ Xa ) )
% 5.01/5.33 = ( modulo_modulo_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % modulo_integer.rep_eq
% 5.01/5.33 thf(fact_9478_less__eq__integer_Orep__eq,axiom,
% 5.01/5.33 ( ord_le3102999989581377725nteger
% 5.01/5.33 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % less_eq_integer.rep_eq
% 5.01/5.33 thf(fact_9479_integer__less__eq__iff,axiom,
% 5.01/5.33 ( ord_le3102999989581377725nteger
% 5.01/5.33 = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % integer_less_eq_iff
% 5.01/5.33 thf(fact_9480_divmod__integer__def,axiom,
% 5.01/5.33 ( code_divmod_integer
% 5.01/5.33 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L2 ) @ ( modulo364778990260209775nteger @ K2 @ L2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_integer_def
% 5.01/5.33 thf(fact_9481_bit__cut__integer__code,axiom,
% 5.01/5.33 ( code_bit_cut_integer
% 5.01/5.33 = ( ^ [K2: code_integer] :
% 5.01/5.33 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.01/5.33 @ ( produc9125791028180074456eger_o
% 5.01/5.33 @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.01/5.33 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bit_cut_integer_code
% 5.01/5.33 thf(fact_9482_nat__of__integer__code,axiom,
% 5.01/5.33 ( code_nat_of_integer
% 5.01/5.33 = ( ^ [K2: code_integer] :
% 5.01/5.33 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.01/5.33 @ ( produc1555791787009142072er_nat
% 5.01/5.33 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.01/5.33 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_code
% 5.01/5.33 thf(fact_9483_divmod__abs__def,axiom,
% 5.01/5.33 ( code_divmod_abs
% 5.01/5.33 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_abs_def
% 5.01/5.33 thf(fact_9484_nat__of__integer__of__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_of_nat
% 5.01/5.33 thf(fact_9485_nat__of__integer__non__positive,axiom,
% 5.01/5.33 ! [K: code_integer] :
% 5.01/5.33 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.01/5.33 => ( ( code_nat_of_integer @ K )
% 5.01/5.33 = zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_non_positive
% 5.01/5.33 thf(fact_9486_nat__of__integer__code__post_I1_J,axiom,
% 5.01/5.33 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.01/5.33 = zero_zero_nat ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_code_post(1)
% 5.01/5.33 thf(fact_9487_nat__of__integer__code__post_I3_J,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.01/5.33 = ( numeral_numeral_nat @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_code_post(3)
% 5.01/5.33 thf(fact_9488_divmod__abs__code_I6_J,axiom,
% 5.01/5.33 ! [J: code_integer] :
% 5.01/5.33 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.01/5.33 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_abs_code(6)
% 5.01/5.33 thf(fact_9489_nat__of__integer__code__post_I2_J,axiom,
% 5.01/5.33 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.01/5.33 = one_one_nat ) ).
% 5.01/5.33
% 5.01/5.33 % nat_of_integer_code_post(2)
% 5.01/5.33 thf(fact_9490_divmod__abs__code_I5_J,axiom,
% 5.01/5.33 ! [J: code_integer] :
% 5.01/5.33 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.01/5.33 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_abs_code(5)
% 5.01/5.33 thf(fact_9491_divmod__integer__code,axiom,
% 5.01/5.33 ( code_divmod_integer
% 5.01/5.33 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.01/5.33 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.01/5.33 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.01/5.33 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.01/5.33 @ ( produc6916734918728496179nteger
% 5.01/5.33 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 5.01/5.33 @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 5.01/5.33 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.01/5.33 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.01/5.33 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.01/5.33 @ ( produc6916734918728496179nteger
% 5.01/5.33 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 5.01/5.33 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % divmod_integer_code
% 5.01/5.33 thf(fact_9492_or__int__rec,axiom,
% 5.01/5.33 ( bit_se1409905431419307370or_int
% 5.01/5.33 = ( ^ [K2: int,L2: int] :
% 5.01/5.33 ( plus_plus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.01/5.33 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.01/5.33 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_int_rec
% 5.01/5.33 thf(fact_9493_or__nonnegative__int__iff,axiom,
% 5.01/5.33 ! [K: int,L: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.01/5.33 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.01/5.33 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nonnegative_int_iff
% 5.01/5.33 thf(fact_9494_or__negative__int__iff,axiom,
% 5.01/5.33 ! [K: int,L: int] :
% 5.01/5.33 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.01/5.33 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.01/5.33 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_negative_int_iff
% 5.01/5.33 thf(fact_9495_or__minus__numerals_I6_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(6)
% 5.01/5.33 thf(fact_9496_or__minus__numerals_I2_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(2)
% 5.01/5.33 thf(fact_9497_or__minus__minus__numerals,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_minus_numerals
% 5.01/5.33 thf(fact_9498_and__minus__minus__numerals,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_minus_minus_numerals
% 5.01/5.33 thf(fact_9499_bit__or__int__iff,axiom,
% 5.01/5.33 ! [K: int,L: int,N: nat] :
% 5.01/5.33 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 5.01/5.33 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.01/5.33 | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bit_or_int_iff
% 5.01/5.33 thf(fact_9500_or__greater__eq,axiom,
% 5.01/5.33 ! [L: int,K: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.01/5.33 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_greater_eq
% 5.01/5.33 thf(fact_9501_OR__lower,axiom,
% 5.01/5.33 ! [X2: int,Y: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % OR_lower
% 5.01/5.33 thf(fact_9502_plus__and__or,axiom,
% 5.01/5.33 ! [X2: int,Y: int] :
% 5.01/5.33 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se1409905431419307370or_int @ X2 @ Y ) )
% 5.01/5.33 = ( plus_plus_int @ X2 @ Y ) ) ).
% 5.01/5.33
% 5.01/5.33 % plus_and_or
% 5.01/5.33 thf(fact_9503_or__int__def,axiom,
% 5.01/5.33 ( bit_se1409905431419307370or_int
% 5.01/5.33 = ( ^ [K2: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_int_def
% 5.01/5.33 thf(fact_9504_or__not__numerals_I1_J,axiom,
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(1)
% 5.01/5.33 thf(fact_9505_xor__int__def,axiom,
% 5.01/5.33 ( bit_se6526347334894502574or_int
% 5.01/5.33 = ( ^ [K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % xor_int_def
% 5.01/5.33 thf(fact_9506_concat__bit__def,axiom,
% 5.01/5.33 ( bit_concat_bit
% 5.01/5.33 = ( ^ [N4: nat,K2: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N4 @ K2 ) @ ( bit_se545348938243370406it_int @ N4 @ L2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % concat_bit_def
% 5.01/5.33 thf(fact_9507_set__bit__int__def,axiom,
% 5.01/5.33 ( bit_se7879613467334960850it_int
% 5.01/5.33 = ( ^ [N4: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_bit_int_def
% 5.01/5.33 thf(fact_9508_or__not__numerals_I2_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(2)
% 5.01/5.33 thf(fact_9509_or__not__numerals_I4_J,axiom,
% 5.01/5.33 ! [M: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(4)
% 5.01/5.33 thf(fact_9510_or__not__numerals_I3_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(3)
% 5.01/5.33 thf(fact_9511_or__not__numerals_I7_J,axiom,
% 5.01/5.33 ! [M: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.01/5.33 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(7)
% 5.01/5.33 thf(fact_9512_or__not__numerals_I6_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.33 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(6)
% 5.01/5.33 thf(fact_9513_OR__upper,axiom,
% 5.01/5.33 ! [X2: int,N: nat,Y: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.33 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.33 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.01/5.33 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % OR_upper
% 5.01/5.33 thf(fact_9514_or__not__numerals_I5_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(5)
% 5.01/5.33 thf(fact_9515_or__not__numerals_I8_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(8)
% 5.01/5.33 thf(fact_9516_or__not__numerals_I9_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_numerals(9)
% 5.01/5.33 thf(fact_9517_or__minus__numerals_I5_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(5)
% 5.01/5.33 thf(fact_9518_or__minus__numerals_I1_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(1)
% 5.01/5.33 thf(fact_9519_or__nat__numerals_I4_J,axiom,
% 5.01/5.33 ! [X2: num] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_numerals(4)
% 5.01/5.33 thf(fact_9520_or__nat__numerals_I2_J,axiom,
% 5.01/5.33 ! [Y: num] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_numerals(2)
% 5.01/5.33 thf(fact_9521_or__nat__numerals_I3_J,axiom,
% 5.01/5.33 ! [X2: num] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_numerals(3)
% 5.01/5.33 thf(fact_9522_or__nat__numerals_I1_J,axiom,
% 5.01/5.33 ! [Y: num] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.01/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_numerals(1)
% 5.01/5.33 thf(fact_9523_or__minus__numerals_I8_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(8)
% 5.01/5.33 thf(fact_9524_or__minus__numerals_I4_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(4)
% 5.01/5.33 thf(fact_9525_or__minus__numerals_I3_J,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(3)
% 5.01/5.33 thf(fact_9526_or__minus__numerals_I7_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_minus_numerals(7)
% 5.01/5.33 thf(fact_9527_or__not__num__neg_Osimps_I1_J,axiom,
% 5.01/5.33 ( ( bit_or_not_num_neg @ one @ one )
% 5.01/5.33 = one ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(1)
% 5.01/5.33 thf(fact_9528_set__bit__nat__def,axiom,
% 5.01/5.33 ( bit_se7882103937844011126it_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_bit_nat_def
% 5.01/5.33 thf(fact_9529_or__not__num__neg_Osimps_I4_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.01/5.33 = ( bit0 @ one ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(4)
% 5.01/5.33 thf(fact_9530_or__not__num__neg_Osimps_I6_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.01/5.33 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(6)
% 5.01/5.33 thf(fact_9531_or__not__num__neg_Osimps_I3_J,axiom,
% 5.01/5.33 ! [M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.01/5.33 = ( bit1 @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(3)
% 5.01/5.33 thf(fact_9532_or__not__num__neg_Osimps_I7_J,axiom,
% 5.01/5.33 ! [N: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.01/5.33 = one ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(7)
% 5.01/5.33 thf(fact_9533_or__not__num__neg_Osimps_I5_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(5)
% 5.01/5.33 thf(fact_9534_or__not__num__neg_Osimps_I9_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(9)
% 5.01/5.33 thf(fact_9535_or__nat__def,axiom,
% 5.01/5.33 ( bit_se1412395901928357646or_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_def
% 5.01/5.33 thf(fact_9536_or__not__num__neg_Osimps_I2_J,axiom,
% 5.01/5.33 ! [M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.01/5.33 = ( bit1 @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(2)
% 5.01/5.33 thf(fact_9537_or__not__num__neg_Osimps_I8_J,axiom,
% 5.01/5.33 ! [N: num,M: num] :
% 5.01/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.simps(8)
% 5.01/5.33 thf(fact_9538_or__not__num__neg_Oelims,axiom,
% 5.01/5.33 ! [X2: num,Xa: num,Y: num] :
% 5.01/5.33 ( ( ( bit_or_not_num_neg @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( Y != one ) ) )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bit1 @ M4 ) ) ) )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bit1 @ M4 ) ) ) )
% 5.01/5.33 => ( ( ? [N3: num] :
% 5.01/5.33 ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bit0 @ one ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.01/5.33 => ( ( ? [N3: num] :
% 5.01/5.33 ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( Y != one ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.01/5.33 => ~ ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.elims
% 5.01/5.33 thf(fact_9539_int__numeral__or__not__num__neg,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_numeral_or_not_num_neg
% 5.01/5.33 thf(fact_9540_int__numeral__not__or__num__neg,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % int_numeral_not_or_num_neg
% 5.01/5.33 thf(fact_9541_numeral__or__not__num__eq,axiom,
% 5.01/5.33 ! [M: num,N: num] :
% 5.01/5.33 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.01/5.33 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % numeral_or_not_num_eq
% 5.01/5.33 thf(fact_9542_floor__real__def,axiom,
% 5.01/5.33 ( archim6058952711729229775r_real
% 5.01/5.33 = ( ^ [X3: real] :
% 5.01/5.33 ( the_int
% 5.01/5.33 @ ^ [Z5: int] :
% 5.01/5.33 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X3 )
% 5.01/5.33 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % floor_real_def
% 5.01/5.33 thf(fact_9543_Suc__0__or__eq,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.33 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Suc_0_or_eq
% 5.01/5.33 thf(fact_9544_or__Suc__0__eq,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.33 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_Suc_0_eq
% 5.01/5.33 thf(fact_9545_or__nat__rec,axiom,
% 5.01/5.33 ( bit_se1412395901928357646or_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.33 ( plus_plus_nat
% 5.01/5.33 @ ( zero_n2687167440665602831ol_nat
% 5.01/5.33 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.01/5.33 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.33 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_rec
% 5.01/5.33 thf(fact_9546_or__not__num__neg_Opelims,axiom,
% 5.01/5.33 ! [X2: num,Xa: num,Y: num] :
% 5.01/5.33 ( ( ( bit_or_not_num_neg @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X2 @ Xa ) )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( ( Y = one )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.01/5.33 => ( ( ( X2 = one )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bit0 @ one ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit0 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ( ( Xa = one )
% 5.01/5.33 => ( ( Y = one )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.01/5.33 => ( ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit0 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.01/5.33 => ~ ! [N3: num] :
% 5.01/5.33 ( ( X2
% 5.01/5.33 = ( bit1 @ N3 ) )
% 5.01/5.33 => ! [M4: num] :
% 5.01/5.33 ( ( Xa
% 5.01/5.33 = ( bit1 @ M4 ) )
% 5.01/5.33 => ( ( Y
% 5.01/5.33 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.01/5.33 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_not_num_neg.pelims
% 5.01/5.33 thf(fact_9547_or__int__unfold,axiom,
% 5.01/5.33 ( bit_se1409905431419307370or_int
% 5.01/5.33 = ( ^ [K2: int,L2: int] :
% 5.01/5.33 ( if_int
% 5.01/5.33 @ ( ( K2
% 5.01/5.33 = ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.33 | ( L2
% 5.01/5.33 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.01/5.33 @ ( uminus_uminus_int @ one_one_int )
% 5.01/5.33 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_int_unfold
% 5.01/5.33 thf(fact_9548_floor__rat__def,axiom,
% 5.01/5.33 ( archim3151403230148437115or_rat
% 5.01/5.33 = ( ^ [X3: rat] :
% 5.01/5.33 ( the_int
% 5.01/5.33 @ ^ [Z5: int] :
% 5.01/5.33 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X3 )
% 5.01/5.33 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % floor_rat_def
% 5.01/5.33 thf(fact_9549_max__enat__simps_I3_J,axiom,
% 5.01/5.33 ! [Q2: extended_enat] :
% 5.01/5.33 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.01/5.33 = Q2 ) ).
% 5.01/5.33
% 5.01/5.33 % max_enat_simps(3)
% 5.01/5.33 thf(fact_9550_max__enat__simps_I2_J,axiom,
% 5.01/5.33 ! [Q2: extended_enat] :
% 5.01/5.33 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.01/5.33 = Q2 ) ).
% 5.01/5.33
% 5.01/5.33 % max_enat_simps(2)
% 5.01/5.33 thf(fact_9551_max__Suc__Suc,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.01/5.33 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_Suc_Suc
% 5.01/5.33 thf(fact_9552_max__nat_Oeq__neutr__iff,axiom,
% 5.01/5.33 ! [A: nat,B: nat] :
% 5.01/5.33 ( ( ( ord_max_nat @ A @ B )
% 5.01/5.33 = zero_zero_nat )
% 5.01/5.33 = ( ( A = zero_zero_nat )
% 5.01/5.33 & ( B = zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_nat.eq_neutr_iff
% 5.01/5.33 thf(fact_9553_max__nat_Oleft__neutral,axiom,
% 5.01/5.33 ! [A: nat] :
% 5.01/5.33 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.01/5.33 = A ) ).
% 5.01/5.33
% 5.01/5.33 % max_nat.left_neutral
% 5.01/5.33 thf(fact_9554_max__nat_Oneutr__eq__iff,axiom,
% 5.01/5.33 ! [A: nat,B: nat] :
% 5.01/5.33 ( ( zero_zero_nat
% 5.01/5.33 = ( ord_max_nat @ A @ B ) )
% 5.01/5.33 = ( ( A = zero_zero_nat )
% 5.01/5.33 & ( B = zero_zero_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_nat.neutr_eq_iff
% 5.01/5.33 thf(fact_9555_max__nat_Oright__neutral,axiom,
% 5.01/5.33 ! [A: nat] :
% 5.01/5.33 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.01/5.33 = A ) ).
% 5.01/5.33
% 5.01/5.33 % max_nat.right_neutral
% 5.01/5.33 thf(fact_9556_max__0L,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % max_0L
% 5.01/5.33 thf(fact_9557_max__0R,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % max_0R
% 5.01/5.33 thf(fact_9558_of__nat__of__integer,axiom,
% 5.01/5.33 ! [K: code_integer] :
% 5.01/5.33 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 5.01/5.33 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % of_nat_of_integer
% 5.01/5.33 thf(fact_9559_max__numeral__Suc,axiom,
% 5.01/5.33 ! [K: num,N: nat] :
% 5.01/5.33 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.01/5.33 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_numeral_Suc
% 5.01/5.33 thf(fact_9560_max__Suc__numeral,axiom,
% 5.01/5.33 ! [N: nat,K: num] :
% 5.01/5.33 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_Suc_numeral
% 5.01/5.33 thf(fact_9561_nat__add__max__right,axiom,
% 5.01/5.33 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.33 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.01/5.33 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_add_max_right
% 5.01/5.33 thf(fact_9562_nat__add__max__left,axiom,
% 5.01/5.33 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.33 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.01/5.33 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_add_max_left
% 5.01/5.33 thf(fact_9563_nat__mult__max__right,axiom,
% 5.01/5.33 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.33 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.01/5.33 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_mult_max_right
% 5.01/5.33 thf(fact_9564_nat__mult__max__left,axiom,
% 5.01/5.33 ! [M: nat,N: nat,Q2: nat] :
% 5.01/5.33 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.01/5.33 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_mult_max_left
% 5.01/5.33 thf(fact_9565_abs__rat__def,axiom,
% 5.01/5.33 ( abs_abs_rat
% 5.01/5.33 = ( ^ [A4: rat] : ( if_rat @ ( ord_less_rat @ A4 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A4 ) @ A4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % abs_rat_def
% 5.01/5.33 thf(fact_9566_less__eq__rat__def,axiom,
% 5.01/5.33 ( ord_less_eq_rat
% 5.01/5.33 = ( ^ [X3: rat,Y2: rat] :
% 5.01/5.33 ( ( ord_less_rat @ X3 @ Y2 )
% 5.01/5.33 | ( X3 = Y2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % less_eq_rat_def
% 5.01/5.33 thf(fact_9567_sgn__rat__def,axiom,
% 5.01/5.33 ( sgn_sgn_rat
% 5.01/5.33 = ( ^ [A4: rat] : ( if_rat @ ( A4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sgn_rat_def
% 5.01/5.33 thf(fact_9568_obtain__pos__sum,axiom,
% 5.01/5.33 ! [R: rat] :
% 5.01/5.33 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.01/5.33 => ~ ! [S3: rat] :
% 5.01/5.33 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.01/5.33 => ! [T3: rat] :
% 5.01/5.33 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.01/5.33 => ( R
% 5.01/5.33 != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % obtain_pos_sum
% 5.01/5.33 thf(fact_9569_nat__minus__add__max,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.01/5.33 = ( ord_max_nat @ N @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % nat_minus_add_max
% 5.01/5.33 thf(fact_9570_max__Suc1,axiom,
% 5.01/5.33 ! [N: nat,M: nat] :
% 5.01/5.33 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.01/5.33 = ( case_nat_nat @ ( suc @ N )
% 5.01/5.33 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 5.01/5.33 @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_Suc1
% 5.01/5.33 thf(fact_9571_max__Suc2,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.01/5.33 = ( case_nat_nat @ ( suc @ N )
% 5.01/5.33 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 5.01/5.33 @ M ) ) ).
% 5.01/5.33
% 5.01/5.33 % max_Suc2
% 5.01/5.33 thf(fact_9572_or__nat__unfold,axiom,
% 5.01/5.33 ( bit_se1412395901928357646or_nat
% 5.01/5.33 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % or_nat_unfold
% 5.01/5.33 thf(fact_9573_rat__inverse__code,axiom,
% 5.01/5.33 ! [P4: rat] :
% 5.01/5.33 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A4 ) @ B3 ) @ ( abs_abs_int @ A4 ) ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_inverse_code
% 5.01/5.33 thf(fact_9574_normalize__negative,axiom,
% 5.01/5.33 ! [Q2: int,P4: int] :
% 5.01/5.33 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.01/5.33 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.01/5.33 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % normalize_negative
% 5.01/5.33 thf(fact_9575_prod__decode__aux_Oelims,axiom,
% 5.01/5.33 ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.01/5.33 ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 5.01/5.33 & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_decode_aux.elims
% 5.01/5.33 thf(fact_9576_quotient__of__number_I3_J,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.01/5.33 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_number(3)
% 5.01/5.33 thf(fact_9577_normalize__denom__zero,axiom,
% 5.01/5.33 ! [P4: int] :
% 5.01/5.33 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 5.01/5.33 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % normalize_denom_zero
% 5.01/5.33 thf(fact_9578_rat__one__code,axiom,
% 5.01/5.33 ( ( quotient_of @ one_one_rat )
% 5.01/5.33 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_one_code
% 5.01/5.33 thf(fact_9579_rat__zero__code,axiom,
% 5.01/5.33 ( ( quotient_of @ zero_zero_rat )
% 5.01/5.33 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_zero_code
% 5.01/5.33 thf(fact_9580_quotient__of__number_I5_J,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.01/5.33 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_number(5)
% 5.01/5.33 thf(fact_9581_quotient__of__number_I4_J,axiom,
% 5.01/5.33 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.01/5.33 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_number(4)
% 5.01/5.33 thf(fact_9582_diff__rat__def,axiom,
% 5.01/5.33 ( minus_minus_rat
% 5.01/5.33 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % diff_rat_def
% 5.01/5.33 thf(fact_9583_rat__divide__code,axiom,
% 5.01/5.33 ! [P4: rat,Q2: rat] :
% 5.01/5.33 ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q2 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int,C2: int] :
% 5.01/5.33 ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [B3: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ D3 ) @ ( times_times_int @ C2 @ B3 ) ) )
% 5.01/5.33 @ ( quotient_of @ Q2 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_divide_code
% 5.01/5.33 thf(fact_9584_rat__times__code,axiom,
% 5.01/5.33 ! [P4: rat,Q2: rat] :
% 5.01/5.33 ( ( quotient_of @ ( times_times_rat @ P4 @ Q2 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int,C2: int] :
% 5.01/5.33 ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [B3: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A4 @ B3 ) @ ( times_times_int @ C2 @ D3 ) ) )
% 5.01/5.33 @ ( quotient_of @ Q2 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_times_code
% 5.01/5.33 thf(fact_9585_quotient__of__div,axiom,
% 5.01/5.33 ! [R: rat,N: int,D: int] :
% 5.01/5.33 ( ( ( quotient_of @ R )
% 5.01/5.33 = ( product_Pair_int_int @ N @ D ) )
% 5.01/5.33 => ( R
% 5.01/5.33 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_div
% 5.01/5.33 thf(fact_9586_rat__plus__code,axiom,
% 5.01/5.33 ! [P4: rat,Q2: rat] :
% 5.01/5.33 ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q2 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int,C2: int] :
% 5.01/5.33 ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [B3: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A4 @ D3 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D3 ) ) )
% 5.01/5.33 @ ( quotient_of @ Q2 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_plus_code
% 5.01/5.33 thf(fact_9587_rat__minus__code,axiom,
% 5.01/5.33 ! [P4: rat,Q2: rat] :
% 5.01/5.33 ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q2 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int,C2: int] :
% 5.01/5.33 ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [B3: int,D3: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A4 @ D3 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D3 ) ) )
% 5.01/5.33 @ ( quotient_of @ Q2 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_minus_code
% 5.01/5.33 thf(fact_9588_quotient__of__denom__pos,axiom,
% 5.01/5.33 ! [R: rat,P4: int,Q2: int] :
% 5.01/5.33 ( ( ( quotient_of @ R )
% 5.01/5.33 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.01/5.33 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_denom_pos
% 5.01/5.33 thf(fact_9589_rat__uminus__code,axiom,
% 5.01/5.33 ! [P4: rat] :
% 5.01/5.33 ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A4 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_uminus_code
% 5.01/5.33 thf(fact_9590_rat__abs__code,axiom,
% 5.01/5.33 ! [P4: rat] :
% 5.01/5.33 ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 5.01/5.33 = ( produc4245557441103728435nt_int
% 5.01/5.33 @ ^ [A4: int] : ( product_Pair_int_int @ ( abs_abs_int @ A4 ) )
% 5.01/5.33 @ ( quotient_of @ P4 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_abs_code
% 5.01/5.33 thf(fact_9591_normalize__denom__pos,axiom,
% 5.01/5.33 ! [R: product_prod_int_int,P4: int,Q2: int] :
% 5.01/5.33 ( ( ( normalize @ R )
% 5.01/5.33 = ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.01/5.33 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % normalize_denom_pos
% 5.01/5.33 thf(fact_9592_normalize__crossproduct,axiom,
% 5.01/5.33 ! [Q2: int,S2: int,P4: int,R: int] :
% 5.01/5.33 ( ( Q2 != zero_zero_int )
% 5.01/5.33 => ( ( S2 != zero_zero_int )
% 5.01/5.33 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q2 ) )
% 5.01/5.33 = ( normalize @ ( product_Pair_int_int @ R @ S2 ) ) )
% 5.01/5.33 => ( ( times_times_int @ P4 @ S2 )
% 5.01/5.33 = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % normalize_crossproduct
% 5.01/5.33 thf(fact_9593_rat__floor__code,axiom,
% 5.01/5.33 ( archim3151403230148437115or_rat
% 5.01/5.33 = ( ^ [P5: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P5 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_floor_code
% 5.01/5.33 thf(fact_9594_rat__less__eq__code,axiom,
% 5.01/5.33 ( ord_less_eq_rat
% 5.01/5.33 = ( ^ [P5: rat,Q4: rat] :
% 5.01/5.33 ( produc4947309494688390418_int_o
% 5.01/5.33 @ ^ [A4: int,C2: int] :
% 5.01/5.33 ( produc4947309494688390418_int_o
% 5.01/5.33 @ ^ [B3: int,D3: int] : ( ord_less_eq_int @ ( times_times_int @ A4 @ D3 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.01/5.33 @ ( quotient_of @ Q4 ) )
% 5.01/5.33 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % rat_less_eq_code
% 5.01/5.33 thf(fact_9595_prod__decode__aux_Osimps,axiom,
% 5.01/5.33 ( nat_prod_decode_aux
% 5.01/5.33 = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_decode_aux.simps
% 5.01/5.33 thf(fact_9596_prod__decode__aux_Opelims,axiom,
% 5.01/5.33 ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.01/5.33 ( ( ( nat_prod_decode_aux @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 5.01/5.33 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X2 )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X2 @ Xa ) ) ) )
% 5.01/5.33 & ( ~ ( ord_less_eq_nat @ Xa @ X2 )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa @ ( suc @ X2 ) ) ) ) ) )
% 5.01/5.33 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % prod_decode_aux.pelims
% 5.01/5.33 thf(fact_9597_quotient__of__int,axiom,
% 5.01/5.33 ! [A: int] :
% 5.01/5.33 ( ( quotient_of @ ( of_int @ A ) )
% 5.01/5.33 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % quotient_of_int
% 5.01/5.33 thf(fact_9598_bezw__0,axiom,
% 5.01/5.33 ! [X2: nat] :
% 5.01/5.33 ( ( bezw @ X2 @ zero_zero_nat )
% 5.01/5.33 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % bezw_0
% 5.01/5.33 thf(fact_9599_Frct__code__post_I5_J,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.01/5.33 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(5)
% 5.01/5.33 thf(fact_9600_Frct__code__post_I6_J,axiom,
% 5.01/5.33 ! [K: num,L: num] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.01/5.33 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(6)
% 5.01/5.33 thf(fact_9601_finite__atLeastAtMost,axiom,
% 5.01/5.33 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atLeastAtMost
% 5.01/5.33 thf(fact_9602_finite__atLeastLessThan,axiom,
% 5.01/5.33 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atLeastLessThan
% 5.01/5.33 thf(fact_9603_finite__lessThan,axiom,
% 5.01/5.33 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_lessThan
% 5.01/5.33 thf(fact_9604_finite__atMost,axiom,
% 5.01/5.33 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atMost
% 5.01/5.33 thf(fact_9605_set__encode__inverse,axiom,
% 5.01/5.33 ! [A2: set_nat] :
% 5.01/5.33 ( ( finite_finite_nat @ A2 )
% 5.01/5.33 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 5.01/5.33 = A2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_inverse
% 5.01/5.33 thf(fact_9606_finite__nat__set__iff__bounded__le,axiom,
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 = ( ^ [N8: set_nat] :
% 5.01/5.33 ? [M3: nat] :
% 5.01/5.33 ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ N8 )
% 5.01/5.33 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nat_set_iff_bounded_le
% 5.01/5.33 thf(fact_9607_bounded__nat__set__is__finite,axiom,
% 5.01/5.33 ! [N2: set_nat,N: nat] :
% 5.01/5.33 ( ! [X4: nat] :
% 5.01/5.33 ( ( member_nat @ X4 @ N2 )
% 5.01/5.33 => ( ord_less_nat @ X4 @ N ) )
% 5.01/5.33 => ( finite_finite_nat @ N2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % bounded_nat_set_is_finite
% 5.01/5.33 thf(fact_9608_finite__nat__set__iff__bounded,axiom,
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 = ( ^ [N8: set_nat] :
% 5.01/5.33 ? [M3: nat] :
% 5.01/5.33 ! [X3: nat] :
% 5.01/5.33 ( ( member_nat @ X3 @ N8 )
% 5.01/5.33 => ( ord_less_nat @ X3 @ M3 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nat_set_iff_bounded
% 5.01/5.33 thf(fact_9609_finite__M__bounded__by__nat,axiom,
% 5.01/5.33 ! [P: nat > $o,I: nat] :
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( P @ K2 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_M_bounded_by_nat
% 5.01/5.33 thf(fact_9610_finite__less__ub,axiom,
% 5.01/5.33 ! [F: nat > nat,U: nat] :
% 5.01/5.33 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.01/5.33 => ( finite_finite_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_less_ub
% 5.01/5.33 thf(fact_9611_set__encode__eq,axiom,
% 5.01/5.33 ! [A2: set_nat,B4: set_nat] :
% 5.01/5.33 ( ( finite_finite_nat @ A2 )
% 5.01/5.33 => ( ( finite_finite_nat @ B4 )
% 5.01/5.33 => ( ( ( nat_set_encode @ A2 )
% 5.01/5.33 = ( nat_set_encode @ B4 ) )
% 5.01/5.33 = ( A2 = B4 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_eq
% 5.01/5.33 thf(fact_9612_finite__set__decode,axiom,
% 5.01/5.33 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_set_decode
% 5.01/5.33 thf(fact_9613_set__encode__inf,axiom,
% 5.01/5.33 ! [A2: set_nat] :
% 5.01/5.33 ( ~ ( finite_finite_nat @ A2 )
% 5.01/5.33 => ( ( nat_set_encode @ A2 )
% 5.01/5.33 = zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_inf
% 5.01/5.33 thf(fact_9614_finite__divisors__nat,axiom,
% 5.01/5.33 ! [M: nat] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.33 => ( finite_finite_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ M ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_divisors_nat
% 5.01/5.33 thf(fact_9615_subset__eq__atLeast0__atMost__finite,axiom,
% 5.01/5.33 ! [N2: set_nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_set_nat @ N2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 => ( finite_finite_nat @ N2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % subset_eq_atLeast0_atMost_finite
% 5.01/5.33 thf(fact_9616_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.01/5.33 ! [N2: set_nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_set_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 => ( finite_finite_nat @ N2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % subset_eq_atLeast0_lessThan_finite
% 5.01/5.33 thf(fact_9617_Frct__code__post_I2_J,axiom,
% 5.01/5.33 ! [A: int] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.01/5.33 = zero_zero_rat ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(2)
% 5.01/5.33 thf(fact_9618_Frct__code__post_I1_J,axiom,
% 5.01/5.33 ! [A: int] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.01/5.33 = zero_zero_rat ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(1)
% 5.01/5.33 thf(fact_9619_Frct__code__post_I7_J,axiom,
% 5.01/5.33 ! [A: int,B: int] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.01/5.33 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(7)
% 5.01/5.33 thf(fact_9620_Frct__code__post_I8_J,axiom,
% 5.01/5.33 ! [A: int,B: int] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.01/5.33 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(8)
% 5.01/5.33 thf(fact_9621_Frct__code__post_I3_J,axiom,
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.01/5.33 = one_one_rat ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(3)
% 5.01/5.33 thf(fact_9622_even__set__encode__iff,axiom,
% 5.01/5.33 ! [A2: set_nat] :
% 5.01/5.33 ( ( finite_finite_nat @ A2 )
% 5.01/5.33 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.01/5.33 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % even_set_encode_iff
% 5.01/5.33 thf(fact_9623_Frct__code__post_I4_J,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.01/5.33 = ( numeral_numeral_rat @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % Frct_code_post(4)
% 5.01/5.33 thf(fact_9624_finite__Collect__le__nat,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_Collect_le_nat
% 5.01/5.33 thf(fact_9625_finite__Collect__less__nat,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [N4: nat] : ( ord_less_nat @ N4 @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_Collect_less_nat
% 5.01/5.33 thf(fact_9626_finite__atLeastAtMost__int,axiom,
% 5.01/5.33 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atLeastAtMost_int
% 5.01/5.33 thf(fact_9627_finite__atLeastLessThan__int,axiom,
% 5.01/5.33 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atLeastLessThan_int
% 5.01/5.33 thf(fact_9628_finite__interval__int1,axiom,
% 5.01/5.33 ! [A: int,B: int] :
% 5.01/5.33 ( finite_finite_int
% 5.01/5.33 @ ( collect_int
% 5.01/5.33 @ ^ [I4: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ A @ I4 )
% 5.01/5.33 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_interval_int1
% 5.01/5.33 thf(fact_9629_finite__interval__int2,axiom,
% 5.01/5.33 ! [A: int,B: int] :
% 5.01/5.33 ( finite_finite_int
% 5.01/5.33 @ ( collect_int
% 5.01/5.33 @ ^ [I4: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ A @ I4 )
% 5.01/5.33 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_interval_int2
% 5.01/5.33 thf(fact_9630_finite__interval__int3,axiom,
% 5.01/5.33 ! [A: int,B: int] :
% 5.01/5.33 ( finite_finite_int
% 5.01/5.33 @ ( collect_int
% 5.01/5.33 @ ^ [I4: int] :
% 5.01/5.33 ( ( ord_less_int @ A @ I4 )
% 5.01/5.33 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_interval_int3
% 5.01/5.33 thf(fact_9631_finite__nth__roots,axiom,
% 5.01/5.33 ! [N: nat,C: complex] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( finite3207457112153483333omplex
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = C ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nth_roots
% 5.01/5.33 thf(fact_9632_finite__atLeastZeroLessThan__int,axiom,
% 5.01/5.33 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_atLeastZeroLessThan_int
% 5.01/5.33 thf(fact_9633_finite__divisors__int,axiom,
% 5.01/5.33 ! [I: int] :
% 5.01/5.33 ( ( I != zero_zero_int )
% 5.01/5.33 => ( finite_finite_int
% 5.01/5.33 @ ( collect_int
% 5.01/5.33 @ ^ [D3: int] : ( dvd_dvd_int @ D3 @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_divisors_int
% 5.01/5.33 thf(fact_9634_finite__nat__iff__bounded__le,axiom,
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 = ( ^ [S5: set_nat] :
% 5.01/5.33 ? [K2: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nat_iff_bounded_le
% 5.01/5.33 thf(fact_9635_finite__nat__bounded,axiom,
% 5.01/5.33 ! [S: set_nat] :
% 5.01/5.33 ( ( finite_finite_nat @ S )
% 5.01/5.33 => ? [K3: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nat_bounded
% 5.01/5.33 thf(fact_9636_finite__nat__iff__bounded,axiom,
% 5.01/5.33 ( finite_finite_nat
% 5.01/5.33 = ( ^ [S5: set_nat] :
% 5.01/5.33 ? [K2: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % finite_nat_iff_bounded
% 5.01/5.33 thf(fact_9637_infinite__int__iff__unbounded__le,axiom,
% 5.01/5.33 ! [S: set_int] :
% 5.01/5.33 ( ( ~ ( finite_finite_int @ S ) )
% 5.01/5.33 = ( ! [M3: int] :
% 5.01/5.33 ? [N4: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N4 ) )
% 5.01/5.33 & ( member_int @ N4 @ S ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % infinite_int_iff_unbounded_le
% 5.01/5.33 thf(fact_9638_unbounded__k__infinite,axiom,
% 5.01/5.33 ! [K: nat,S: set_nat] :
% 5.01/5.33 ( ! [M4: nat] :
% 5.01/5.33 ( ( ord_less_nat @ K @ M4 )
% 5.01/5.33 => ? [N6: nat] :
% 5.01/5.33 ( ( ord_less_nat @ M4 @ N6 )
% 5.01/5.33 & ( member_nat @ N6 @ S ) ) )
% 5.01/5.33 => ~ ( finite_finite_nat @ S ) ) ).
% 5.01/5.33
% 5.01/5.33 % unbounded_k_infinite
% 5.01/5.33 thf(fact_9639_infinite__nat__iff__unbounded,axiom,
% 5.01/5.33 ! [S: set_nat] :
% 5.01/5.33 ( ( ~ ( finite_finite_nat @ S ) )
% 5.01/5.33 = ( ! [M3: nat] :
% 5.01/5.33 ? [N4: nat] :
% 5.01/5.33 ( ( ord_less_nat @ M3 @ N4 )
% 5.01/5.33 & ( member_nat @ N4 @ S ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % infinite_nat_iff_unbounded
% 5.01/5.33 thf(fact_9640_infinite__nat__iff__unbounded__le,axiom,
% 5.01/5.33 ! [S: set_nat] :
% 5.01/5.33 ( ( ~ ( finite_finite_nat @ S ) )
% 5.01/5.33 = ( ! [M3: nat] :
% 5.01/5.33 ? [N4: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M3 @ N4 )
% 5.01/5.33 & ( member_nat @ N4 @ S ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % infinite_nat_iff_unbounded_le
% 5.01/5.33 thf(fact_9641_bij__betw__nth__root__unity,axiom,
% 5.01/5.33 ! [C: complex,N: nat] :
% 5.01/5.33 ( ( C != zero_zero_complex )
% 5.01/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = one_one_complex ) )
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = C ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % bij_betw_nth_root_unity
% 5.01/5.33 thf(fact_9642_real__root__zero,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( root @ N @ zero_zero_real )
% 5.01/5.33 = zero_zero_real ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_zero
% 5.01/5.33 thf(fact_9643_real__root__Suc__0,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.01/5.33 = X2 ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_Suc_0
% 5.01/5.33 thf(fact_9644_root__0,axiom,
% 5.01/5.33 ! [X2: real] :
% 5.01/5.33 ( ( root @ zero_zero_nat @ X2 )
% 5.01/5.33 = zero_zero_real ) ).
% 5.01/5.33
% 5.01/5.33 % root_0
% 5.01/5.33 thf(fact_9645_real__root__eq__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ( root @ N @ X2 )
% 5.01/5.33 = ( root @ N @ Y ) )
% 5.01/5.33 = ( X2 = Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_eq_iff
% 5.01/5.33 thf(fact_9646_real__root__eq__0__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ( root @ N @ X2 )
% 5.01/5.33 = zero_zero_real )
% 5.01/5.33 = ( X2 = zero_zero_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_eq_0_iff
% 5.01/5.33 thf(fact_9647_real__root__less__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_real @ X2 @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_less_iff
% 5.01/5.33 thf(fact_9648_real__root__le__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_le_iff
% 5.01/5.33 thf(fact_9649_real__root__eq__1__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ( root @ N @ X2 )
% 5.01/5.33 = one_one_real )
% 5.01/5.33 = ( X2 = one_one_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_eq_1_iff
% 5.01/5.33 thf(fact_9650_real__root__one,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( root @ N @ one_one_real )
% 5.01/5.33 = one_one_real ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_one
% 5.01/5.33 thf(fact_9651_real__root__gt__0__iff,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_gt_0_iff
% 5.01/5.33 thf(fact_9652_real__root__lt__0__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_lt_0_iff
% 5.01/5.33 thf(fact_9653_real__root__le__0__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.01/5.33 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_le_0_iff
% 5.01/5.33 thf(fact_9654_real__root__ge__0__iff,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_ge_0_iff
% 5.01/5.33 thf(fact_9655_real__root__lt__1__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.01/5.33 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_lt_1_iff
% 5.01/5.33 thf(fact_9656_real__root__gt__1__iff,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_gt_1_iff
% 5.01/5.33 thf(fact_9657_real__root__ge__1__iff,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 5.01/5.33 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_ge_1_iff
% 5.01/5.33 thf(fact_9658_real__root__le__1__iff,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.01/5.33 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_le_1_iff
% 5.01/5.33 thf(fact_9659_real__root__pow__pos2,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.01/5.33 = X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_pow_pos2
% 5.01/5.33 thf(fact_9660_real__root__inverse,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( root @ N @ ( inverse_inverse_real @ X2 ) )
% 5.01/5.33 = ( inverse_inverse_real @ ( root @ N @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_inverse
% 5.01/5.33 thf(fact_9661_real__root__commute,axiom,
% 5.01/5.33 ! [M: nat,N: nat,X2: real] :
% 5.01/5.33 ( ( root @ M @ ( root @ N @ X2 ) )
% 5.01/5.33 = ( root @ N @ ( root @ M @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_commute
% 5.01/5.33 thf(fact_9662_real__root__divide,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( root @ N @ ( divide_divide_real @ X2 @ Y ) )
% 5.01/5.33 = ( divide_divide_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_divide
% 5.01/5.33 thf(fact_9663_real__root__mult__exp,axiom,
% 5.01/5.33 ! [M: nat,N: nat,X2: real] :
% 5.01/5.33 ( ( root @ ( times_times_nat @ M @ N ) @ X2 )
% 5.01/5.33 = ( root @ M @ ( root @ N @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_mult_exp
% 5.01/5.33 thf(fact_9664_real__root__mult,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( root @ N @ ( times_times_real @ X2 @ Y ) )
% 5.01/5.33 = ( times_times_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_mult
% 5.01/5.33 thf(fact_9665_real__root__minus,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( root @ N @ ( uminus_uminus_real @ X2 ) )
% 5.01/5.33 = ( uminus_uminus_real @ ( root @ N @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_minus
% 5.01/5.33 thf(fact_9666_real__root__pos__pos__le,axiom,
% 5.01/5.33 ! [X2: real,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_pos_pos_le
% 5.01/5.33 thf(fact_9667_real__root__less__mono,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ X2 @ Y )
% 5.01/5.33 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_less_mono
% 5.01/5.33 thf(fact_9668_real__root__le__mono,axiom,
% 5.01/5.33 ! [N: nat,X2: real,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.01/5.33 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_le_mono
% 5.01/5.33 thf(fact_9669_real__root__power,axiom,
% 5.01/5.33 ! [N: nat,X2: real,K: nat] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.01/5.33 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_power
% 5.01/5.33 thf(fact_9670_real__root__abs,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.01/5.33 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_abs
% 5.01/5.33 thf(fact_9671_sgn__root,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.01/5.33 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sgn_root
% 5.01/5.33 thf(fact_9672_real__root__gt__zero,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_gt_zero
% 5.01/5.33 thf(fact_9673_real__root__strict__decreasing,axiom,
% 5.01/5.33 ! [N: nat,N2: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_nat @ N @ N2 )
% 5.01/5.33 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.33 => ( ord_less_real @ ( root @ N2 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_strict_decreasing
% 5.01/5.33 thf(fact_9674_sqrt__def,axiom,
% 5.01/5.33 ( sqrt
% 5.01/5.33 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sqrt_def
% 5.01/5.33 thf(fact_9675_root__abs__power,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 5.01/5.33 = ( abs_abs_real @ Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % root_abs_power
% 5.01/5.33 thf(fact_9676_real__root__pos__pos,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_pos_pos
% 5.01/5.33 thf(fact_9677_real__root__strict__increasing,axiom,
% 5.01/5.33 ! [N: nat,N2: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_nat @ N @ N2 )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.33 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N2 @ X2 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_strict_increasing
% 5.01/5.33 thf(fact_9678_real__root__decreasing,axiom,
% 5.01/5.33 ! [N: nat,N2: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.33 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.01/5.33 => ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_decreasing
% 5.01/5.33 thf(fact_9679_real__root__pow__pos,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.01/5.33 = X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_pow_pos
% 5.01/5.33 thf(fact_9680_real__root__power__cancel,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.01/5.33 = X2 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_power_cancel
% 5.01/5.33 thf(fact_9681_real__root__pos__unique,axiom,
% 5.01/5.33 ! [N: nat,Y: real,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.01/5.33 => ( ( ( power_power_real @ Y @ N )
% 5.01/5.33 = X2 )
% 5.01/5.33 => ( ( root @ N @ X2 )
% 5.01/5.33 = Y ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_pos_unique
% 5.01/5.33 thf(fact_9682_odd__real__root__power__cancel,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.33 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % odd_real_root_power_cancel
% 5.01/5.33 thf(fact_9683_odd__real__root__unique,axiom,
% 5.01/5.33 ! [N: nat,Y: real,X2: real] :
% 5.01/5.33 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.33 => ( ( ( power_power_real @ Y @ N )
% 5.01/5.33 = X2 )
% 5.01/5.33 => ( ( root @ N @ X2 )
% 5.01/5.33 = Y ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % odd_real_root_unique
% 5.01/5.33 thf(fact_9684_odd__real__root__pow,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.33 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % odd_real_root_pow
% 5.01/5.33 thf(fact_9685_real__root__increasing,axiom,
% 5.01/5.33 ! [N: nat,N2: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_eq_nat @ N @ N2 )
% 5.01/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.01/5.33 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N2 @ X2 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % real_root_increasing
% 5.01/5.33 thf(fact_9686_sgn__power__root,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.01/5.33 = X2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % sgn_power_root
% 5.01/5.33 thf(fact_9687_root__sgn__power,axiom,
% 5.01/5.33 ! [N: nat,Y: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 5.01/5.33 = Y ) ) ).
% 5.01/5.33
% 5.01/5.33 % root_sgn_power
% 5.01/5.33 thf(fact_9688_ln__root,axiom,
% 5.01/5.33 ! [N: nat,B: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.33 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.01/5.33 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % ln_root
% 5.01/5.33 thf(fact_9689_log__root,axiom,
% 5.01/5.33 ! [N: nat,A: real,B: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.01/5.33 => ( ( log @ B @ ( root @ N @ A ) )
% 5.01/5.33 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % log_root
% 5.01/5.33 thf(fact_9690_log__base__root,axiom,
% 5.01/5.33 ! [N: nat,B: real,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.01/5.33 => ( ( log @ ( root @ N @ B ) @ X2 )
% 5.01/5.33 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % log_base_root
% 5.01/5.33 thf(fact_9691_split__root,axiom,
% 5.01/5.33 ! [P: real > $o,N: nat,X2: real] :
% 5.01/5.33 ( ( P @ ( root @ N @ X2 ) )
% 5.01/5.33 = ( ( ( N = zero_zero_nat )
% 5.01/5.33 => ( P @ zero_zero_real ) )
% 5.01/5.33 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ! [Y2: real] :
% 5.01/5.33 ( ( ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N ) )
% 5.01/5.33 = X2 )
% 5.01/5.33 => ( P @ Y2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % split_root
% 5.01/5.33 thf(fact_9692_root__powr__inverse,axiom,
% 5.01/5.33 ! [N: nat,X2: real] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.33 => ( ( root @ N @ X2 )
% 5.01/5.33 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % root_powr_inverse
% 5.01/5.33 thf(fact_9693_set__encode__insert,axiom,
% 5.01/5.33 ! [A2: set_nat,N: nat] :
% 5.01/5.33 ( ( finite_finite_nat @ A2 )
% 5.01/5.33 => ( ~ ( member_nat @ N @ A2 )
% 5.01/5.33 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.01/5.33 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_insert
% 5.01/5.33 thf(fact_9694_card__lessThan,axiom,
% 5.01/5.33 ! [U: nat] :
% 5.01/5.33 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.01/5.33 = U ) ).
% 5.01/5.33
% 5.01/5.33 % card_lessThan
% 5.01/5.33 thf(fact_9695_card__Collect__less__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.01/5.33 = N ) ).
% 5.01/5.33
% 5.01/5.33 % card_Collect_less_nat
% 5.01/5.33 thf(fact_9696_card__atMost,axiom,
% 5.01/5.33 ! [U: nat] :
% 5.01/5.33 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.01/5.33 = ( suc @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atMost
% 5.01/5.33 thf(fact_9697_card__atLeastLessThan,axiom,
% 5.01/5.33 ! [L: nat,U: nat] :
% 5.01/5.33 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.01/5.33 = ( minus_minus_nat @ U @ L ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atLeastLessThan
% 5.01/5.33 thf(fact_9698_card__Collect__le__nat,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.01/5.33 = ( suc @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_Collect_le_nat
% 5.01/5.33 thf(fact_9699_card__atLeastAtMost,axiom,
% 5.01/5.33 ! [L: nat,U: nat] :
% 5.01/5.33 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.01/5.33 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atLeastAtMost
% 5.01/5.33 thf(fact_9700_card__atLeastLessThan__int,axiom,
% 5.01/5.33 ! [L: int,U: int] :
% 5.01/5.33 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.01/5.33 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atLeastLessThan_int
% 5.01/5.33 thf(fact_9701_card__atLeastAtMost__int,axiom,
% 5.01/5.33 ! [L: int,U: int] :
% 5.01/5.33 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.01/5.33 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atLeastAtMost_int
% 5.01/5.33 thf(fact_9702_sum__list__upt,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.01/5.33 = ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sum_list_upt
% 5.01/5.33 thf(fact_9703_lessThan__Suc,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.01/5.33 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_Suc
% 5.01/5.33 thf(fact_9704_atMost__Suc,axiom,
% 5.01/5.33 ! [K: nat] :
% 5.01/5.33 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.01/5.33 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atMost_Suc
% 5.01/5.33 thf(fact_9705_card__length__sum__list__rec,axiom,
% 5.01/5.33 ! [M: nat,N2: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.01/5.33 => ( ( finite_card_list_nat
% 5.01/5.33 @ ( collect_list_nat
% 5.01/5.33 @ ^ [L2: list_nat] :
% 5.01/5.33 ( ( ( size_size_list_nat @ L2 )
% 5.01/5.33 = M )
% 5.01/5.33 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.01/5.33 = N2 ) ) ) )
% 5.01/5.33 = ( plus_plus_nat
% 5.01/5.33 @ ( finite_card_list_nat
% 5.01/5.33 @ ( collect_list_nat
% 5.01/5.33 @ ^ [L2: list_nat] :
% 5.01/5.33 ( ( ( size_size_list_nat @ L2 )
% 5.01/5.33 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.01/5.33 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.01/5.33 = N2 ) ) ) )
% 5.01/5.33 @ ( finite_card_list_nat
% 5.01/5.33 @ ( collect_list_nat
% 5.01/5.33 @ ^ [L2: list_nat] :
% 5.01/5.33 ( ( ( size_size_list_nat @ L2 )
% 5.01/5.33 = M )
% 5.01/5.33 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.01/5.33 = N2 ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_length_sum_list_rec
% 5.01/5.33 thf(fact_9706_card__length__sum__list,axiom,
% 5.01/5.33 ! [M: nat,N2: nat] :
% 5.01/5.33 ( ( finite_card_list_nat
% 5.01/5.33 @ ( collect_list_nat
% 5.01/5.33 @ ^ [L2: list_nat] :
% 5.01/5.33 ( ( ( size_size_list_nat @ L2 )
% 5.01/5.33 = M )
% 5.01/5.33 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.01/5.33 = N2 ) ) ) )
% 5.01/5.33 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ N2 ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_length_sum_list
% 5.01/5.33 thf(fact_9707_atLeast0__atMost__Suc,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.01/5.33 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeast0_atMost_Suc
% 5.01/5.33 thf(fact_9708_atLeast0__lessThan__Suc,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.01/5.33 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeast0_lessThan_Suc
% 5.01/5.33 thf(fact_9709_atLeastAtMost__insertL,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.01/5.33 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastAtMost_insertL
% 5.01/5.33 thf(fact_9710_atLeastAtMostSuc__conv,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.01/5.33 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.01/5.33 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastAtMostSuc_conv
% 5.01/5.33 thf(fact_9711_Icc__eq__insert__lb__nat,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.01/5.33 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Icc_eq_insert_lb_nat
% 5.01/5.33 thf(fact_9712_lessThan__nat__numeral,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_nat_numeral
% 5.01/5.33 thf(fact_9713_card__less__Suc2,axiom,
% 5.01/5.33 ! [M7: set_nat,I: nat] :
% 5.01/5.33 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.01/5.33 => ( ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.01/5.33 = ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( member_nat @ K2 @ M7 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_less_Suc2
% 5.01/5.33 thf(fact_9714_card__less__Suc,axiom,
% 5.01/5.33 ! [M7: set_nat,I: nat] :
% 5.01/5.33 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.01/5.33 => ( ( suc
% 5.01/5.33 @ ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.01/5.33 = ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( member_nat @ K2 @ M7 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_less_Suc
% 5.01/5.33 thf(fact_9715_card__less,axiom,
% 5.01/5.33 ! [M7: set_nat,I: nat] :
% 5.01/5.33 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.01/5.33 => ( ( finite_card_nat
% 5.01/5.33 @ ( collect_nat
% 5.01/5.33 @ ^ [K2: nat] :
% 5.01/5.33 ( ( member_nat @ K2 @ M7 )
% 5.01/5.33 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.01/5.33 != zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_less
% 5.01/5.33 thf(fact_9716_atMost__nat__numeral,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atMost_nat_numeral
% 5.01/5.33 thf(fact_9717_card__atLeastZeroLessThan__int,axiom,
% 5.01/5.33 ! [U: int] :
% 5.01/5.33 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.01/5.33 = ( nat2 @ U ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_atLeastZeroLessThan_int
% 5.01/5.33 thf(fact_9718_subset__card__intvl__is__intvl,axiom,
% 5.01/5.33 ! [A2: set_nat,K: nat] :
% 5.01/5.33 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.01/5.33 => ( A2
% 5.01/5.33 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % subset_card_intvl_is_intvl
% 5.01/5.33 thf(fact_9719_subset__eq__atLeast0__lessThan__card,axiom,
% 5.01/5.33 ! [N2: set_nat,N: nat] :
% 5.01/5.33 ( ( ord_less_eq_set_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.01/5.33 => ( ord_less_eq_nat @ ( finite_card_nat @ N2 ) @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % subset_eq_atLeast0_lessThan_card
% 5.01/5.33 thf(fact_9720_card__sum__le__nat__sum,axiom,
% 5.01/5.33 ! [S: set_nat] :
% 5.01/5.33 ( ord_less_eq_nat
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.01/5.33 @ ( groups3542108847815614940at_nat
% 5.01/5.33 @ ^ [X3: nat] : X3
% 5.01/5.33 @ S ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_sum_le_nat_sum
% 5.01/5.33 thf(fact_9721_card__nth__roots,axiom,
% 5.01/5.33 ! [C: complex,N: nat] :
% 5.01/5.33 ( ( C != zero_zero_complex )
% 5.01/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( finite_card_complex
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = C ) ) )
% 5.01/5.33 = N ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_nth_roots
% 5.01/5.33 thf(fact_9722_card__roots__unity__eq,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.33 => ( ( finite_card_complex
% 5.01/5.33 @ ( collect_complex
% 5.01/5.33 @ ^ [Z5: complex] :
% 5.01/5.33 ( ( power_power_complex @ Z5 @ N )
% 5.01/5.33 = one_one_complex ) ) )
% 5.01/5.33 = N ) ) ).
% 5.01/5.33
% 5.01/5.33 % card_roots_unity_eq
% 5.01/5.33 thf(fact_9723_set__decode__plus__power__2,axiom,
% 5.01/5.33 ! [N: nat,Z: nat] :
% 5.01/5.33 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.01/5.33 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.01/5.33 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % set_decode_plus_power_2
% 5.01/5.33 thf(fact_9724_distinct__upt,axiom,
% 5.01/5.33 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 5.01/5.33
% 5.01/5.33 % distinct_upt
% 5.01/5.33 thf(fact_9725_sorted__wrt__upt,axiom,
% 5.01/5.33 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % sorted_wrt_upt
% 5.01/5.33 thf(fact_9726_sorted__upt,axiom,
% 5.01/5.33 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % sorted_upt
% 5.01/5.33 thf(fact_9727_atLeastAtMostPlus1__int__conv,axiom,
% 5.01/5.33 ! [M: int,N: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.01/5.33 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.01/5.33 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastAtMostPlus1_int_conv
% 5.01/5.33 thf(fact_9728_sorted__wrt__less__idx,axiom,
% 5.01/5.33 ! [Ns: list_nat,I: nat] :
% 5.01/5.33 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.01/5.33 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.01/5.33 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % sorted_wrt_less_idx
% 5.01/5.33 thf(fact_9729_and__int_Osimps,axiom,
% 5.01/5.33 ( bit_se725231765392027082nd_int
% 5.01/5.33 = ( ^ [K2: int,L2: int] :
% 5.01/5.33 ( if_int
% 5.01/5.33 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 @ ( uminus_uminus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.01/5.33 @ ( plus_plus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.01/5.33 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_int.simps
% 5.01/5.33 thf(fact_9730_and__int_Oelims,axiom,
% 5.01/5.33 ! [X2: int,Xa: int,Y: int] :
% 5.01/5.33 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( uminus_uminus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( plus_plus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.01/5.33 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_int.elims
% 5.01/5.33 thf(fact_9731_and__int_Opsimps,axiom,
% 5.01/5.33 ! [K: int,L: int] :
% 5.01/5.33 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.01/5.33 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.01/5.33 = ( uminus_uminus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.01/5.33 = ( plus_plus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.01/5.33 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_int.psimps
% 5.01/5.33 thf(fact_9732_simp__from__to,axiom,
% 5.01/5.33 ( set_or1266510415728281911st_int
% 5.01/5.33 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % simp_from_to
% 5.01/5.33 thf(fact_9733_and__int_Opinduct,axiom,
% 5.01/5.33 ! [A0: int,A12: int,P: int > int > $o] :
% 5.01/5.33 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.01/5.33 => ( ! [K3: int,L3: int] :
% 5.01/5.33 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L3 ) )
% 5.01/5.33 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.01/5.33 => ( P @ K3 @ L3 ) ) )
% 5.01/5.33 => ( P @ A0 @ A12 ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_int.pinduct
% 5.01/5.33 thf(fact_9734_and__int_Opelims,axiom,
% 5.01/5.33 ! [X2: int,Xa: int,Y: int] :
% 5.01/5.33 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa )
% 5.01/5.33 = Y )
% 5.01/5.33 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 5.01/5.33 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( uminus_uminus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.01/5.33 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.01/5.33 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.01/5.33 => ( Y
% 5.01/5.33 = ( plus_plus_int
% 5.01/5.33 @ ( zero_n2684676970156552555ol_int
% 5.01/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.01/5.33 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.01/5.33 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.01/5.33 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % and_int.pelims
% 5.01/5.33 thf(fact_9735_lessThan__0,axiom,
% 5.01/5.33 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.01/5.33 = bot_bot_set_nat ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_0
% 5.01/5.33 thf(fact_9736_set__decode__zero,axiom,
% 5.01/5.33 ( ( nat_set_decode @ zero_zero_nat )
% 5.01/5.33 = bot_bot_set_nat ) ).
% 5.01/5.33
% 5.01/5.33 % set_decode_zero
% 5.01/5.33 thf(fact_9737_set__encode__empty,axiom,
% 5.01/5.33 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.01/5.33 = zero_zero_nat ) ).
% 5.01/5.33
% 5.01/5.33 % set_encode_empty
% 5.01/5.33 thf(fact_9738_atLeastLessThan__singleton,axiom,
% 5.01/5.33 ! [M: nat] :
% 5.01/5.33 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.01/5.33 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThan_singleton
% 5.01/5.33 thf(fact_9739_atMost__0,axiom,
% 5.01/5.33 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.01/5.33 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % atMost_0
% 5.01/5.33 thf(fact_9740_bot__enat__def,axiom,
% 5.01/5.33 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.01/5.33
% 5.01/5.33 % bot_enat_def
% 5.01/5.33 thf(fact_9741_bot__nat__def,axiom,
% 5.01/5.33 bot_bot_nat = zero_zero_nat ).
% 5.01/5.33
% 5.01/5.33 % bot_nat_def
% 5.01/5.33 thf(fact_9742_atLeastLessThan0,axiom,
% 5.01/5.33 ! [M: nat] :
% 5.01/5.33 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.01/5.33 = bot_bot_set_nat ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThan0
% 5.01/5.33 thf(fact_9743_lessThan__empty__iff,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( ( set_ord_lessThan_nat @ N )
% 5.01/5.33 = bot_bot_set_nat )
% 5.01/5.33 = ( N = zero_zero_nat ) ) ).
% 5.01/5.33
% 5.01/5.33 % lessThan_empty_iff
% 5.01/5.33 thf(fact_9744_atLeastLessThanSuc,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.01/5.33 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.01/5.33 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.01/5.33 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.01/5.33 = bot_bot_set_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThanSuc
% 5.01/5.33 thf(fact_9745_atLeast1__lessThan__eq__remove0,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.33 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeast1_lessThan_eq_remove0
% 5.01/5.33 thf(fact_9746_atLeast1__atMost__eq__remove0,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.01/5.33 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeast1_atMost_eq_remove0
% 5.01/5.33 thf(fact_9747_atLeastLessThan__nat__numeral,axiom,
% 5.01/5.33 ! [M: nat,K: num] :
% 5.01/5.33 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.01/5.33 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.01/5.33 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.01/5.33 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = bot_bot_set_nat ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % atLeastLessThan_nat_numeral
% 5.01/5.33 thf(fact_9748_sorted__list__of__set__range,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.01/5.33 = ( upt @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % sorted_list_of_set_range
% 5.01/5.33 thf(fact_9749_binomial__def,axiom,
% 5.01/5.33 ( binomial
% 5.01/5.33 = ( ^ [N4: nat,K2: nat] :
% 5.01/5.33 ( finite_card_set_nat
% 5.01/5.33 @ ( collect_set_nat
% 5.01/5.33 @ ^ [K7: set_nat] :
% 5.01/5.33 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 5.01/5.33 & ( ( finite_card_nat @ K7 )
% 5.01/5.33 = K2 ) ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % binomial_def
% 5.01/5.33 thf(fact_9750_Suc__0__div__numeral,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Suc_0_div_numeral
% 5.01/5.33 thf(fact_9751_Suc__0__mod__numeral,axiom,
% 5.01/5.33 ! [K: num] :
% 5.01/5.33 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.01/5.33 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % Suc_0_mod_numeral
% 5.01/5.33 thf(fact_9752_drop__bit__numeral__minus__bit1,axiom,
% 5.01/5.33 ! [L: num,K: num] :
% 5.01/5.33 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.33 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.01/5.33
% 5.01/5.33 % drop_bit_numeral_minus_bit1
% 5.01/5.33 thf(fact_9753_drop__bit__nonnegative__int__iff,axiom,
% 5.01/5.33 ! [N: nat,K: int] :
% 5.01/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.01/5.33 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.01/5.33
% 5.01/5.33 % drop_bit_nonnegative_int_iff
% 5.01/5.33 thf(fact_9754_drop__bit__negative__int__iff,axiom,
% 5.01/5.33 ! [N: nat,K: int] :
% 5.01/5.33 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.01/5.33 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % drop_bit_negative_int_iff
% 5.01/5.33 thf(fact_9755_drop__bit__minus__one,axiom,
% 5.01/5.33 ! [N: nat] :
% 5.01/5.33 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.01/5.33 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.01/5.33
% 5.01/5.33 % drop_bit_minus_one
% 5.01/5.33 thf(fact_9756_fst__divmod__nat,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.01/5.33 = ( divide_divide_nat @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % fst_divmod_nat
% 5.01/5.33 thf(fact_9757_snd__divmod__nat,axiom,
% 5.01/5.33 ! [M: nat,N: nat] :
% 5.01/5.33 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.01/5.33 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.01/5.33
% 5.01/5.33 % snd_divmod_nat
% 5.01/5.33 thf(fact_9758_drop__bit__Suc__minus__bit0,axiom,
% 5.01/5.33 ! [N: nat,K: num] :
% 5.01/5.33 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.34 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_Suc_minus_bit0
% 5.01/5.34 thf(fact_9759_drop__bit__numeral__minus__bit0,axiom,
% 5.01/5.34 ! [L: num,K: num] :
% 5.01/5.34 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.01/5.34 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_numeral_minus_bit0
% 5.01/5.34 thf(fact_9760_drop__bit__Suc__minus__bit1,axiom,
% 5.01/5.34 ! [N: nat,K: num] :
% 5.01/5.34 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.01/5.34 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_Suc_minus_bit1
% 5.01/5.34 thf(fact_9761_drop__bit__push__bit__int,axiom,
% 5.01/5.34 ! [M: nat,N: nat,K: int] :
% 5.01/5.34 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.01/5.34 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_push_bit_int
% 5.01/5.34 thf(fact_9762_drop__bit__int__def,axiom,
% 5.01/5.34 ( bit_se8568078237143864401it_int
% 5.01/5.34 = ( ^ [N4: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_int_def
% 5.01/5.34 thf(fact_9763_snd__divmod__integer,axiom,
% 5.01/5.34 ! [K: code_integer,L: code_integer] :
% 5.01/5.34 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 5.01/5.34 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 5.01/5.34
% 5.01/5.34 % snd_divmod_integer
% 5.01/5.34 thf(fact_9764_snd__divmod__abs,axiom,
% 5.01/5.34 ! [K: code_integer,L: code_integer] :
% 5.01/5.34 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 5.01/5.34 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % snd_divmod_abs
% 5.01/5.34 thf(fact_9765_drop__bit__of__Suc__0,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.01/5.34 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_of_Suc_0
% 5.01/5.34 thf(fact_9766_drop__bit__nat__eq,axiom,
% 5.01/5.34 ! [N: nat,K: int] :
% 5.01/5.34 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.01/5.34 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_nat_eq
% 5.01/5.34 thf(fact_9767_quotient__of__denom__pos_H,axiom,
% 5.01/5.34 ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % quotient_of_denom_pos'
% 5.01/5.34 thf(fact_9768_bezw__non__0,axiom,
% 5.01/5.34 ! [Y: nat,X2: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.01/5.34 => ( ( bezw @ X2 @ Y )
% 5.01/5.34 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezw_non_0
% 5.01/5.34 thf(fact_9769_bezw_Osimps,axiom,
% 5.01/5.34 ( bezw
% 5.01/5.34 = ( ^ [X3: nat,Y2: nat] : ( if_Pro3027730157355071871nt_int @ ( Y2 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezw.simps
% 5.01/5.34 thf(fact_9770_bezw_Oelims,axiom,
% 5.01/5.34 ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 5.01/5.34 ( ( ( bezw @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( ( Xa = zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.01/5.34 & ( ( Xa != zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezw.elims
% 5.01/5.34 thf(fact_9771_drop__bit__nat__def,axiom,
% 5.01/5.34 ( bit_se8570568707652914677it_nat
% 5.01/5.34 = ( ^ [N4: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % drop_bit_nat_def
% 5.01/5.34 thf(fact_9772_rat__sgn__code,axiom,
% 5.01/5.34 ! [P4: rat] :
% 5.01/5.34 ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 5.01/5.34 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % rat_sgn_code
% 5.01/5.34 thf(fact_9773_bezw_Opelims,axiom,
% 5.01/5.34 ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
% 5.01/5.34 ( ( ( bezw @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 5.01/5.34 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.01/5.34 & ( ( Xa != zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa ) ) ) ) ) ) ) )
% 5.01/5.34 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezw.pelims
% 5.01/5.34 thf(fact_9774_minus__one__mod__numeral,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % minus_one_mod_numeral
% 5.01/5.34 thf(fact_9775_one__mod__minus__numeral,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % one_mod_minus_numeral
% 5.01/5.34 thf(fact_9776_numeral__mod__minus__numeral,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % numeral_mod_minus_numeral
% 5.01/5.34 thf(fact_9777_minus__numeral__mod__numeral,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % minus_numeral_mod_numeral
% 5.01/5.34 thf(fact_9778_Divides_Oadjust__mod__def,axiom,
% 5.01/5.34 ( adjust_mod
% 5.01/5.34 = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Divides.adjust_mod_def
% 5.01/5.34 thf(fact_9779_normalize__def,axiom,
% 5.01/5.34 ( normalize
% 5.01/5.34 = ( ^ [P5: product_prod_int_int] :
% 5.01/5.34 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.01/5.34 @ ( if_Pro3027730157355071871nt_int
% 5.01/5.34 @ ( ( product_snd_int_int @ P5 )
% 5.01/5.34 = zero_zero_int )
% 5.01/5.34 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.01/5.34 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % normalize_def
% 5.01/5.34 thf(fact_9780_gcd__1__int,axiom,
% 5.01/5.34 ! [M: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ M @ one_one_int )
% 5.01/5.34 = one_one_int ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_1_int
% 5.01/5.34 thf(fact_9781_gcd__neg1__int,axiom,
% 5.01/5.34 ! [X2: int,Y: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y )
% 5.01/5.34 = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_neg1_int
% 5.01/5.34 thf(fact_9782_gcd__neg2__int,axiom,
% 5.01/5.34 ! [X2: int,Y: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) )
% 5.01/5.34 = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_neg2_int
% 5.01/5.34 thf(fact_9783_gcd__pos__int,axiom,
% 5.01/5.34 ! [M: int,N: int] :
% 5.01/5.34 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.01/5.34 = ( ( M != zero_zero_int )
% 5.01/5.34 | ( N != zero_zero_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_pos_int
% 5.01/5.34 thf(fact_9784_gcd__neg__numeral__1__int,axiom,
% 5.01/5.34 ! [N: num,X2: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X2 )
% 5.01/5.34 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_neg_numeral_1_int
% 5.01/5.34 thf(fact_9785_gcd__neg__numeral__2__int,axiom,
% 5.01/5.34 ! [X2: int,N: num] :
% 5.01/5.34 ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_neg_numeral_2_int
% 5.01/5.34 thf(fact_9786_gcd__0__left__int,axiom,
% 5.01/5.34 ! [X2: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ zero_zero_int @ X2 )
% 5.01/5.34 = ( abs_abs_int @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_0_left_int
% 5.01/5.34 thf(fact_9787_gcd__0__int,axiom,
% 5.01/5.34 ! [X2: int] :
% 5.01/5.34 ( ( gcd_gcd_int @ X2 @ zero_zero_int )
% 5.01/5.34 = ( abs_abs_int @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_0_int
% 5.01/5.34 thf(fact_9788_gcd__ge__0__int,axiom,
% 5.01/5.34 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_ge_0_int
% 5.01/5.34 thf(fact_9789_gcd__red__int,axiom,
% 5.01/5.34 ( gcd_gcd_int
% 5.01/5.34 = ( ^ [X3: int,Y2: int] : ( gcd_gcd_int @ Y2 @ ( modulo_modulo_int @ X3 @ Y2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_red_int
% 5.01/5.34 thf(fact_9790_bezout__int,axiom,
% 5.01/5.34 ! [X2: int,Y: int] :
% 5.01/5.34 ? [U2: int,V2: int] :
% 5.01/5.34 ( ( plus_plus_int @ ( times_times_int @ U2 @ X2 ) @ ( times_times_int @ V2 @ Y ) )
% 5.01/5.34 = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezout_int
% 5.01/5.34 thf(fact_9791_gcd__le1__int,axiom,
% 5.01/5.34 ! [A: int,B: int] :
% 5.01/5.34 ( ( ord_less_int @ zero_zero_int @ A )
% 5.01/5.34 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_le1_int
% 5.01/5.34 thf(fact_9792_gcd__le2__int,axiom,
% 5.01/5.34 ! [B: int,A: int] :
% 5.01/5.34 ( ( ord_less_int @ zero_zero_int @ B )
% 5.01/5.34 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_le2_int
% 5.01/5.34 thf(fact_9793_gcd__cases__int,axiom,
% 5.01/5.34 ! [X2: int,Y: int,P: int > $o] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.34 => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) )
% 5.01/5.34 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.01/5.34 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.01/5.34 => ( P @ ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.01/5.34 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.01/5.34 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.01/5.34 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y ) ) ) )
% 5.01/5.34 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.01/5.34 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.01/5.34 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.01/5.34 => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_cases_int
% 5.01/5.34 thf(fact_9794_gcd__unique__int,axiom,
% 5.01/5.34 ! [D: int,A: int,B: int] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.01/5.34 & ( dvd_dvd_int @ D @ A )
% 5.01/5.34 & ( dvd_dvd_int @ D @ B )
% 5.01/5.34 & ! [E3: int] :
% 5.01/5.34 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.01/5.34 & ( dvd_dvd_int @ E3 @ B ) )
% 5.01/5.34 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.01/5.34 = ( D
% 5.01/5.34 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_unique_int
% 5.01/5.34 thf(fact_9795_gcd__non__0__int,axiom,
% 5.01/5.34 ! [Y: int,X2: int] :
% 5.01/5.34 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.01/5.34 => ( ( gcd_gcd_int @ X2 @ Y )
% 5.01/5.34 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X2 @ Y ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_non_0_int
% 5.01/5.34 thf(fact_9796_gcd__code__int,axiom,
% 5.01/5.34 ( gcd_gcd_int
% 5.01/5.34 = ( ^ [K2: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_code_int
% 5.01/5.34 thf(fact_9797_finite__enumerate,axiom,
% 5.01/5.34 ! [S: set_nat] :
% 5.01/5.34 ( ( finite_finite_nat @ S )
% 5.01/5.34 => ? [R4: nat > nat] :
% 5.01/5.34 ( ( strict1292158309912662752at_nat @ R4 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 5.01/5.34 & ! [N6: nat] :
% 5.01/5.34 ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S ) )
% 5.01/5.34 => ( member_nat @ ( R4 @ N6 ) @ S ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_enumerate
% 5.01/5.34 thf(fact_9798_divmod__integer__eq__cases,axiom,
% 5.01/5.34 ( code_divmod_integer
% 5.01/5.34 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.01/5.34 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.01/5.34 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.01/5.34 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.01/5.34 @ ( if_Pro6119634080678213985nteger
% 5.01/5.34 @ ( ( sgn_sgn_Code_integer @ K2 )
% 5.01/5.34 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.01/5.34 @ ( code_divmod_abs @ K2 @ L2 )
% 5.01/5.34 @ ( produc6916734918728496179nteger
% 5.01/5.34 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S4 ) ) )
% 5.01/5.34 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % divmod_integer_eq_cases
% 5.01/5.34 thf(fact_9799_gcd__nat_Oeq__neutr__iff,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( ( gcd_gcd_nat @ A @ B )
% 5.01/5.34 = zero_zero_nat )
% 5.01/5.34 = ( ( A = zero_zero_nat )
% 5.01/5.34 & ( B = zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.eq_neutr_iff
% 5.01/5.34 thf(fact_9800_gcd__nat_Oleft__neutral,axiom,
% 5.01/5.34 ! [A: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.01/5.34 = A ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.left_neutral
% 5.01/5.34 thf(fact_9801_gcd__nat_Oneutr__eq__iff,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( zero_zero_nat
% 5.01/5.34 = ( gcd_gcd_nat @ A @ B ) )
% 5.01/5.34 = ( ( A = zero_zero_nat )
% 5.01/5.34 & ( B = zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.neutr_eq_iff
% 5.01/5.34 thf(fact_9802_gcd__nat_Oright__neutral,axiom,
% 5.01/5.34 ! [A: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.01/5.34 = A ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.right_neutral
% 5.01/5.34 thf(fact_9803_gcd__0__nat,axiom,
% 5.01/5.34 ! [X2: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ X2 @ zero_zero_nat )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_0_nat
% 5.01/5.34 thf(fact_9804_gcd__0__left__nat,axiom,
% 5.01/5.34 ! [X2: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ zero_zero_nat @ X2 )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_0_left_nat
% 5.01/5.34 thf(fact_9805_gcd__1__nat,axiom,
% 5.01/5.34 ! [M: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.01/5.34 = one_one_nat ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_1_nat
% 5.01/5.34 thf(fact_9806_gcd__Suc__0,axiom,
% 5.01/5.34 ! [M: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.01/5.34 = ( suc @ zero_zero_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_Suc_0
% 5.01/5.34 thf(fact_9807_gcd__pos__nat,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.01/5.34 = ( ( M != zero_zero_nat )
% 5.01/5.34 | ( N != zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_pos_nat
% 5.01/5.34 thf(fact_9808_gcd__int__int__eq,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.01/5.34 = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_int_int_eq
% 5.01/5.34 thf(fact_9809_gcd__nat__abs__left__eq,axiom,
% 5.01/5.34 ! [K: int,N: nat] :
% 5.01/5.34 ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.01/5.34 = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat_abs_left_eq
% 5.01/5.34 thf(fact_9810_gcd__nat__abs__right__eq,axiom,
% 5.01/5.34 ! [N: nat,K: int] :
% 5.01/5.34 ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.01/5.34 = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat_abs_right_eq
% 5.01/5.34 thf(fact_9811_gcd__diff1__nat,axiom,
% 5.01/5.34 ! [N: nat,M: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ N @ M )
% 5.01/5.34 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.01/5.34 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_diff1_nat
% 5.01/5.34 thf(fact_9812_gcd__diff2__nat,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.01/5.34 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.01/5.34 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_diff2_nat
% 5.01/5.34 thf(fact_9813_gcd__le2__nat,axiom,
% 5.01/5.34 ! [B: nat,A: nat] :
% 5.01/5.34 ( ( B != zero_zero_nat )
% 5.01/5.34 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_le2_nat
% 5.01/5.34 thf(fact_9814_gcd__le1__nat,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( A != zero_zero_nat )
% 5.01/5.34 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_le1_nat
% 5.01/5.34 thf(fact_9815_gcd__nat_Oelims,axiom,
% 5.01/5.34 ! [X2: nat,Xa: nat,Y: nat] :
% 5.01/5.34 ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( ( Xa = zero_zero_nat )
% 5.01/5.34 => ( Y = X2 ) )
% 5.01/5.34 & ( ( Xa != zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.elims
% 5.01/5.34 thf(fact_9816_gcd__nat_Osimps,axiom,
% 5.01/5.34 ( gcd_gcd_nat
% 5.01/5.34 = ( ^ [X3: nat,Y2: nat] : ( if_nat @ ( Y2 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.simps
% 5.01/5.34 thf(fact_9817_gcd__non__0__nat,axiom,
% 5.01/5.34 ! [Y: nat,X2: nat] :
% 5.01/5.34 ( ( Y != zero_zero_nat )
% 5.01/5.34 => ( ( gcd_gcd_nat @ X2 @ Y )
% 5.01/5.34 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_non_0_nat
% 5.01/5.34 thf(fact_9818_gcd__mult__distrib__nat,axiom,
% 5.01/5.34 ! [K: nat,M: nat,N: nat] :
% 5.01/5.34 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.01/5.34 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_mult_distrib_nat
% 5.01/5.34 thf(fact_9819_gcd__red__nat,axiom,
% 5.01/5.34 ( gcd_gcd_nat
% 5.01/5.34 = ( ^ [X3: nat,Y2: nat] : ( gcd_gcd_nat @ Y2 @ ( modulo_modulo_nat @ X3 @ Y2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_red_nat
% 5.01/5.34 thf(fact_9820_bezout__nat,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( A != zero_zero_nat )
% 5.01/5.34 => ? [X4: nat,Y3: nat] :
% 5.01/5.34 ( ( times_times_nat @ A @ X4 )
% 5.01/5.34 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezout_nat
% 5.01/5.34 thf(fact_9821_bezout__gcd__nat_H,axiom,
% 5.01/5.34 ! [B: nat,A: nat] :
% 5.01/5.34 ? [X4: nat,Y3: nat] :
% 5.01/5.34 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X4 ) )
% 5.01/5.34 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.01/5.34 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.01/5.34 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X4 ) )
% 5.01/5.34 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.01/5.34 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezout_gcd_nat'
% 5.01/5.34 thf(fact_9822_gcd__code__integer,axiom,
% 5.01/5.34 ( gcd_gcd_Code_integer
% 5.01/5.34 = ( ^ [K2: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_code_integer
% 5.01/5.34 thf(fact_9823_gcd__int__def,axiom,
% 5.01/5.34 ( gcd_gcd_int
% 5.01/5.34 = ( ^ [X3: int,Y2: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X3 ) ) @ ( nat2 @ ( abs_abs_int @ Y2 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_int_def
% 5.01/5.34 thf(fact_9824_bezw__aux,axiom,
% 5.01/5.34 ! [X2: nat,Y: nat] :
% 5.01/5.34 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X2 @ Y ) )
% 5.01/5.34 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % bezw_aux
% 5.01/5.34 thf(fact_9825_nat__descend__induct,axiom,
% 5.01/5.34 ! [N: nat,P: nat > $o,M: nat] :
% 5.01/5.34 ( ! [K3: nat] :
% 5.01/5.34 ( ( ord_less_nat @ N @ K3 )
% 5.01/5.34 => ( P @ K3 ) )
% 5.01/5.34 => ( ! [K3: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ K3 @ N )
% 5.01/5.34 => ( ! [I2: nat] :
% 5.01/5.34 ( ( ord_less_nat @ K3 @ I2 )
% 5.01/5.34 => ( P @ I2 ) )
% 5.01/5.34 => ( P @ K3 ) ) )
% 5.01/5.34 => ( P @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nat_descend_induct
% 5.01/5.34 thf(fact_9826_gcd__nat_Opelims,axiom,
% 5.01/5.34 ! [X2: nat,Xa: nat,Y: nat] :
% 5.01/5.34 ( ( ( gcd_gcd_nat @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) )
% 5.01/5.34 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.01/5.34 => ( Y = X2 ) )
% 5.01/5.34 & ( ( Xa != zero_zero_nat )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X2 @ Xa ) ) ) ) )
% 5.01/5.34 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.pelims
% 5.01/5.34 thf(fact_9827_card_Ocomp__fun__commute__on,axiom,
% 5.01/5.34 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.01/5.34 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.01/5.34
% 5.01/5.34 % card.comp_fun_commute_on
% 5.01/5.34 thf(fact_9828_Code__Target__Int_Onegative__def,axiom,
% 5.01/5.34 ( code_Target_negative
% 5.01/5.34 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % Code_Target_Int.negative_def
% 5.01/5.34 thf(fact_9829_card__greaterThanLessThan__int,axiom,
% 5.01/5.34 ! [L: int,U: int] :
% 5.01/5.34 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.01/5.34 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_greaterThanLessThan_int
% 5.01/5.34 thf(fact_9830_xor__minus__numerals_I2_J,axiom,
% 5.01/5.34 ! [K: int,N: num] :
% 5.01/5.34 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % xor_minus_numerals(2)
% 5.01/5.34 thf(fact_9831_finite__greaterThanLessThan__int,axiom,
% 5.01/5.34 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_greaterThanLessThan_int
% 5.01/5.34 thf(fact_9832_xor__minus__numerals_I1_J,axiom,
% 5.01/5.34 ! [N: num,K: int] :
% 5.01/5.34 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.01/5.34 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % xor_minus_numerals(1)
% 5.01/5.34 thf(fact_9833_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.01/5.34 ! [L: int,U: int] :
% 5.01/5.34 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.01/5.34 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.01/5.34 thf(fact_9834_sub__BitM__One__eq,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.01/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sub_BitM_One_eq
% 5.01/5.34 thf(fact_9835_finite__greaterThanLessThan,axiom,
% 5.01/5.34 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_greaterThanLessThan
% 5.01/5.34 thf(fact_9836_card__greaterThanLessThan,axiom,
% 5.01/5.34 ! [L: nat,U: nat] :
% 5.01/5.34 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.01/5.34 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_greaterThanLessThan
% 5.01/5.34 thf(fact_9837_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.01/5.34 ! [L: nat,U: nat] :
% 5.01/5.34 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.01/5.34 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastSucLessThan_greaterThanLessThan
% 5.01/5.34 thf(fact_9838_tanh__real__bounds,axiom,
% 5.01/5.34 ! [X2: real] : ( member_real @ ( tanh_real @ X2 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % tanh_real_bounds
% 5.01/5.34 thf(fact_9839_greaterThanLessThan__upt,axiom,
% 5.01/5.34 ( set_or5834768355832116004an_nat
% 5.01/5.34 = ( ^ [N4: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThanLessThan_upt
% 5.01/5.34 thf(fact_9840_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.01/5.34 ! [N: nat,J: nat,I: nat] :
% 5.01/5.34 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.01/5.34 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.01/5.34 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nth_sorted_list_of_set_greaterThanLessThan
% 5.01/5.34 thf(fact_9841_Suc__funpow,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( compow_nat_nat @ N @ suc )
% 5.01/5.34 = ( plus_plus_nat @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % Suc_funpow
% 5.01/5.34 thf(fact_9842_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.01/5.34 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ X3 )
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] : ( ord_less_nat @ Y2 @ X3 ) ) ).
% 5.01/5.34
% 5.01/5.34 % max_nat.semilattice_neutr_order_axioms
% 5.01/5.34 thf(fact_9843_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.01/5.34 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.01/5.34 @ ^ [M3: nat,N4: nat] :
% 5.01/5.34 ( ( dvd_dvd_nat @ M3 @ N4 )
% 5.01/5.34 & ( M3 != N4 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_nat.semilattice_neutr_order_axioms
% 5.01/5.34 thf(fact_9844_Sup__nat__empty,axiom,
% 5.01/5.34 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.01/5.34 = zero_zero_nat ) ).
% 5.01/5.34
% 5.01/5.34 % Sup_nat_empty
% 5.01/5.34 thf(fact_9845_upt__conv__Nil,axiom,
% 5.01/5.34 ! [J: nat,I: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ J @ I )
% 5.01/5.34 => ( ( upt @ I @ J )
% 5.01/5.34 = nil_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_conv_Nil
% 5.01/5.34 thf(fact_9846_upt__eq__Nil__conv,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ( upt @ I @ J )
% 5.01/5.34 = nil_nat )
% 5.01/5.34 = ( ( J = zero_zero_nat )
% 5.01/5.34 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_eq_Nil_conv
% 5.01/5.34 thf(fact_9847_upt__0,axiom,
% 5.01/5.34 ! [I: nat] :
% 5.01/5.34 ( ( upt @ I @ zero_zero_nat )
% 5.01/5.34 = nil_nat ) ).
% 5.01/5.34
% 5.01/5.34 % upt_0
% 5.01/5.34 thf(fact_9848_times__int_Oabs__eq,axiom,
% 5.01/5.34 ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( abs_Integ
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y2 @ U3 ) ) ) )
% 5.01/5.34 @ Xa
% 5.01/5.34 @ X2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % times_int.abs_eq
% 5.01/5.34 thf(fact_9849_hd__upt,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ord_less_nat @ I @ J )
% 5.01/5.34 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.01/5.34 = I ) ) ).
% 5.01/5.34
% 5.01/5.34 % hd_upt
% 5.01/5.34 thf(fact_9850_eq__Abs__Integ,axiom,
% 5.01/5.34 ! [Z: int] :
% 5.01/5.34 ~ ! [X4: nat,Y3: nat] :
% 5.01/5.34 ( Z
% 5.01/5.34 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eq_Abs_Integ
% 5.01/5.34 thf(fact_9851_nat_Oabs__eq,axiom,
% 5.01/5.34 ! [X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( nat2 @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % nat.abs_eq
% 5.01/5.34 thf(fact_9852_zero__int__def,axiom,
% 5.01/5.34 ( zero_zero_int
% 5.01/5.34 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % zero_int_def
% 5.01/5.34 thf(fact_9853_int__def,axiom,
% 5.01/5.34 ( semiri1314217659103216013at_int
% 5.01/5.34 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % int_def
% 5.01/5.34 thf(fact_9854_uminus__int_Oabs__eq,axiom,
% 5.01/5.34 ! [X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( abs_Integ
% 5.01/5.34 @ ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X3 )
% 5.01/5.34 @ X2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % uminus_int.abs_eq
% 5.01/5.34 thf(fact_9855_one__int__def,axiom,
% 5.01/5.34 ( one_one_int
% 5.01/5.34 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % one_int_def
% 5.01/5.34 thf(fact_9856_less__int_Oabs__eq,axiom,
% 5.01/5.34 ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( produc8739625826339149834_nat_o
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc6081775807080527818_nat_o
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y2 ) ) )
% 5.01/5.34 @ Xa
% 5.01/5.34 @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % less_int.abs_eq
% 5.01/5.34 thf(fact_9857_less__eq__int_Oabs__eq,axiom,
% 5.01/5.34 ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( produc8739625826339149834_nat_o
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc6081775807080527818_nat_o
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y2 ) ) )
% 5.01/5.34 @ Xa
% 5.01/5.34 @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % less_eq_int.abs_eq
% 5.01/5.34 thf(fact_9858_plus__int_Oabs__eq,axiom,
% 5.01/5.34 ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( abs_Integ
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) )
% 5.01/5.34 @ Xa
% 5.01/5.34 @ X2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % plus_int.abs_eq
% 5.01/5.34 thf(fact_9859_minus__int_Oabs__eq,axiom,
% 5.01/5.34 ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.01/5.34 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X2 ) )
% 5.01/5.34 = ( abs_Integ
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y2 @ U3 ) ) )
% 5.01/5.34 @ Xa
% 5.01/5.34 @ X2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % minus_int.abs_eq
% 5.01/5.34 thf(fact_9860_Gcd__remove0__nat,axiom,
% 5.01/5.34 ! [M7: set_nat] :
% 5.01/5.34 ( ( finite_finite_nat @ M7 )
% 5.01/5.34 => ( ( gcd_Gcd_nat @ M7 )
% 5.01/5.34 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_remove0_nat
% 5.01/5.34 thf(fact_9861_Gcd__nat__eq__one,axiom,
% 5.01/5.34 ! [N2: set_nat] :
% 5.01/5.34 ( ( member_nat @ one_one_nat @ N2 )
% 5.01/5.34 => ( ( gcd_Gcd_nat @ N2 )
% 5.01/5.34 = one_one_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_nat_eq_one
% 5.01/5.34 thf(fact_9862_less__eq__int_Orep__eq,axiom,
% 5.01/5.34 ( ord_less_eq_int
% 5.01/5.34 = ( ^ [X3: int,Xa4: int] :
% 5.01/5.34 ( produc8739625826339149834_nat_o
% 5.01/5.34 @ ^ [Y2: nat,Z5: nat] :
% 5.01/5.34 ( produc6081775807080527818_nat_o
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 5.01/5.34 @ ( rep_Integ @ X3 )
% 5.01/5.34 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % less_eq_int.rep_eq
% 5.01/5.34 thf(fact_9863_less__int_Orep__eq,axiom,
% 5.01/5.34 ( ord_less_int
% 5.01/5.34 = ( ^ [X3: int,Xa4: int] :
% 5.01/5.34 ( produc8739625826339149834_nat_o
% 5.01/5.34 @ ^ [Y2: nat,Z5: nat] :
% 5.01/5.34 ( produc6081775807080527818_nat_o
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y2 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 5.01/5.34 @ ( rep_Integ @ X3 )
% 5.01/5.34 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % less_int.rep_eq
% 5.01/5.34 thf(fact_9864_Gcd__int__greater__eq__0,axiom,
% 5.01/5.34 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_int_greater_eq_0
% 5.01/5.34 thf(fact_9865_nat_Orep__eq,axiom,
% 5.01/5.34 ( nat2
% 5.01/5.34 = ( ^ [X3: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nat.rep_eq
% 5.01/5.34 thf(fact_9866_uminus__int__def,axiom,
% 5.01/5.34 ( uminus_uminus_int
% 5.01/5.34 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.01/5.34 @ ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] : ( product_Pair_nat_nat @ Y2 @ X3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % uminus_int_def
% 5.01/5.34 thf(fact_9867_times__int__def,axiom,
% 5.01/5.34 ( times_times_int
% 5.01/5.34 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y2 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y2 @ U3 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % times_int_def
% 5.01/5.34 thf(fact_9868_minus__int__def,axiom,
% 5.01/5.34 ( minus_minus_int
% 5.01/5.34 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y2 @ U3 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % minus_int_def
% 5.01/5.34 thf(fact_9869_plus__int__def,axiom,
% 5.01/5.34 ( plus_plus_int
% 5.01/5.34 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.01/5.34 @ ( produc27273713700761075at_nat
% 5.01/5.34 @ ^ [X3: nat,Y2: nat] :
% 5.01/5.34 ( produc2626176000494625587at_nat
% 5.01/5.34 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y2 @ V4 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % plus_int_def
% 5.01/5.34 thf(fact_9870_prod__encode__def,axiom,
% 5.01/5.34 ( nat_prod_encode
% 5.01/5.34 = ( produc6842872674320459806at_nat
% 5.01/5.34 @ ^ [M3: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N4 ) ) @ M3 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % prod_encode_def
% 5.01/5.34 thf(fact_9871_prod__encode__eq,axiom,
% 5.01/5.34 ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.01/5.34 ( ( ( nat_prod_encode @ X2 )
% 5.01/5.34 = ( nat_prod_encode @ Y ) )
% 5.01/5.34 = ( X2 = Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % prod_encode_eq
% 5.01/5.34 thf(fact_9872_le__prod__encode__1,axiom,
% 5.01/5.34 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % le_prod_encode_1
% 5.01/5.34 thf(fact_9873_le__prod__encode__2,axiom,
% 5.01/5.34 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % le_prod_encode_2
% 5.01/5.34 thf(fact_9874_prod__encode__prod__decode__aux,axiom,
% 5.01/5.34 ! [K: nat,M: nat] :
% 5.01/5.34 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.01/5.34 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.01/5.34
% 5.01/5.34 % prod_encode_prod_decode_aux
% 5.01/5.34 thf(fact_9875_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.01/5.34 ! [N: nat,J: nat,I: nat] :
% 5.01/5.34 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.01/5.34 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.01/5.34 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nth_sorted_list_of_set_greaterThanAtMost
% 5.01/5.34 thf(fact_9876_finite__greaterThanAtMost,axiom,
% 5.01/5.34 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_greaterThanAtMost
% 5.01/5.34 thf(fact_9877_card__greaterThanAtMost,axiom,
% 5.01/5.34 ! [L: nat,U: nat] :
% 5.01/5.34 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.01/5.34 = ( minus_minus_nat @ U @ L ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_greaterThanAtMost
% 5.01/5.34 thf(fact_9878_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.01/5.34 ! [L: nat,U: nat] :
% 5.01/5.34 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.01/5.34 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastSucAtMost_greaterThanAtMost
% 5.01/5.34 thf(fact_9879_greaterThanAtMost__upt,axiom,
% 5.01/5.34 ( set_or6659071591806873216st_nat
% 5.01/5.34 = ( ^ [N4: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M3 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThanAtMost_upt
% 5.01/5.34 thf(fact_9880_num__of__nat_Osimps_I2_J,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( num_of_nat @ ( suc @ N ) )
% 5.01/5.34 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( num_of_nat @ ( suc @ N ) )
% 5.01/5.34 = one ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat.simps(2)
% 5.01/5.34 thf(fact_9881_finite__greaterThanAtMost__int,axiom,
% 5.01/5.34 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_greaterThanAtMost_int
% 5.01/5.34 thf(fact_9882_num__of__nat__numeral__eq,axiom,
% 5.01/5.34 ! [Q2: num] :
% 5.01/5.34 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.01/5.34 = Q2 ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat_numeral_eq
% 5.01/5.34 thf(fact_9883_card__greaterThanAtMost__int,axiom,
% 5.01/5.34 ! [L: int,U: int] :
% 5.01/5.34 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.01/5.34 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_greaterThanAtMost_int
% 5.01/5.34 thf(fact_9884_num__of__nat_Osimps_I1_J,axiom,
% 5.01/5.34 ( ( num_of_nat @ zero_zero_nat )
% 5.01/5.34 = one ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat.simps(1)
% 5.01/5.34 thf(fact_9885_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.01/5.34 ! [L: int,U: int] :
% 5.01/5.34 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.01/5.34 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.01/5.34 thf(fact_9886_numeral__num__of__nat,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.01/5.34 = N ) ) ).
% 5.01/5.34
% 5.01/5.34 % numeral_num_of_nat
% 5.01/5.34 thf(fact_9887_num__of__nat__One,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.01/5.34 => ( ( num_of_nat @ N )
% 5.01/5.34 = one ) ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat_One
% 5.01/5.34 thf(fact_9888_num__of__nat__code,axiom,
% 5.01/5.34 ( num_of_nat
% 5.01/5.34 = ( comp_C2179886998970519596um_nat @ code_num_of_integer @ semiri4939895301339042750nteger ) ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat_code
% 5.01/5.34 thf(fact_9889_num__of__nat__double,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.01/5.34 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat_double
% 5.01/5.34 thf(fact_9890_num__of__nat__plus__distrib,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.01/5.34 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.01/5.34 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % num_of_nat_plus_distrib
% 5.01/5.34 thf(fact_9891_pred__nat__def,axiom,
% 5.01/5.34 ( pred_nat
% 5.01/5.34 = ( collec3392354462482085612at_nat
% 5.01/5.34 @ ( produc6081775807080527818_nat_o
% 5.01/5.34 @ ^ [M3: nat,N4: nat] :
% 5.01/5.34 ( N4
% 5.01/5.34 = ( suc @ M3 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % pred_nat_def
% 5.01/5.34 thf(fact_9892_pow_Osimps_I3_J,axiom,
% 5.01/5.34 ! [X2: num,Y: num] :
% 5.01/5.34 ( ( pow @ X2 @ ( bit1 @ Y ) )
% 5.01/5.34 = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y ) ) @ X2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % pow.simps(3)
% 5.01/5.34 thf(fact_9893_sqr__conv__mult,axiom,
% 5.01/5.34 ( sqr
% 5.01/5.34 = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sqr_conv_mult
% 5.01/5.34 thf(fact_9894_sqr_Osimps_I2_J,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( sqr @ ( bit0 @ N ) )
% 5.01/5.34 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sqr.simps(2)
% 5.01/5.34 thf(fact_9895_sqr_Osimps_I1_J,axiom,
% 5.01/5.34 ( ( sqr @ one )
% 5.01/5.34 = one ) ).
% 5.01/5.34
% 5.01/5.34 % sqr.simps(1)
% 5.01/5.34 thf(fact_9896_pow_Osimps_I2_J,axiom,
% 5.01/5.34 ! [X2: num,Y: num] :
% 5.01/5.34 ( ( pow @ X2 @ ( bit0 @ Y ) )
% 5.01/5.34 = ( sqr @ ( pow @ X2 @ Y ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % pow.simps(2)
% 5.01/5.34 thf(fact_9897_sqr_Osimps_I3_J,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( sqr @ ( bit1 @ N ) )
% 5.01/5.34 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sqr.simps(3)
% 5.01/5.34 thf(fact_9898_image__minus__const__atLeastLessThan__nat,axiom,
% 5.01/5.34 ! [C: nat,Y: nat,X2: nat] :
% 5.01/5.34 ( ( ( ord_less_nat @ C @ Y )
% 5.01/5.34 => ( ( image_nat_nat
% 5.01/5.34 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.01/5.34 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.01/5.34 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_nat @ C @ Y )
% 5.01/5.34 => ( ( ( ord_less_nat @ X2 @ Y )
% 5.01/5.34 => ( ( image_nat_nat
% 5.01/5.34 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.01/5.34 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.01/5.34 & ( ~ ( ord_less_nat @ X2 @ Y )
% 5.01/5.34 => ( ( image_nat_nat
% 5.01/5.34 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.01/5.34 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.01/5.34 = bot_bot_set_nat ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_minus_const_atLeastLessThan_nat
% 5.01/5.34 thf(fact_9899_bij__betw__Suc,axiom,
% 5.01/5.34 ! [M7: set_nat,N2: set_nat] :
% 5.01/5.34 ( ( bij_betw_nat_nat @ suc @ M7 @ N2 )
% 5.01/5.34 = ( ( image_nat_nat @ suc @ M7 )
% 5.01/5.34 = N2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % bij_betw_Suc
% 5.01/5.34 thf(fact_9900_image__Suc__atLeastAtMost,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.01/5.34 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_Suc_atLeastAtMost
% 5.01/5.34 thf(fact_9901_image__Suc__atLeastLessThan,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.01/5.34 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_Suc_atLeastLessThan
% 5.01/5.34 thf(fact_9902_zero__notin__Suc__image,axiom,
% 5.01/5.34 ! [A2: set_nat] :
% 5.01/5.34 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % zero_notin_Suc_image
% 5.01/5.34 thf(fact_9903_image__Suc__lessThan,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_Suc_lessThan
% 5.01/5.34 thf(fact_9904_image__Suc__atMost,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.01/5.34 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_Suc_atMost
% 5.01/5.34 thf(fact_9905_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeast0_atMost_Suc_eq_insert_0
% 5.01/5.34 thf(fact_9906_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeast0_lessThan_Suc_eq_insert_0
% 5.01/5.34 thf(fact_9907_lessThan__Suc__eq__insert__0,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lessThan_Suc_eq_insert_0
% 5.01/5.34 thf(fact_9908_atMost__Suc__eq__insert__0,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atMost_Suc_eq_insert_0
% 5.01/5.34 thf(fact_9909_Gcd__int__eq,axiom,
% 5.01/5.34 ! [N2: set_nat] :
% 5.01/5.34 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N2 ) )
% 5.01/5.34 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_int_eq
% 5.01/5.34 thf(fact_9910_finite__int__iff__bounded,axiom,
% 5.01/5.34 ( finite_finite_int
% 5.01/5.34 = ( ^ [S5: set_int] :
% 5.01/5.34 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_int_iff_bounded
% 5.01/5.34 thf(fact_9911_finite__int__iff__bounded__le,axiom,
% 5.01/5.34 ( finite_finite_int
% 5.01/5.34 = ( ^ [S5: set_int] :
% 5.01/5.34 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % finite_int_iff_bounded_le
% 5.01/5.34 thf(fact_9912_UN__atMost__UNIV,axiom,
% 5.01/5.34 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % UN_atMost_UNIV
% 5.01/5.34 thf(fact_9913_UN__lessThan__UNIV,axiom,
% 5.01/5.34 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % UN_lessThan_UNIV
% 5.01/5.34 thf(fact_9914_Inf__real__def,axiom,
% 5.01/5.34 ( comple4887499456419720421f_real
% 5.01/5.34 = ( ^ [X5: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X5 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Inf_real_def
% 5.01/5.34 thf(fact_9915_Inf__int__def,axiom,
% 5.01/5.34 ( complete_Inf_Inf_int
% 5.01/5.34 = ( ^ [X5: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X5 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Inf_int_def
% 5.01/5.34 thf(fact_9916_image__int__atLeastAtMost,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.01/5.34 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_int_atLeastAtMost
% 5.01/5.34 thf(fact_9917_image__int__atLeastLessThan,axiom,
% 5.01/5.34 ! [A: nat,B: nat] :
% 5.01/5.34 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.01/5.34 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_int_atLeastLessThan
% 5.01/5.34 thf(fact_9918_suminf__eq__SUP__real,axiom,
% 5.01/5.34 ! [X8: nat > real] :
% 5.01/5.34 ( ( summable_real @ X8 )
% 5.01/5.34 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I3 ) )
% 5.01/5.34 => ( ( suminf_real @ X8 )
% 5.01/5.34 = ( comple1385675409528146559p_real
% 5.01/5.34 @ ( image_nat_real
% 5.01/5.34 @ ^ [I4: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I4 ) )
% 5.01/5.34 @ top_top_set_nat ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % suminf_eq_SUP_real
% 5.01/5.34 thf(fact_9919_image__add__int__atLeastLessThan,axiom,
% 5.01/5.34 ! [L: int,U: int] :
% 5.01/5.34 ( ( image_int_int
% 5.01/5.34 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 5.01/5.34 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.01/5.34 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_add_int_atLeastLessThan
% 5.01/5.34 thf(fact_9920_Gcd__int__def,axiom,
% 5.01/5.34 ( gcd_Gcd_int
% 5.01/5.34 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_int_def
% 5.01/5.34 thf(fact_9921_range__mod,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( image_nat_nat
% 5.01/5.34 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 5.01/5.34 @ top_top_set_nat )
% 5.01/5.34 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % range_mod
% 5.01/5.34 thf(fact_9922_image__atLeastZeroLessThan__int,axiom,
% 5.01/5.34 ! [U: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.01/5.34 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.01/5.34 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % image_atLeastZeroLessThan_int
% 5.01/5.34 thf(fact_9923_UNIV__nat__eq,axiom,
% 5.01/5.34 ( top_top_set_nat
% 5.01/5.34 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % UNIV_nat_eq
% 5.01/5.34 thf(fact_9924_card__UNIV__unit,axiom,
% 5.01/5.34 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.01/5.34 = one_one_nat ) ).
% 5.01/5.34
% 5.01/5.34 % card_UNIV_unit
% 5.01/5.34 thf(fact_9925_card__UNIV__bool,axiom,
% 5.01/5.34 ( ( finite_card_o @ top_top_set_o )
% 5.01/5.34 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_UNIV_bool
% 5.01/5.34 thf(fact_9926_range__mult,axiom,
% 5.01/5.34 ! [A: real] :
% 5.01/5.34 ( ( ( A = zero_zero_real )
% 5.01/5.34 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.01/5.34 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.01/5.34 & ( ( A != zero_zero_real )
% 5.01/5.34 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.01/5.34 = top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % range_mult
% 5.01/5.34 thf(fact_9927_int__in__range__abs,axiom,
% 5.01/5.34 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % int_in_range_abs
% 5.01/5.34 thf(fact_9928_bij__prod__encode,axiom,
% 5.01/5.34 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 5.01/5.34
% 5.01/5.34 % bij_prod_encode
% 5.01/5.34 thf(fact_9929_surj__prod__encode,axiom,
% 5.01/5.34 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % surj_prod_encode
% 5.01/5.34 thf(fact_9930_root__def,axiom,
% 5.01/5.34 ( root
% 5.01/5.34 = ( ^ [N4: nat,X3: real] :
% 5.01/5.34 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 5.01/5.34 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.01/5.34 @ ^ [Y2: real] : ( times_times_real @ ( sgn_sgn_real @ Y2 ) @ ( power_power_real @ ( abs_abs_real @ Y2 ) @ N4 ) )
% 5.01/5.34 @ X3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % root_def
% 5.01/5.34 thf(fact_9931_card__UNIV__char,axiom,
% 5.01/5.34 ( ( finite_card_char @ top_top_set_char )
% 5.01/5.34 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_UNIV_char
% 5.01/5.34 thf(fact_9932_UNIV__char__of__nat,axiom,
% 5.01/5.34 ( top_top_set_char
% 5.01/5.34 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % UNIV_char_of_nat
% 5.01/5.34 thf(fact_9933_remdups__upt,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( remdups_nat @ ( upt @ M @ N ) )
% 5.01/5.34 = ( upt @ M @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % remdups_upt
% 5.01/5.34 thf(fact_9934_char_Osize_I2_J,axiom,
% 5.01/5.34 ! [X1: $o,X23: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.01/5.34 ( ( size_size_char @ ( char2 @ X1 @ X23 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.01/5.34 = zero_zero_nat ) ).
% 5.01/5.34
% 5.01/5.34 % char.size(2)
% 5.01/5.34 thf(fact_9935_nat__of__char__less__256,axiom,
% 5.01/5.34 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nat_of_char_less_256
% 5.01/5.34 thf(fact_9936_range__nat__of__char,axiom,
% 5.01/5.34 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.01/5.34 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % range_nat_of_char
% 5.01/5.34 thf(fact_9937_integer__of__char__code,axiom,
% 5.01/5.34 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.01/5.34 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.01/5.34 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % integer_of_char_code
% 5.01/5.34 thf(fact_9938_char_Osize__gen,axiom,
% 5.01/5.34 ! [X1: $o,X23: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.01/5.34 ( ( size_char @ ( char2 @ X1 @ X23 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.01/5.34 = zero_zero_nat ) ).
% 5.01/5.34
% 5.01/5.34 % char.size_gen
% 5.01/5.34 thf(fact_9939_String_Ochar__of__ascii__of,axiom,
% 5.01/5.34 ! [C: char] :
% 5.01/5.34 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.01/5.34 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % String.char_of_ascii_of
% 5.01/5.34 thf(fact_9940_upt__rec__numeral,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.34 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.34 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.34 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.01/5.34 = nil_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_rec_numeral
% 5.01/5.34 thf(fact_9941_list__encode_Ocases,axiom,
% 5.01/5.34 ! [X2: list_nat] :
% 5.01/5.34 ( ( X2 != nil_nat )
% 5.01/5.34 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.01/5.34 ( X2
% 5.01/5.34 != ( cons_nat @ X4 @ Xs2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode.cases
% 5.01/5.34 thf(fact_9942_upt__conv__Cons__Cons,axiom,
% 5.01/5.34 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.01/5.34 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.01/5.34 = ( upt @ M @ Q2 ) )
% 5.01/5.34 = ( ( cons_nat @ N @ Ns )
% 5.01/5.34 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_conv_Cons_Cons
% 5.01/5.34 thf(fact_9943_upt__conv__Cons,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ord_less_nat @ I @ J )
% 5.01/5.34 => ( ( upt @ I @ J )
% 5.01/5.34 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_conv_Cons
% 5.01/5.34 thf(fact_9944_upt__eq__Cons__conv,axiom,
% 5.01/5.34 ! [I: nat,J: nat,X2: nat,Xs: list_nat] :
% 5.01/5.34 ( ( ( upt @ I @ J )
% 5.01/5.34 = ( cons_nat @ X2 @ Xs ) )
% 5.01/5.34 = ( ( ord_less_nat @ I @ J )
% 5.01/5.34 & ( I = X2 )
% 5.01/5.34 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.01/5.34 = Xs ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_eq_Cons_conv
% 5.01/5.34 thf(fact_9945_upt__rec,axiom,
% 5.01/5.34 ( upt
% 5.01/5.34 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_rec
% 5.01/5.34 thf(fact_9946_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.01/5.34 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.01/5.34 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_list_of_set_greaterThanAtMost
% 5.01/5.34 thf(fact_9947_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.01/5.34 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.01/5.34 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_list_of_set_greaterThanLessThan
% 5.01/5.34 thf(fact_9948_list__encode_Oelims,axiom,
% 5.01/5.34 ! [X2: list_nat,Y: nat] :
% 5.01/5.34 ( ( ( nat_list_encode @ X2 )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( ( X2 = nil_nat )
% 5.01/5.34 => ( Y != zero_zero_nat ) )
% 5.01/5.34 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.01/5.34 ( ( X2
% 5.01/5.34 = ( cons_nat @ X4 @ Xs2 ) )
% 5.01/5.34 => ( Y
% 5.01/5.34 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode.elims
% 5.01/5.34 thf(fact_9949_tl__upt,axiom,
% 5.01/5.34 ! [M: nat,N: nat] :
% 5.01/5.34 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.01/5.34 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % tl_upt
% 5.01/5.34 thf(fact_9950_bij__list__encode,axiom,
% 5.01/5.34 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 5.01/5.34
% 5.01/5.34 % bij_list_encode
% 5.01/5.34 thf(fact_9951_list__encode__eq,axiom,
% 5.01/5.34 ! [X2: list_nat,Y: list_nat] :
% 5.01/5.34 ( ( ( nat_list_encode @ X2 )
% 5.01/5.34 = ( nat_list_encode @ Y ) )
% 5.01/5.34 = ( X2 = Y ) ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode_eq
% 5.01/5.34 thf(fact_9952_surj__list__encode,axiom,
% 5.01/5.34 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % surj_list_encode
% 5.01/5.34 thf(fact_9953_list__encode_Osimps_I1_J,axiom,
% 5.01/5.34 ( ( nat_list_encode @ nil_nat )
% 5.01/5.34 = zero_zero_nat ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode.simps(1)
% 5.01/5.34 thf(fact_9954_list__encode_Osimps_I2_J,axiom,
% 5.01/5.34 ! [X2: nat,Xs: list_nat] :
% 5.01/5.34 ( ( nat_list_encode @ ( cons_nat @ X2 @ Xs ) )
% 5.01/5.34 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode.simps(2)
% 5.01/5.34 thf(fact_9955_list__encode_Opelims,axiom,
% 5.01/5.34 ! [X2: list_nat,Y: nat] :
% 5.01/5.34 ( ( ( nat_list_encode @ X2 )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.01/5.34 => ( ( ( X2 = nil_nat )
% 5.01/5.34 => ( ( Y = zero_zero_nat )
% 5.01/5.34 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.01/5.34 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.01/5.34 ( ( X2
% 5.01/5.34 = ( cons_nat @ X4 @ Xs2 ) )
% 5.01/5.34 => ( ( Y
% 5.01/5.34 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 5.01/5.34 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % list_encode.pelims
% 5.01/5.34 thf(fact_9956_sorted__list__of__set__lessThan__Suc,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.01/5.34 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_list_of_set_lessThan_Suc
% 5.01/5.34 thf(fact_9957_sorted__list__of__set__atMost__Suc,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.01/5.34 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_list_of_set_atMost_Suc
% 5.01/5.34 thf(fact_9958_sup__nat__def,axiom,
% 5.01/5.34 sup_sup_nat = ord_max_nat ).
% 5.01/5.34
% 5.01/5.34 % sup_nat_def
% 5.01/5.34 thf(fact_9959_sup__enat__def,axiom,
% 5.01/5.34 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.01/5.34
% 5.01/5.34 % sup_enat_def
% 5.01/5.34 thf(fact_9960_upt__add__eq__append,axiom,
% 5.01/5.34 ! [I: nat,J: nat,K: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.01/5.34 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.01/5.34 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_add_eq_append
% 5.01/5.34 thf(fact_9961_atLeastLessThan__add__Un,axiom,
% 5.01/5.34 ! [I: nat,J: nat,K: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.01/5.34 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.01/5.34 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastLessThan_add_Un
% 5.01/5.34 thf(fact_9962_upt__Suc,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ( ord_less_eq_nat @ I @ J )
% 5.01/5.34 => ( ( upt @ I @ ( suc @ J ) )
% 5.01/5.34 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.01/5.34 => ( ( upt @ I @ ( suc @ J ) )
% 5.01/5.34 = nil_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_Suc
% 5.01/5.34 thf(fact_9963_upt__Suc__append,axiom,
% 5.01/5.34 ! [I: nat,J: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.01/5.34 => ( ( upt @ I @ ( suc @ J ) )
% 5.01/5.34 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upt_Suc_append
% 5.01/5.34 thf(fact_9964_upto__aux__rec,axiom,
% 5.01/5.34 ( upto_aux
% 5.01/5.34 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_aux_rec
% 5.01/5.34 thf(fact_9965_upto_Opsimps,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.01/5.34 => ( ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( upto @ I @ J )
% 5.01/5.34 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( upto @ I @ J )
% 5.01/5.34 = nil_int ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto.psimps
% 5.01/5.34 thf(fact_9966_upto_Opelims,axiom,
% 5.01/5.34 ! [X2: int,Xa: int,Y: list_int] :
% 5.01/5.34 ( ( ( upto @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) )
% 5.01/5.34 => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 5.01/5.34 => ( Y = nil_int ) ) )
% 5.01/5.34 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto.pelims
% 5.01/5.34 thf(fact_9967_upto__empty,axiom,
% 5.01/5.34 ! [J: int,I: int] :
% 5.01/5.34 ( ( ord_less_int @ J @ I )
% 5.01/5.34 => ( ( upto @ I @ J )
% 5.01/5.34 = nil_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_empty
% 5.01/5.34 thf(fact_9968_upto__Nil2,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( nil_int
% 5.01/5.34 = ( upto @ I @ J ) )
% 5.01/5.34 = ( ord_less_int @ J @ I ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_Nil2
% 5.01/5.34 thf(fact_9969_upto__Nil,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( ( upto @ I @ J )
% 5.01/5.34 = nil_int )
% 5.01/5.34 = ( ord_less_int @ J @ I ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_Nil
% 5.01/5.34 thf(fact_9970_upto__single,axiom,
% 5.01/5.34 ! [I: int] :
% 5.01/5.34 ( ( upto @ I @ I )
% 5.01/5.34 = ( cons_int @ I @ nil_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_single
% 5.01/5.34 thf(fact_9971_nth__upto,axiom,
% 5.01/5.34 ! [I: int,K: nat,J: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.01/5.34 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.01/5.34 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nth_upto
% 5.01/5.34 thf(fact_9972_length__upto,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.01/5.34 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % length_upto
% 5.01/5.34 thf(fact_9973_upto__rec__numeral_I1_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec_numeral(1)
% 5.01/5.34 thf(fact_9974_upto__rec__numeral_I4_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec_numeral(4)
% 5.01/5.34 thf(fact_9975_upto__rec__numeral_I3_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec_numeral(3)
% 5.01/5.34 thf(fact_9976_upto__rec__numeral_I2_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec_numeral(2)
% 5.01/5.34 thf(fact_9977_upto__aux__def,axiom,
% 5.01/5.34 ( upto_aux
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( append_int @ ( upto @ I4 @ J3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_aux_def
% 5.01/5.34 thf(fact_9978_upto__code,axiom,
% 5.01/5.34 ( upto
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( upto_aux @ I4 @ J3 @ nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_code
% 5.01/5.34 thf(fact_9979_distinct__upto,axiom,
% 5.01/5.34 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 5.01/5.34
% 5.01/5.34 % distinct_upto
% 5.01/5.34 thf(fact_9980_sorted__wrt__upto,axiom,
% 5.01/5.34 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_wrt_upto
% 5.01/5.34 thf(fact_9981_atLeastAtMost__upto,axiom,
% 5.01/5.34 ( set_or1266510415728281911st_int
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ J3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastAtMost_upto
% 5.01/5.34 thf(fact_9982_sorted__upto,axiom,
% 5.01/5.34 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % sorted_upto
% 5.01/5.34 thf(fact_9983_upto__split2,axiom,
% 5.01/5.34 ! [I: int,J: int,K: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( ord_less_eq_int @ J @ K )
% 5.01/5.34 => ( ( upto @ I @ K )
% 5.01/5.34 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_split2
% 5.01/5.34 thf(fact_9984_upto__split1,axiom,
% 5.01/5.34 ! [I: int,J: int,K: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( ord_less_eq_int @ J @ K )
% 5.01/5.34 => ( ( upto @ I @ K )
% 5.01/5.34 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_split1
% 5.01/5.34 thf(fact_9985_atLeastLessThan__upto,axiom,
% 5.01/5.34 ( set_or4662586982721622107an_int
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeastLessThan_upto
% 5.01/5.34 thf(fact_9986_greaterThanAtMost__upto,axiom,
% 5.01/5.34 ( set_or6656581121297822940st_int
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThanAtMost_upto
% 5.01/5.34 thf(fact_9987_upto_Oelims,axiom,
% 5.01/5.34 ! [X2: int,Xa: int,Y: list_int] :
% 5.01/5.34 ( ( ( upto @ X2 @ Xa )
% 5.01/5.34 = Y )
% 5.01/5.34 => ( ( ( ord_less_eq_int @ X2 @ Xa )
% 5.01/5.34 => ( Y
% 5.01/5.34 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa ) ) ) )
% 5.01/5.34 & ( ~ ( ord_less_eq_int @ X2 @ Xa )
% 5.01/5.34 => ( Y = nil_int ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto.elims
% 5.01/5.34 thf(fact_9988_upto_Osimps,axiom,
% 5.01/5.34 ( upto
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto.simps
% 5.01/5.34 thf(fact_9989_upto__rec1,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( upto @ I @ J )
% 5.01/5.34 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec1
% 5.01/5.34 thf(fact_9990_upto__rec2,axiom,
% 5.01/5.34 ! [I: int,J: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( upto @ I @ J )
% 5.01/5.34 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_rec2
% 5.01/5.34 thf(fact_9991_greaterThanLessThan__upto,axiom,
% 5.01/5.34 ( set_or5832277885323065728an_int
% 5.01/5.34 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThanLessThan_upto
% 5.01/5.34 thf(fact_9992_upto__split3,axiom,
% 5.01/5.34 ! [I: int,J: int,K: int] :
% 5.01/5.34 ( ( ord_less_eq_int @ I @ J )
% 5.01/5.34 => ( ( ord_less_eq_int @ J @ K )
% 5.01/5.34 => ( ( upto @ I @ K )
% 5.01/5.34 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % upto_split3
% 5.01/5.34 thf(fact_9993_take__bit__numeral__minus__numeral__int,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int
% 5.01/5.34 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.01/5.34 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_numeral_minus_numeral_int
% 5.01/5.34 thf(fact_9994_take__bit__num__simps_I1_J,axiom,
% 5.01/5.34 ! [M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.01/5.34 = none_num ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(1)
% 5.01/5.34 thf(fact_9995_take__bit__num__simps_I2_J,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.01/5.34 = ( some_num @ one ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(2)
% 5.01/5.34 thf(fact_9996_take__bit__num__simps_I5_J,axiom,
% 5.01/5.34 ! [R: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 5.01/5.34 = ( some_num @ one ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(5)
% 5.01/5.34 thf(fact_9997_take__bit__num__simps_I3_J,axiom,
% 5.01/5.34 ! [N: nat,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.01/5.34 = ( case_o6005452278849405969um_num @ none_num
% 5.01/5.34 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.01/5.34 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(3)
% 5.01/5.34 thf(fact_9998_take__bit__num__simps_I4_J,axiom,
% 5.01/5.34 ! [N: nat,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.01/5.34 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(4)
% 5.01/5.34 thf(fact_9999_take__bit__num__simps_I6_J,axiom,
% 5.01/5.34 ! [R: num,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 5.01/5.34 = ( case_o6005452278849405969um_num @ none_num
% 5.01/5.34 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.01/5.34 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(6)
% 5.01/5.34 thf(fact_10000_take__bit__num__simps_I7_J,axiom,
% 5.01/5.34 ! [R: num,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 5.01/5.34 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_simps(7)
% 5.01/5.34 thf(fact_10001_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.01/5.34 ! [N: nat,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.01/5.34 = ( case_nat_option_num @ none_num
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( case_o6005452278849405969um_num @ none_num
% 5.01/5.34 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.01/5.34 @ ( bit_take_bit_num @ N4 @ M ) )
% 5.01/5.34 @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.01/5.34 thf(fact_10002_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( bit_take_bit_num @ N @ one )
% 5.01/5.34 = ( case_nat_option_num @ none_num
% 5.01/5.34 @ ^ [N4: nat] : ( some_num @ one )
% 5.01/5.34 @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.01/5.34 thf(fact_10003_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.01/5.34 ! [N: nat,M: num] :
% 5.01/5.34 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.01/5.34 = ( case_nat_option_num @ none_num
% 5.01/5.34 @ ^ [N4: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N4 @ M ) ) )
% 5.01/5.34 @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.01/5.34 thf(fact_10004_take__bit__num__def,axiom,
% 5.01/5.34 ( bit_take_bit_num
% 5.01/5.34 = ( ^ [N4: nat,M3: num] :
% 5.01/5.34 ( if_option_num
% 5.01/5.34 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M3 ) )
% 5.01/5.34 = zero_zero_nat )
% 5.01/5.34 @ none_num
% 5.01/5.34 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % take_bit_num_def
% 5.01/5.34 thf(fact_10005_and__minus__numerals_I3_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_minus_numerals(3)
% 5.01/5.34 thf(fact_10006_and__minus__numerals_I7_J,axiom,
% 5.01/5.34 ! [N: num,M: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_minus_numerals(7)
% 5.01/5.34 thf(fact_10007_and__minus__numerals_I4_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_minus_numerals(4)
% 5.01/5.34 thf(fact_10008_and__minus__numerals_I8_J,axiom,
% 5.01/5.34 ! [N: num,M: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_minus_numerals(8)
% 5.01/5.34 thf(fact_10009_and__not__num_Osimps_I1_J,axiom,
% 5.01/5.34 ( ( bit_and_not_num @ one @ one )
% 5.01/5.34 = none_num ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(1)
% 5.01/5.34 thf(fact_10010_and__not__num_Osimps_I3_J,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.01/5.34 = none_num ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(3)
% 5.01/5.34 thf(fact_10011_and__not__num_Osimps_I4_J,axiom,
% 5.01/5.34 ! [M: num] :
% 5.01/5.34 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.01/5.34 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(4)
% 5.01/5.34 thf(fact_10012_and__not__num_Osimps_I2_J,axiom,
% 5.01/5.34 ! [N: num] :
% 5.01/5.34 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.01/5.34 = ( some_num @ one ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(2)
% 5.01/5.34 thf(fact_10013_and__not__num_Osimps_I7_J,axiom,
% 5.01/5.34 ! [M: num] :
% 5.01/5.34 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.01/5.34 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(7)
% 5.01/5.34 thf(fact_10014_and__not__num__eq__Some__iff,axiom,
% 5.01/5.34 ! [M: num,N: num,Q2: num] :
% 5.01/5.34 ( ( ( bit_and_not_num @ M @ N )
% 5.01/5.34 = ( some_num @ Q2 ) )
% 5.01/5.34 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num_eq_Some_iff
% 5.01/5.34 thf(fact_10015_and__not__num_Osimps_I8_J,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.01/5.34 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.01/5.34 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.01/5.34 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num.simps(8)
% 5.01/5.34 thf(fact_10016_and__not__num__eq__None__iff,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( ( bit_and_not_num @ M @ N )
% 5.01/5.34 = none_num )
% 5.01/5.34 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = zero_zero_int ) ) ).
% 5.01/5.34
% 5.01/5.34 % and_not_num_eq_None_iff
% 5.01/5.34 thf(fact_10017_int__numeral__and__not__num,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % int_numeral_and_not_num
% 5.01/5.34 thf(fact_10018_int__numeral__not__and__num,axiom,
% 5.01/5.34 ! [M: num,N: num] :
% 5.01/5.34 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.01/5.34 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % int_numeral_not_and_num
% 5.01/5.34 thf(fact_10019_Bit__Operations_Otake__bit__num__code,axiom,
% 5.01/5.34 ( bit_take_bit_num
% 5.01/5.34 = ( ^ [N4: nat,M3: num] :
% 5.01/5.34 ( produc478579273971653890on_num
% 5.01/5.34 @ ^ [A4: nat,X3: num] :
% 5.01/5.34 ( case_nat_option_num @ none_num
% 5.01/5.34 @ ^ [O: nat] :
% 5.01/5.34 ( case_num_option_num @ ( some_num @ one )
% 5.01/5.34 @ ^ [P5: num] :
% 5.01/5.34 ( case_o6005452278849405969um_num @ none_num
% 5.01/5.34 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.01/5.34 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.01/5.34 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.01/5.34 @ X3 )
% 5.01/5.34 @ A4 )
% 5.01/5.34 @ ( product_Pair_nat_num @ N4 @ M3 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Bit_Operations.take_bit_num_code
% 5.01/5.34 thf(fact_10020_DERIV__real__root__generic,axiom,
% 5.01/5.34 ! [N: nat,X2: real,D4: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( X2 != zero_zero_real )
% 5.01/5.34 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( D4
% 5.01/5.34 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.01/5.34 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.34 => ( D4
% 5.01/5.34 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.01/5.34 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( D4
% 5.01/5.34 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_real_root_generic
% 5.01/5.34 thf(fact_10021_DERIV__even__real__root,axiom,
% 5.01/5.34 ! [N: nat,X2: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_even_real_root
% 5.01/5.34 thf(fact_10022_DERIV__neg__imp__decreasing,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.01/5.34 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_neg_imp_decreasing
% 5.01/5.34 thf(fact_10023_DERIV__pos__imp__increasing,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.01/5.34 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_pos_imp_increasing
% 5.01/5.34 thf(fact_10024_MVT2,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.01/5.34 => ? [Z3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ Z3 )
% 5.01/5.34 & ( ord_less_real @ Z3 @ B )
% 5.01/5.34 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.01/5.34 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % MVT2
% 5.01/5.34 thf(fact_10025_DERIV__local__min,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,D: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.01/5.34 => ( ! [Y3: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.01/5.34 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 5.01/5.34 => ( L = zero_zero_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_local_min
% 5.01/5.34 thf(fact_10026_DERIV__local__max,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,D: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.01/5.34 => ( ! [Y3: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.01/5.34 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 5.01/5.34 => ( L = zero_zero_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_local_max
% 5.01/5.34 thf(fact_10027_has__real__derivative__pos__inc__left,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( member_real @ ( minus_minus_real @ X2 @ H3 ) @ S )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H3 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % has_real_derivative_pos_inc_left
% 5.01/5.34 thf(fact_10028_has__real__derivative__neg__dec__left,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.01/5.34 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( member_real @ ( minus_minus_real @ X2 @ H3 ) @ S )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % has_real_derivative_neg_dec_left
% 5.01/5.34 thf(fact_10029_has__real__derivative__pos__inc__right,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( member_real @ ( plus_plus_real @ X2 @ H3 ) @ S )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % has_real_derivative_pos_inc_right
% 5.01/5.34 thf(fact_10030_has__real__derivative__neg__dec__right,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,S: set_real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S ) )
% 5.01/5.34 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( member_real @ ( plus_plus_real @ X2 @ H3 ) @ S )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H3 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % has_real_derivative_neg_dec_right
% 5.01/5.34 thf(fact_10031_DERIV__isconst3,axiom,
% 5.01/5.34 ! [A: real,B: real,X2: real,Y: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ( F @ X2 )
% 5.01/5.34 = ( F @ Y ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_isconst3
% 5.01/5.34 thf(fact_10032_DERIV__local__const,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real,D: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.01/5.34 => ( ! [Y3: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.01/5.34 => ( ( F @ X2 )
% 5.01/5.34 = ( F @ Y3 ) ) )
% 5.01/5.34 => ( L = zero_zero_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_local_const
% 5.01/5.34 thf(fact_10033_DERIV__pos__inc__left,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H3 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_pos_inc_left
% 5.01/5.34 thf(fact_10034_DERIV__neg__dec__left,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H3 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_neg_dec_left
% 5.01/5.34 thf(fact_10035_DERIV__ln,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_ln
% 5.01/5.34 thf(fact_10036_DERIV__neg__dec__right,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H3 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_neg_dec_right
% 5.01/5.34 thf(fact_10037_DERIV__pos__inc__right,axiom,
% 5.01/5.34 ! [F: real > real,L: real,X2: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.01/5.34 => ? [D2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.01/5.34 & ! [H3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H3 )
% 5.01/5.34 => ( ( ord_less_real @ H3 @ D2 )
% 5.01/5.34 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H3 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_pos_inc_right
% 5.01/5.34 thf(fact_10038_DERIV__ln__divide,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_ln_divide
% 5.01/5.34 thf(fact_10039_DERIV__pow,axiom,
% 5.01/5.34 ! [N: nat,X2: real,S2: set_real] :
% 5.01/5.34 ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 5.01/5.34 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_pow
% 5.01/5.34 thf(fact_10040_DERIV__mirror,axiom,
% 5.01/5.34 ! [F: real > real,Y: real,X2: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ X2 ) @ top_top_set_real ) )
% 5.01/5.34 = ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( F @ ( uminus_uminus_real @ X3 ) )
% 5.01/5.34 @ ( uminus_uminus_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_mirror
% 5.01/5.34 thf(fact_10041_DERIV__isconst__all,axiom,
% 5.01/5.34 ! [F: real > real,X2: real,Y: real] :
% 5.01/5.34 ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ( ( F @ X2 )
% 5.01/5.34 = ( F @ Y ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_isconst_all
% 5.01/5.34 thf(fact_10042_DERIV__const__ratio__const2,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real,K: real] :
% 5.01/5.34 ( ( A != B )
% 5.01/5.34 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.01/5.34 = K ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_const_ratio_const2
% 5.01/5.34 thf(fact_10043_DERIV__const__ratio__const,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real,K: real] :
% 5.01/5.34 ( ( A != B )
% 5.01/5.34 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.01/5.34 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_const_ratio_const
% 5.01/5.34 thf(fact_10044_DERIV__const__average,axiom,
% 5.01/5.34 ! [A: real,B: real,V: real > real,K: real] :
% 5.01/5.34 ( ( A != B )
% 5.01/5.34 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.01/5.34 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_const_average
% 5.01/5.34 thf(fact_10045_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.01/5.34 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_nonpos_imp_nonincreasing
% 5.01/5.34 thf(fact_10046_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.01/5.34 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_nonneg_imp_nondecreasing
% 5.01/5.34 thf(fact_10047_deriv__nonneg__imp__mono,axiom,
% 5.01/5.34 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.01/5.34 ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.01/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 5.01/5.34 => ( ( ord_less_eq_real @ A @ B )
% 5.01/5.34 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % deriv_nonneg_imp_mono
% 5.01/5.34 thf(fact_10048_DERIV__fun__pow,axiom,
% 5.01/5.34 ! [G: real > real,M: real,X2: real,N: nat] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 5.01/5.34 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_fun_pow
% 5.01/5.34 thf(fact_10049_has__real__derivative__powr,axiom,
% 5.01/5.34 ! [Z: real,R: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [Z5: real] : ( powr_real @ Z5 @ R )
% 5.01/5.34 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % has_real_derivative_powr
% 5.01/5.34 thf(fact_10050_DERIV__log,axiom,
% 5.01/5.34 ! [X2: real,B: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_log
% 5.01/5.34 thf(fact_10051_DERIV__fun__powr,axiom,
% 5.01/5.34 ! [G: real > real,M: real,X2: real,R: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R )
% 5.01/5.34 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_fun_powr
% 5.01/5.34 thf(fact_10052_DERIV__powr,axiom,
% 5.01/5.34 ! [G: real > real,M: real,X2: real,F: real > real,R: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.01/5.34 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 5.01/5.34 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_powr
% 5.01/5.34 thf(fact_10053_DERIV__real__sqrt,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_real_sqrt
% 5.01/5.34 thf(fact_10054_DERIV__series_H,axiom,
% 5.01/5.34 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L4: nat > real] :
% 5.01/5.34 ( ! [N3: nat] :
% 5.01/5.34 ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( F @ X3 @ N3 )
% 5.01/5.34 @ ( F4 @ X0 @ N3 )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( summable_real @ ( F @ X4 ) ) )
% 5.01/5.34 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.01/5.34 => ( ( summable_real @ L4 )
% 5.01/5.34 => ( ! [N3: nat,X4: real,Y3: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L4 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) ) ) ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 5.01/5.34 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_series'
% 5.01/5.34 thf(fact_10055_DERIV__arctan,axiom,
% 5.01/5.34 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_arctan
% 5.01/5.34 thf(fact_10056_arsinh__real__has__field__derivative,axiom,
% 5.01/5.34 ! [X2: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ).
% 5.01/5.34
% 5.01/5.34 % arsinh_real_has_field_derivative
% 5.01/5.34 thf(fact_10057_DERIV__real__sqrt__generic,axiom,
% 5.01/5.34 ! [X2: real,D4: real] :
% 5.01/5.34 ( ( X2 != zero_zero_real )
% 5.01/5.34 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( D4
% 5.01/5.34 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.34 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.01/5.34 => ( D4
% 5.01/5.34 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_real_sqrt_generic
% 5.01/5.34 thf(fact_10058_arcosh__real__has__field__derivative,axiom,
% 5.01/5.34 ! [X2: real,A2: set_real] :
% 5.01/5.34 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % arcosh_real_has_field_derivative
% 5.01/5.34 thf(fact_10059_artanh__real__has__field__derivative,axiom,
% 5.01/5.34 ! [X2: real,A2: set_real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A2 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % artanh_real_has_field_derivative
% 5.01/5.34 thf(fact_10060_DERIV__power__series_H,axiom,
% 5.01/5.34 ! [R2: real,F: nat > real,X0: real] :
% 5.01/5.34 ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.01/5.34 => ( summable_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X4 @ N4 ) ) ) )
% 5.01/5.34 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( suminf_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X3 @ ( suc @ N4 ) ) ) )
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_power_series'
% 5.01/5.34 thf(fact_10061_DERIV__real__root,axiom,
% 5.01/5.34 ! [N: nat,X2: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_real_root
% 5.01/5.34 thf(fact_10062_DERIV__arccos,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_arccos
% 5.01/5.34 thf(fact_10063_DERIV__arcsin,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_arcsin
% 5.01/5.34 thf(fact_10064_Maclaurin__all__le,axiom,
% 5.01/5.34 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.01/5.34 ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.34 & ( ( F @ X2 )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_all_le
% 5.01/5.34 thf(fact_10065_Maclaurin__all__le__objl,axiom,
% 5.01/5.34 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.01/5.34 ( ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.34 & ( ( F @ X2 )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_all_le_objl
% 5.01/5.34 thf(fact_10066_DERIV__odd__real__root,axiom,
% 5.01/5.34 ! [N: nat,X2: real] :
% 5.01/5.34 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( ( X2 != zero_zero_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_odd_real_root
% 5.01/5.34 thf(fact_10067_Maclaurin__minus,axiom,
% 5.01/5.34 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ H @ zero_zero_real )
% 5.01/5.34 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ H @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ H @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.01/5.34 & ( ( F @ H )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_minus
% 5.01/5.34 thf(fact_10068_Maclaurin2,axiom,
% 5.01/5.34 ! [H: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ H ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ H )
% 5.01/5.34 & ( ( F @ H )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin2
% 5.01/5.34 thf(fact_10069_Maclaurin,axiom,
% 5.01/5.34 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ H )
% 5.01/5.34 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ H ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ H )
% 5.01/5.34 & ( ( F @ H )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin
% 5.01/5.34 thf(fact_10070_Maclaurin__all__lt,axiom,
% 5.01/5.34 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.01/5.34 ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( X2 != zero_zero_real )
% 5.01/5.34 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.01/5.34 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.34 & ( ( F @ X2 )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_all_lt
% 5.01/5.34 thf(fact_10071_Maclaurin__bi__le,axiom,
% 5.01/5.34 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.01/5.34 ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.01/5.34 & ( ( F @ X2 )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X2 @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_bi_le
% 5.01/5.34 thf(fact_10072_Taylor,axiom,
% 5.01/5.34 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X2: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ A @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ B ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ( ord_less_eq_real @ A @ C )
% 5.01/5.34 => ( ( ord_less_eq_real @ C @ B )
% 5.01/5.34 => ( ( ord_less_eq_real @ A @ X2 )
% 5.01/5.34 => ( ( ord_less_eq_real @ X2 @ B )
% 5.01/5.34 => ( ( X2 != C )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ( ord_less_real @ X2 @ C )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ C ) ) )
% 5.01/5.34 & ( ~ ( ord_less_real @ X2 @ C )
% 5.01/5.34 => ( ( ord_less_real @ C @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ X2 ) ) )
% 5.01/5.34 & ( ( F @ X2 )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Taylor
% 5.01/5.34 thf(fact_10073_Taylor__up,axiom,
% 5.01/5.34 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ A @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ B ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ( ord_less_eq_real @ A @ C )
% 5.01/5.34 => ( ( ord_less_real @ C @ B )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ C @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ B )
% 5.01/5.34 & ( ( F @ B )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Taylor_up
% 5.01/5.34 thf(fact_10074_Taylor__down,axiom,
% 5.01/5.34 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( ( Diff @ zero_zero_nat )
% 5.01/5.34 = F )
% 5.01/5.34 => ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ A @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ B ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ( ord_less_real @ A @ C )
% 5.01/5.34 => ( ( ord_less_eq_real @ C @ B )
% 5.01/5.34 => ? [T3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ T3 )
% 5.01/5.34 & ( ord_less_real @ T3 @ C )
% 5.01/5.34 & ( ( F @ A )
% 5.01/5.34 = ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ N ) )
% 5.01/5.34 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Taylor_down
% 5.01/5.34 thf(fact_10075_Maclaurin__lemma2,axiom,
% 5.01/5.34 ! [N: nat,H: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.01/5.34 ( ! [M4: nat,T3: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M4 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.01/5.34 & ( ord_less_eq_real @ T3 @ H ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.01/5.34 => ( ( N
% 5.01/5.34 = ( suc @ K ) )
% 5.01/5.34 => ! [M2: nat,T4: real] :
% 5.01/5.34 ( ( ( ord_less_nat @ M2 @ N )
% 5.01/5.34 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.01/5.34 & ( ord_less_eq_real @ T4 @ H ) )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [U3: real] :
% 5.01/5.34 ( minus_minus_real @ ( Diff @ M2 @ U3 )
% 5.01/5.34 @ ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U3 @ P5 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.01/5.34 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U3 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.01/5.34 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 5.01/5.34 @ ( plus_plus_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T4 @ P5 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.01/5.34 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Maclaurin_lemma2
% 5.01/5.34 thf(fact_10076_DERIV__arctan__series,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.34 => ( has_fi5821293074295781190e_real
% 5.01/5.34 @ ^ [X9: real] :
% 5.01/5.34 ( suminf_real
% 5.01/5.34 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_arctan_series
% 5.01/5.34 thf(fact_10077_LIM__fun__less__zero,axiom,
% 5.01/5.34 ! [F: real > real,L: real,C: real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.01/5.34 => ? [R4: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.01/5.34 & ! [X: real] :
% 5.01/5.34 ( ( ( X != C )
% 5.01/5.34 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R4 ) )
% 5.01/5.34 => ( ord_less_real @ ( F @ X ) @ zero_zero_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIM_fun_less_zero
% 5.01/5.34 thf(fact_10078_LIM__fun__not__zero,axiom,
% 5.01/5.34 ! [F: real > real,L: real,C: real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.01/5.34 => ( ( L != zero_zero_real )
% 5.01/5.34 => ? [R4: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.01/5.34 & ! [X: real] :
% 5.01/5.34 ( ( ( X != C )
% 5.01/5.34 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R4 ) )
% 5.01/5.34 => ( ( F @ X )
% 5.01/5.34 != zero_zero_real ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIM_fun_not_zero
% 5.01/5.34 thf(fact_10079_LIM__fun__gt__zero,axiom,
% 5.01/5.34 ! [F: real > real,L: real,C: real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.01/5.34 => ? [R4: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.01/5.34 & ! [X: real] :
% 5.01/5.34 ( ( ( X != C )
% 5.01/5.34 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X ) ) @ R4 ) )
% 5.01/5.34 => ( ord_less_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIM_fun_gt_zero
% 5.01/5.34 thf(fact_10080_isCont__real__root,axiom,
% 5.01/5.34 ! [X2: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_real_root
% 5.01/5.34 thf(fact_10081_isCont__real__sqrt,axiom,
% 5.01/5.34 ! [X2: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ sqrt ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_real_sqrt
% 5.01/5.34 thf(fact_10082_isCont__Lb__Ub,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ B )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 & ( ord_less_eq_real @ X4 @ B ) )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.01/5.34 => ? [L5: real,M9: real] :
% 5.01/5.34 ( ! [X: real] :
% 5.01/5.34 ( ( ( ord_less_eq_real @ A @ X )
% 5.01/5.34 & ( ord_less_eq_real @ X @ B ) )
% 5.01/5.34 => ( ( ord_less_eq_real @ L5 @ ( F @ X ) )
% 5.01/5.34 & ( ord_less_eq_real @ ( F @ X ) @ M9 ) ) )
% 5.01/5.34 & ! [Y4: real] :
% 5.01/5.34 ( ( ( ord_less_eq_real @ L5 @ Y4 )
% 5.01/5.34 & ( ord_less_eq_real @ Y4 @ M9 ) )
% 5.01/5.34 => ? [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ X4 )
% 5.01/5.34 & ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 & ( ( F @ X4 )
% 5.01/5.34 = Y4 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_Lb_Ub
% 5.01/5.34 thf(fact_10083_continuous__frac,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ~ ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ archim2898591450579166408c_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % continuous_frac
% 5.01/5.34 thf(fact_10084_isCont__inverse__function2,axiom,
% 5.01/5.34 ! [A: real,X2: real,B: real,G: real > real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ B )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.01/5.34 => ( ( G @ ( F @ Z3 ) )
% 5.01/5.34 = Z3 ) ) )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_inverse_function2
% 5.01/5.34 thf(fact_10085_isCont__ln,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( X2 != zero_zero_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ ln_ln_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_ln
% 5.01/5.34 thf(fact_10086_isCont__arcosh,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_arcosh
% 5.01/5.34 thf(fact_10087_LIM__cos__div__sin,axiom,
% 5.01/5.34 ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIM_cos_div_sin
% 5.01/5.34 thf(fact_10088_continuous__floor,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ~ ( member_real @ X2 @ ring_1_Ints_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ ( comp_int_real_real @ ring_1_of_int_real @ archim6058952711729229775r_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % continuous_floor
% 5.01/5.34 thf(fact_10089_DERIV__inverse__function,axiom,
% 5.01/5.34 ! [F: real > real,D4: real,G: real > real,X2: real,A: real,B: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X2 ) @ top_top_set_real ) )
% 5.01/5.34 => ( ( D4 != zero_zero_real )
% 5.01/5.34 => ( ( ord_less_real @ A @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ B )
% 5.01/5.34 => ( ! [Y3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ Y3 )
% 5.01/5.34 => ( ( ord_less_real @ Y3 @ B )
% 5.01/5.34 => ( ( F @ ( G @ Y3 ) )
% 5.01/5.34 = Y3 ) ) )
% 5.01/5.34 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ G )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_inverse_function
% 5.01/5.34 thf(fact_10090_isCont__arccos,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_arccos
% 5.01/5.34 thf(fact_10091_isCont__arcsin,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_arcsin
% 5.01/5.34 thf(fact_10092_LIM__less__bound,axiom,
% 5.01/5.34 ! [B: real,X2: real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ B @ X2 )
% 5.01/5.34 => ( ! [X4: real] :
% 5.01/5.34 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X2 ) )
% 5.01/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.01/5.34 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.01/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIM_less_bound
% 5.01/5.34 thf(fact_10093_isCont__artanh,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_artanh
% 5.01/5.34 thf(fact_10094_isCont__inverse__function,axiom,
% 5.01/5.34 ! [D: real,X2: real,G: real > real,F: real > real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ D )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D )
% 5.01/5.34 => ( ( G @ ( F @ Z3 ) )
% 5.01/5.34 = Z3 ) )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X2 ) ) @ D )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % isCont_inverse_function
% 5.01/5.34 thf(fact_10095_GMVT_H,axiom,
% 5.01/5.34 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.01/5.34 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_real @ Z3 @ B )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.01/5.34 => ( ! [Z3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ Z3 )
% 5.01/5.34 => ( ( ord_less_real @ Z3 @ B )
% 5.01/5.34 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.01/5.34 => ? [C3: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ C3 )
% 5.01/5.34 & ( ord_less_real @ C3 @ B )
% 5.01/5.34 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.01/5.34 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % GMVT'
% 5.01/5.34 thf(fact_10096_summable__Leibniz_I3_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ( topolo6980174941875973593q_real @ A )
% 5.01/5.34 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.01/5.34 => ! [N6: nat] :
% 5.01/5.34 ( member_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.01/5.34 @ ( set_or1222579329274155063t_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz(3)
% 5.01/5.34 thf(fact_10097_summable__Leibniz_I2_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ( topolo6980174941875973593q_real @ A )
% 5.01/5.34 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.01/5.34 => ! [N6: nat] :
% 5.01/5.34 ( member_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.01/5.34 @ ( set_or1222579329274155063t_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz(2)
% 5.01/5.34 thf(fact_10098_filterlim__Suc,axiom,
% 5.01/5.34 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.01/5.34
% 5.01/5.34 % filterlim_Suc
% 5.01/5.34 thf(fact_10099_mult__nat__right__at__top,axiom,
% 5.01/5.34 ! [C: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.34 => ( filterlim_nat_nat
% 5.01/5.34 @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 5.01/5.34 @ at_top_nat
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % mult_nat_right_at_top
% 5.01/5.34 thf(fact_10100_mult__nat__left__at__top,axiom,
% 5.01/5.34 ! [C: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.01/5.34 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % mult_nat_left_at_top
% 5.01/5.34 thf(fact_10101_monoseq__convergent,axiom,
% 5.01/5.34 ! [X8: nat > real,B4: real] :
% 5.01/5.34 ( ( topolo6980174941875973593q_real @ X8 )
% 5.01/5.34 => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I3 ) ) @ B4 )
% 5.01/5.34 => ~ ! [L5: real] :
% 5.01/5.34 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % monoseq_convergent
% 5.01/5.34 thf(fact_10102_LIMSEQ__root,axiom,
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( root @ N4 @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_root
% 5.01/5.34 thf(fact_10103_nested__sequence__unique,axiom,
% 5.01/5.34 ! [F: nat > real,G: nat > real] :
% 5.01/5.34 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.01/5.34 => ( ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 => ? [L3: real] :
% 5.01/5.34 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L3 )
% 5.01/5.34 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat )
% 5.01/5.34 & ! [N6: nat] : ( ord_less_eq_real @ L3 @ ( G @ N6 ) )
% 5.01/5.34 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L3 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % nested_sequence_unique
% 5.01/5.34 thf(fact_10104_LIMSEQ__inverse__zero,axiom,
% 5.01/5.34 ! [X8: nat > real] :
% 5.01/5.34 ( ! [R4: real] :
% 5.01/5.34 ? [N7: nat] :
% 5.01/5.34 ! [N3: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.01/5.34 => ( ord_less_real @ R4 @ ( X8 @ N3 ) ) )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X8 @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_zero
% 5.01/5.34 thf(fact_10105_lim__inverse__n_H,axiom,
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % lim_inverse_n'
% 5.01/5.34 thf(fact_10106_LIMSEQ__root__const,axiom,
% 5.01/5.34 ! [C: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ C )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( root @ N4 @ C )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_root_const
% 5.01/5.34 thf(fact_10107_LIMSEQ__inverse__real__of__nat,axiom,
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_real_of_nat
% 5.01/5.34 thf(fact_10108_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.01/5.34 ! [R: real] :
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ R )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_real_of_nat_add
% 5.01/5.34 thf(fact_10109_increasing__LIMSEQ,axiom,
% 5.01/5.34 ! [F: nat > real,L: real] :
% 5.01/5.34 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 5.01/5.34 => ( ! [E2: real] :
% 5.01/5.34 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.01/5.34 => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E2 ) ) )
% 5.01/5.34 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % increasing_LIMSEQ
% 5.01/5.34 thf(fact_10110_LIMSEQ__realpow__zero,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.01/5.34 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.01/5.34 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_realpow_zero
% 5.01/5.34 thf(fact_10111_LIMSEQ__divide__realpow__zero,axiom,
% 5.01/5.34 ! [X2: real,A: real] :
% 5.01/5.34 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( divide_divide_real @ A @ ( power_power_real @ X2 @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_divide_realpow_zero
% 5.01/5.34 thf(fact_10112_LIMSEQ__abs__realpow__zero,axiom,
% 5.01/5.34 ! [C: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.01/5.34 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_abs_realpow_zero
% 5.01/5.34 thf(fact_10113_LIMSEQ__abs__realpow__zero2,axiom,
% 5.01/5.34 ! [C: real] :
% 5.01/5.34 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.01/5.34 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_abs_realpow_zero2
% 5.01/5.34 thf(fact_10114_LIMSEQ__inverse__realpow__zero,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_real @ one_one_real @ X2 )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N4 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_realpow_zero
% 5.01/5.34 thf(fact_10115_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.01/5.34 ! [R: real] :
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ R )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.01/5.34 thf(fact_10116_tendsto__exp__limit__sequentially,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N4 ) ) ) @ N4 )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % tendsto_exp_limit_sequentially
% 5.01/5.34 thf(fact_10117_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.01/5.34 ! [R: real] :
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ R )
% 5.01/5.34 @ at_top_nat ) ).
% 5.01/5.34
% 5.01/5.34 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.01/5.34 thf(fact_10118_summable__Leibniz_I1_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ( topolo6980174941875973593q_real @ A )
% 5.01/5.34 => ( summable_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz(1)
% 5.01/5.34 thf(fact_10119_summable,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( summable_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable
% 5.01/5.34 thf(fact_10120_cos__diff__limit__1,axiom,
% 5.01/5.34 ! [Theta: nat > real,Theta2: real] :
% 5.01/5.34 ( ( filterlim_nat_real
% 5.01/5.34 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 => ~ ! [K3: nat > int] :
% 5.01/5.34 ~ ( filterlim_nat_real
% 5.01/5.34 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % cos_diff_limit_1
% 5.01/5.34 thf(fact_10121_cos__limit__1,axiom,
% 5.01/5.34 ! [Theta: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real
% 5.01/5.34 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 => ? [K3: nat > int] :
% 5.01/5.34 ( filterlim_nat_real
% 5.01/5.34 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % cos_limit_1
% 5.01/5.34 thf(fact_10122_summable__Leibniz_I4_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ( topolo6980174941875973593q_real @ A )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.01/5.34 @ at_top_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz(4)
% 5.01/5.34 thf(fact_10123_zeroseq__arctan__series,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % zeroseq_arctan_series
% 5.01/5.34 thf(fact_10124_summable__Leibniz_H_I2_J,axiom,
% 5.01/5.34 ! [A: nat > real,N: nat] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( ord_less_eq_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz'(2)
% 5.01/5.34 thf(fact_10125_summable__Leibniz_H_I3_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.01/5.34 @ at_top_nat ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz'(3)
% 5.01/5.34 thf(fact_10126_sums__alternating__upper__lower,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ? [L3: real] :
% 5.01/5.34 ( ! [N6: nat] :
% 5.01/5.34 ( ord_less_eq_real
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.01/5.34 @ L3 )
% 5.01/5.34 & ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ L3 )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 & ! [N6: nat] :
% 5.01/5.34 ( ord_less_eq_real @ L3
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 5.01/5.34 & ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ L3 )
% 5.01/5.34 @ at_top_nat ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % sums_alternating_upper_lower
% 5.01/5.34 thf(fact_10127_summable__Leibniz_I5_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ( topolo6980174941875973593q_real @ A )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.01/5.34 @ at_top_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz(5)
% 5.01/5.34 thf(fact_10128_summable__Leibniz_H_I5_J,axiom,
% 5.01/5.34 ! [A: nat > real] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( filterlim_nat_real
% 5.01/5.34 @ ^ [N4: nat] :
% 5.01/5.34 ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.01/5.34 @ at_top_nat ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz'(5)
% 5.01/5.34 thf(fact_10129_summable__Leibniz_H_I4_J,axiom,
% 5.01/5.34 ! [A: nat > real,N: nat] :
% 5.01/5.34 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.01/5.34 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.01/5.34 => ( ord_less_eq_real
% 5.01/5.34 @ ( suminf_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.01/5.34 @ ( groups6591440286371151544t_real
% 5.01/5.34 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.01/5.34 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % summable_Leibniz'(4)
% 5.01/5.34 thf(fact_10130_real__bounded__linear,axiom,
% 5.01/5.34 ( real_V5970128139526366754l_real
% 5.01/5.34 = ( ^ [F3: real > real] :
% 5.01/5.34 ? [C2: real] :
% 5.01/5.34 ( F3
% 5.01/5.34 = ( ^ [X3: real] : ( times_times_real @ X3 @ C2 ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % real_bounded_linear
% 5.01/5.34 thf(fact_10131_tendsto__arctan__at__bot,axiom,
% 5.01/5.34 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.01/5.34
% 5.01/5.34 % tendsto_arctan_at_bot
% 5.01/5.34 thf(fact_10132_dist__real__def,axiom,
% 5.01/5.34 ( real_V975177566351809787t_real
% 5.01/5.34 = ( ^ [X3: real,Y2: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % dist_real_def
% 5.01/5.34 thf(fact_10133_dist__complex__def,axiom,
% 5.01/5.34 ( real_V3694042436643373181omplex
% 5.01/5.34 = ( ^ [X3: complex,Y2: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y2 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % dist_complex_def
% 5.01/5.34 thf(fact_10134_exp__at__bot,axiom,
% 5.01/5.34 filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 5.01/5.34
% 5.01/5.34 % exp_at_bot
% 5.01/5.34 thf(fact_10135_filterlim__inverse__at__bot__neg,axiom,
% 5.01/5.34 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_inverse_at_bot_neg
% 5.01/5.34 thf(fact_10136_tanh__real__at__bot,axiom,
% 5.01/5.34 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.01/5.34
% 5.01/5.34 % tanh_real_at_bot
% 5.01/5.34 thf(fact_10137_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.01/5.34 ! [B: real,F: real > real,Flim: real] :
% 5.01/5.34 ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ X4 @ B )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.01/5.34 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_pos_imp_increasing_at_bot
% 5.01/5.34 thf(fact_10138_filterlim__pow__at__bot__odd,axiom,
% 5.01/5.34 ! [N: nat,F: real > real,F5: filter_real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.01/5.34 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ F5 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_pow_at_bot_odd
% 5.01/5.34 thf(fact_10139_tendsto__exp__limit__at__right,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( filterlim_real_real
% 5.01/5.34 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X2 @ Y2 ) ) @ ( divide_divide_real @ one_one_real @ Y2 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % tendsto_exp_limit_at_right
% 5.01/5.34 thf(fact_10140_ln__at__0,axiom,
% 5.01/5.34 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % ln_at_0
% 5.01/5.34 thf(fact_10141_tendsto__arcosh__at__left__1,axiom,
% 5.01/5.34 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % tendsto_arcosh_at_left_1
% 5.01/5.34 thf(fact_10142_artanh__real__at__right__1,axiom,
% 5.01/5.34 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % artanh_real_at_right_1
% 5.01/5.34 thf(fact_10143_filterlim__tan__at__right,axiom,
% 5.01/5.34 filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_tan_at_right
% 5.01/5.34 thf(fact_10144_atLeast__0,axiom,
% 5.01/5.34 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % atLeast_0
% 5.01/5.34 thf(fact_10145_atLeast__Suc__greaterThan,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.01/5.34 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeast_Suc_greaterThan
% 5.01/5.34 thf(fact_10146_INT__greaterThan__UNIV,axiom,
% 5.01/5.34 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.01/5.34 = bot_bot_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % INT_greaterThan_UNIV
% 5.01/5.34 thf(fact_10147_greaterThan__0,axiom,
% 5.01/5.34 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.01/5.34 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThan_0
% 5.01/5.34 thf(fact_10148_greaterThan__Suc,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.01/5.34 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % greaterThan_Suc
% 5.01/5.34 thf(fact_10149_UN__atLeast__UNIV,axiom,
% 5.01/5.34 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.01/5.34 = top_top_set_nat ) ).
% 5.01/5.34
% 5.01/5.34 % UN_atLeast_UNIV
% 5.01/5.34 thf(fact_10150_atLeast__Suc,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.01/5.34 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % atLeast_Suc
% 5.01/5.34 thf(fact_10151_filterlim__pow__at__bot__even,axiom,
% 5.01/5.34 ! [N: nat,F: real > real,F5: filter_real] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.01/5.34 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ F5 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_pow_at_bot_even
% 5.01/5.34 thf(fact_10152_filterlim__tan__at__left,axiom,
% 5.01/5.34 filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_tan_at_left
% 5.01/5.34 thf(fact_10153_sqrt__at__top,axiom,
% 5.01/5.34 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.01/5.34
% 5.01/5.34 % sqrt_at_top
% 5.01/5.34 thf(fact_10154_filterlim__real__sequentially,axiom,
% 5.01/5.34 filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 5.01/5.34
% 5.01/5.34 % filterlim_real_sequentially
% 5.01/5.34 thf(fact_10155_filterlim__uminus__at__top__at__bot,axiom,
% 5.01/5.34 filterlim_real_real @ uminus_uminus_real @ at_top_real @ at_bot_real ).
% 5.01/5.34
% 5.01/5.34 % filterlim_uminus_at_top_at_bot
% 5.01/5.34 thf(fact_10156_filterlim__uminus__at__bot__at__top,axiom,
% 5.01/5.34 filterlim_real_real @ uminus_uminus_real @ at_bot_real @ at_top_real ).
% 5.01/5.34
% 5.01/5.34 % filterlim_uminus_at_bot_at_top
% 5.01/5.34 thf(fact_10157_tanh__real__at__top,axiom,
% 5.01/5.34 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.01/5.34
% 5.01/5.34 % tanh_real_at_top
% 5.01/5.34 thf(fact_10158_ln__x__over__x__tendsto__0,axiom,
% 5.01/5.34 ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_real ) ).
% 5.01/5.34
% 5.01/5.34 % ln_x_over_x_tendsto_0
% 5.01/5.34 thf(fact_10159_artanh__real__at__left__1,axiom,
% 5.01/5.34 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % artanh_real_at_left_1
% 5.01/5.34 thf(fact_10160_filterlim__inverse__at__right__top,axiom,
% 5.01/5.34 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.01/5.34
% 5.01/5.34 % filterlim_inverse_at_right_top
% 5.01/5.34 thf(fact_10161_filterlim__inverse__at__top__right,axiom,
% 5.01/5.34 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % filterlim_inverse_at_top_right
% 5.01/5.34 thf(fact_10162_tendsto__power__div__exp__0,axiom,
% 5.01/5.34 ! [K: nat] :
% 5.01/5.34 ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.01/5.34 @ at_top_real ) ).
% 5.01/5.34
% 5.01/5.34 % tendsto_power_div_exp_0
% 5.01/5.34 thf(fact_10163_tendsto__exp__limit__at__top,axiom,
% 5.01/5.34 ! [X2: real] :
% 5.01/5.34 ( filterlim_real_real
% 5.01/5.34 @ ^ [Y2: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ Y2 ) ) @ Y2 )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.01/5.34 @ at_top_real ) ).
% 5.01/5.34
% 5.01/5.34 % tendsto_exp_limit_at_top
% 5.01/5.34 thf(fact_10164_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.01/5.34 ! [B: real,F: real > real,Flim: real] :
% 5.01/5.34 ( ! [X4: real] :
% 5.01/5.34 ( ( ord_less_eq_real @ B @ X4 )
% 5.01/5.34 => ? [Y4: real] :
% 5.01/5.34 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.01/5.34 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.01/5.34 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % DERIV_neg_imp_decreasing_at_top
% 5.01/5.34 thf(fact_10165_tendsto__arctan__at__top,axiom,
% 5.01/5.34 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.01/5.34
% 5.01/5.34 % tendsto_arctan_at_top
% 5.01/5.34 thf(fact_10166_Gcd__eq__Max,axiom,
% 5.01/5.34 ! [M7: set_nat] :
% 5.01/5.34 ( ( finite_finite_nat @ M7 )
% 5.01/5.34 => ( ( M7 != bot_bot_set_nat )
% 5.01/5.34 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.01/5.34 => ( ( gcd_Gcd_nat @ M7 )
% 5.01/5.34 = ( lattic8265883725875713057ax_nat
% 5.01/5.34 @ ( comple7806235888213564991et_nat
% 5.01/5.34 @ ( image_nat_set_nat
% 5.01/5.34 @ ^ [M3: nat] :
% 5.01/5.34 ( collect_nat
% 5.01/5.34 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ M3 ) )
% 5.01/5.34 @ M7 ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Gcd_eq_Max
% 5.01/5.34 thf(fact_10167_Max__divisors__self__nat,axiom,
% 5.01/5.34 ! [N: nat] :
% 5.01/5.34 ( ( N != zero_zero_nat )
% 5.01/5.34 => ( ( lattic8265883725875713057ax_nat
% 5.01/5.34 @ ( collect_nat
% 5.01/5.34 @ ^ [D3: nat] : ( dvd_dvd_nat @ D3 @ N ) ) )
% 5.01/5.34 = N ) ) ).
% 5.01/5.34
% 5.01/5.34 % Max_divisors_self_nat
% 5.01/5.34 thf(fact_10168_at__top__le__at__infinity,axiom,
% 5.01/5.34 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.01/5.34
% 5.01/5.34 % at_top_le_at_infinity
% 5.01/5.34 thf(fact_10169_at__bot__le__at__infinity,axiom,
% 5.01/5.34 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.01/5.34
% 5.01/5.34 % at_bot_le_at_infinity
% 5.01/5.34 thf(fact_10170_filterlim__real__at__infinity__sequentially,axiom,
% 5.01/5.34 filterlim_nat_real @ semiri5074537144036343181t_real @ at_infinity_real @ at_top_nat ).
% 5.01/5.34
% 5.01/5.34 % filterlim_real_at_infinity_sequentially
% 5.01/5.34 thf(fact_10171_card__le__Suc__Max,axiom,
% 5.01/5.34 ! [S: set_nat] :
% 5.01/5.34 ( ( finite_finite_nat @ S )
% 5.01/5.34 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % card_le_Suc_Max
% 5.01/5.34 thf(fact_10172_Sup__nat__def,axiom,
% 5.01/5.34 ( complete_Sup_Sup_nat
% 5.01/5.34 = ( ^ [X5: set_nat] : ( if_nat @ ( X5 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X5 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Sup_nat_def
% 5.01/5.34 thf(fact_10173_divide__nat__def,axiom,
% 5.01/5.34 ( divide_divide_nat
% 5.01/5.34 = ( ^ [M3: nat,N4: nat] :
% 5.01/5.34 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 5.01/5.34 @ ( lattic8265883725875713057ax_nat
% 5.01/5.34 @ ( collect_nat
% 5.01/5.34 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N4 ) @ M3 ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % divide_nat_def
% 5.01/5.34 thf(fact_10174_gcd__is__Max__divisors__nat,axiom,
% 5.01/5.34 ! [N: nat,M: nat] :
% 5.01/5.34 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.01/5.34 => ( ( gcd_gcd_nat @ M @ N )
% 5.01/5.34 = ( lattic8265883725875713057ax_nat
% 5.01/5.34 @ ( collect_nat
% 5.01/5.34 @ ^ [D3: nat] :
% 5.01/5.34 ( ( dvd_dvd_nat @ D3 @ M )
% 5.01/5.34 & ( dvd_dvd_nat @ D3 @ N ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_is_Max_divisors_nat
% 5.01/5.34 thf(fact_10175_lhopital__left__at__top,axiom,
% 5.01/5.34 ! [G: real > real,X2: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.01/5.34 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_left_at_top
% 5.01/5.34 thf(fact_10176_eventually__sequentially__Suc,axiom,
% 5.01/5.34 ! [P: nat > $o] :
% 5.01/5.34 ( ( eventually_nat
% 5.01/5.34 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_sequentially_Suc
% 5.01/5.34 thf(fact_10177_eventually__sequentially__seg,axiom,
% 5.01/5.34 ! [P: nat > $o,K: nat] :
% 5.01/5.34 ( ( eventually_nat
% 5.01/5.34 @ ^ [N4: nat] : ( P @ ( plus_plus_nat @ N4 @ K ) )
% 5.01/5.34 @ at_top_nat )
% 5.01/5.34 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_sequentially_seg
% 5.01/5.34 thf(fact_10178_Max__divisors__self__int,axiom,
% 5.01/5.34 ! [N: int] :
% 5.01/5.34 ( ( N != zero_zero_int )
% 5.01/5.34 => ( ( lattic8263393255366662781ax_int
% 5.01/5.34 @ ( collect_int
% 5.01/5.34 @ ^ [D3: int] : ( dvd_dvd_int @ D3 @ N ) ) )
% 5.01/5.34 = ( abs_abs_int @ N ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Max_divisors_self_int
% 5.01/5.34 thf(fact_10179_eventually__sequentially,axiom,
% 5.01/5.34 ! [P: nat > $o] :
% 5.01/5.34 ( ( eventually_nat @ P @ at_top_nat )
% 5.01/5.34 = ( ? [N8: nat] :
% 5.01/5.34 ! [N4: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ N8 @ N4 )
% 5.01/5.34 => ( P @ N4 ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_sequentially
% 5.01/5.34 thf(fact_10180_eventually__sequentiallyI,axiom,
% 5.01/5.34 ! [C: nat,P: nat > $o] :
% 5.01/5.34 ( ! [X4: nat] :
% 5.01/5.34 ( ( ord_less_eq_nat @ C @ X4 )
% 5.01/5.34 => ( P @ X4 ) )
% 5.01/5.34 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_sequentiallyI
% 5.01/5.34 thf(fact_10181_le__sequentially,axiom,
% 5.01/5.34 ! [F5: filter_nat] :
% 5.01/5.34 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.01/5.34 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F5 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % le_sequentially
% 5.01/5.34 thf(fact_10182_sequentially__offset,axiom,
% 5.01/5.34 ! [P: nat > $o,K: nat] :
% 5.01/5.34 ( ( eventually_nat @ P @ at_top_nat )
% 5.01/5.34 => ( eventually_nat
% 5.01/5.34 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.01/5.34 @ at_top_nat ) ) ).
% 5.01/5.34
% 5.01/5.34 % sequentially_offset
% 5.01/5.34 thf(fact_10183_gcd__is__Max__divisors__int,axiom,
% 5.01/5.34 ! [N: int,M: int] :
% 5.01/5.34 ( ( N != zero_zero_int )
% 5.01/5.34 => ( ( gcd_gcd_int @ M @ N )
% 5.01/5.34 = ( lattic8263393255366662781ax_int
% 5.01/5.34 @ ( collect_int
% 5.01/5.34 @ ^ [D3: int] :
% 5.01/5.34 ( ( dvd_dvd_int @ D3 @ M )
% 5.01/5.34 & ( dvd_dvd_int @ D3 @ N ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % gcd_is_Max_divisors_int
% 5.01/5.34 thf(fact_10184_eventually__at__right__to__0,axiom,
% 5.01/5.34 ! [P: real > $o,A: real] :
% 5.01/5.34 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 = ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_right_to_0
% 5.01/5.34 thf(fact_10185_eventually__at__left__to__right,axiom,
% 5.01/5.34 ! [P: real > $o,A: real] :
% 5.01/5.34 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 = ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( P @ ( uminus_uminus_real @ X3 ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ A ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_left_to_right
% 5.01/5.34 thf(fact_10186_eventually__at__right__real,axiom,
% 5.01/5.34 ! [A: real,B: real] :
% 5.01/5.34 ( ( ord_less_real @ A @ B )
% 5.01/5.34 => ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_right_real
% 5.01/5.34 thf(fact_10187_eventually__at__left__real,axiom,
% 5.01/5.34 ! [B: real,A: real] :
% 5.01/5.34 ( ( ord_less_real @ B @ A )
% 5.01/5.34 => ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_left_real
% 5.01/5.34 thf(fact_10188_eventually__at__right__to__top,axiom,
% 5.01/5.34 ! [P: real > $o] :
% 5.01/5.34 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 = ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.01/5.34 @ at_top_real ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_right_to_top
% 5.01/5.34 thf(fact_10189_eventually__at__top__to__right,axiom,
% 5.01/5.34 ! [P: real > $o] :
% 5.01/5.34 ( ( eventually_real @ P @ at_top_real )
% 5.01/5.34 = ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % eventually_at_top_to_right
% 5.01/5.34 thf(fact_10190_lhopital__at__top__at__top,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_at_top_at_top
% 5.01/5.34 thf(fact_10191_lhopital,axiom,
% 5.01/5.34 ! [F: real > real,X2: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital
% 5.01/5.34 thf(fact_10192_lhopital__right__at__top__at__top,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right_at_top_at_top
% 5.01/5.34 thf(fact_10193_lhopital__at__top__at__bot,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_at_top_at_bot
% 5.01/5.34 thf(fact_10194_lhopital__left__at__top__at__top,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_top_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_left_at_top_at_top
% 5.01/5.34 thf(fact_10195_lhospital__at__top__at__top,axiom,
% 5.01/5.34 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X2: real] :
% 5.01/5.34 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ at_top_real )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ at_top_real )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ at_top_real )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ X2 )
% 5.01/5.34 @ at_top_real )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ X2 )
% 5.01/5.34 @ at_top_real ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhospital_at_top_at_top
% 5.01/5.34 thf(fact_10196_lhopital__at__top,axiom,
% 5.01/5.34 ! [G: real > real,X2: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.01/5.34 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_at_top
% 5.01/5.34 thf(fact_10197_lhopital__right__0,axiom,
% 5.01/5.34 ! [F0: real > real,G0: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.01/5.34 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G0 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right_0
% 5.01/5.34 thf(fact_10198_lhopital__right,axiom,
% 5.01/5.34 ! [F: real > real,X2: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right
% 5.01/5.34 thf(fact_10199_lhopital__left,axiom,
% 5.01/5.34 ! [F: real > real,X2: real,G: real > real,G2: real > real,F4: real > real,F5: filter_real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ F5
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_left
% 5.01/5.34 thf(fact_10200_lhopital__right__at__top__at__bot,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right_at_top_at_bot
% 5.01/5.34 thf(fact_10201_lhopital__left__at__top__at__bot,axiom,
% 5.01/5.34 ! [F: real > real,A: real,G: real > real,F4: real > real,G2: real > real] :
% 5.01/5.34 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ at_bot_real
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_left_at_top_at_bot
% 5.01/5.34 thf(fact_10202_lhopital__right__0__at__top,axiom,
% 5.01/5.34 ! [G: real > real,G2: real > real,F: real > real,F4: real > real,X2: real] :
% 5.01/5.34 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ X2 )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ X2 )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right_0_at_top
% 5.01/5.34 thf(fact_10203_lhopital__right__at__top,axiom,
% 5.01/5.34 ! [G: real > real,X2: real,G2: real > real,F: real > real,F4: real > real,Y: real] :
% 5.01/5.34 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] :
% 5.01/5.34 ( ( G2 @ X3 )
% 5.01/5.34 != zero_zero_real )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( eventually_real
% 5.01/5.34 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F4 @ X3 ) @ ( G2 @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.01/5.34 => ( filterlim_real_real
% 5.01/5.34 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.01/5.34 @ ( topolo2815343760600316023s_real @ Y )
% 5.01/5.34 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % lhopital_right_at_top
% 5.01/5.34 thf(fact_10204_filterlim__int__sequentially,axiom,
% 5.01/5.34 filterlim_nat_int @ semiri1314217659103216013at_int @ at_top_int @ at_top_nat ).
% 5.01/5.34
% 5.01/5.34 % filterlim_int_sequentially
% 5.01/5.34 thf(fact_10205_GreatestI__ex__nat,axiom,
% 5.01/5.34 ! [P: nat > $o,B: nat] :
% 5.01/5.34 ( ? [X_1: nat] : ( P @ X_1 )
% 5.01/5.34 => ( ! [Y3: nat] :
% 5.01/5.34 ( ( P @ Y3 )
% 5.01/5.34 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.01/5.34 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % GreatestI_ex_nat
% 5.01/5.34 thf(fact_10206_Greatest__le__nat,axiom,
% 5.01/5.34 ! [P: nat > $o,K: nat,B: nat] :
% 5.01/5.34 ( ( P @ K )
% 5.01/5.34 => ( ! [Y3: nat] :
% 5.01/5.34 ( ( P @ Y3 )
% 5.01/5.34 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.01/5.34 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % Greatest_le_nat
% 5.01/5.34 thf(fact_10207_GreatestI__nat,axiom,
% 5.01/5.34 ! [P: nat > $o,K: nat,B: nat] :
% 5.01/5.34 ( ( P @ K )
% 5.01/5.34 => ( ! [Y3: nat] :
% 5.01/5.34 ( ( P @ Y3 )
% 5.01/5.34 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.01/5.34 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.01/5.34
% 5.01/5.34 % GreatestI_nat
% 5.01/5.34
% 5.01/5.34 % Helper facts (38)
% 5.01/5.34 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.01/5.34 ! [X2: int,Y: int] :
% 5.01/5.34 ( ( if_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.01/5.34 ! [X2: int,Y: int] :
% 5.01/5.34 ( ( if_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.01/5.34 ! [X2: nat,Y: nat] :
% 5.01/5.34 ( ( if_nat @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.01/5.34 ! [X2: nat,Y: nat] :
% 5.01/5.34 ( ( if_nat @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.01/5.34 ! [X2: num,Y: num] :
% 5.01/5.34 ( ( if_num @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.01/5.34 ! [X2: num,Y: num] :
% 5.01/5.34 ( ( if_num @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.01/5.34 ! [X2: rat,Y: rat] :
% 5.01/5.34 ( ( if_rat @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.01/5.34 ! [X2: rat,Y: rat] :
% 5.01/5.34 ( ( if_rat @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.01/5.34 ! [X2: real,Y: real] :
% 5.01/5.34 ( ( if_real @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.01/5.34 ! [X2: real,Y: real] :
% 5.01/5.34 ( ( if_real @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.01/5.34 ! [P: real > $o] :
% 5.01/5.34 ( ( P @ ( fChoice_real @ P ) )
% 5.01/5.34 = ( ? [X5: real] : ( P @ X5 ) ) ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.01/5.34 ! [X2: complex,Y: complex] :
% 5.01/5.34 ( ( if_complex @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.01/5.34 ! [X2: complex,Y: complex] :
% 5.01/5.34 ( ( if_complex @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.01/5.34 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.34 ( ( if_Code_integer @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.01/5.34 ! [X2: code_integer,Y: code_integer] :
% 5.01/5.34 ( ( if_Code_integer @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: set_int,Y: set_int] :
% 5.01/5.34 ( ( if_set_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: set_int,Y: set_int] :
% 5.01/5.34 ( ( if_set_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: list_int,Y: list_int] :
% 5.01/5.34 ( ( if_list_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: list_int,Y: list_int] :
% 5.01/5.34 ( ( if_list_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.01/5.34 ! [X2: list_nat,Y: list_nat] :
% 5.01/5.34 ( ( if_list_nat @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.01/5.34 ! [X2: list_nat,Y: list_nat] :
% 5.01/5.34 ( ( if_list_nat @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: int > int,Y: int > int] :
% 5.01/5.34 ( ( if_int_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: int > int,Y: int > int] :
% 5.01/5.34 ( ( if_int_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.01/5.34 ! [X2: option_num,Y: option_num] :
% 5.01/5.34 ( ( if_option_num @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.01/5.34 ! [X2: option_num,Y: option_num] :
% 5.01/5.34 ( ( if_option_num @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.01/5.34 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.01/5.34 ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 5.01/5.34 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.01/5.34 ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.01/5.34 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.01/5.34 ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.01/5.34 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.01/5.34 ! [X2: nat > int > int,Y: nat > int > int] :
% 5.01/5.34 ( ( if_nat_int_int @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.01/5.34 ! [X2: nat > int > int,Y: nat > int > int] :
% 5.01/5.34 ( ( if_nat_int_int @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.01/5.34 ! [X2: nat > nat > nat,Y: nat > nat > nat] :
% 5.01/5.34 ( ( if_nat_nat_nat @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.01/5.34 ! [X2: nat > nat > nat,Y: nat > nat > nat] :
% 5.01/5.34 ( ( if_nat_nat_nat @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.01/5.34 ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.01/5.34 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y )
% 5.01/5.34 = Y ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.01/5.34 ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.01/5.34 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y )
% 5.01/5.34 = X2 ) ).
% 5.01/5.34
% 5.01/5.34 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.98/6.33 ! [P: $o] :
% 5.98/6.33 ( ( P = $true )
% 5.98/6.33 | ( P = $false ) ) ).
% 5.98/6.33
% 5.98/6.33 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.98/6.33 ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.98/6.33 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y )
% 5.98/6.33 = Y ) ).
% 5.98/6.33
% 5.98/6.33 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.98/6.33 ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.98/6.33 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y )
% 5.98/6.33 = X2 ) ).
% 5.98/6.33
% 5.98/6.33 % Conjectures (1)
% 5.98/6.33 thf(conj_0,conjecture,
% 5.98/6.33 ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ deg ) @ c ) ) ).
% 5.98/6.33
% 5.98/6.33 %------------------------------------------------------------------------------
% 5.98/6.33 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.f0lh50PiS1/cvc5---1.0.5_13750.p...
% 5.98/6.33 (declare-sort $$unsorted 0)
% 5.98/6.33 (declare-sort tptp.list_l7035113777618258358nteger 0)
% 5.98/6.33 (declare-sort tptp.list_P7828571989066258726nteger 0)
% 5.98/6.33 (declare-sort tptp.produc1908205239877642774nteger 0)
% 5.98/6.33 (declare-sort tptp.list_l6845168789323398563nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_P651320350408439699nt_int 0)
% 5.98/6.33 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_l1551831396326329630nteger 0)
% 5.98/6.33 (declare-sort tptp.list_P5311841565141990158nteger 0)
% 5.98/6.33 (declare-sort tptp.produc8763457246119570046nteger 0)
% 5.98/6.33 (declare-sort tptp.list_P1316552470764441098e_term 0)
% 5.98/6.33 (declare-sort tptp.list_l5644688499257182253nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_P1743416141875011707e_term 0)
% 5.98/6.33 (declare-sort tptp.list_P8915022641806594461nt_int 0)
% 5.98/6.33 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_C878401137130745250e_term 0)
% 5.98/6.33 (declare-sort tptp.list_i8448526496819171953e_term 0)
% 5.98/6.33 (declare-sort tptp.produc6241069584506657477e_term 0)
% 5.98/6.33 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.produc8551481072490612790e_term 0)
% 5.98/6.33 (declare-sort tptp.list_P5578671422887162913nteger 0)
% 5.98/6.33 (declare-sort tptp.option6357759511663192854e_term 0)
% 5.98/6.33 (declare-sort tptp.list_l1670014477004246597nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 5.98/6.33 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 5.98/6.33 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.produc8923325533196201883nteger 0)
% 5.98/6.33 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 5.98/6.33 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.option4927543243414619207at_nat 0)
% 5.98/6.33 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 5.98/6.33 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 5.98/6.33 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 5.98/6.33 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 5.98/6.33 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 5.98/6.33 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 5.98/6.33 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 5.98/6.33 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 5.98/6.33 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 5.98/6.33 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 5.98/6.33 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 5.98/6.33 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 5.98/6.33 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 5.98/6.33 (declare-sort tptp.product_prod_num_num 0)
% 5.98/6.33 (declare-sort tptp.product_prod_nat_num 0)
% 5.98/6.33 (declare-sort tptp.product_prod_nat_nat 0)
% 5.98/6.33 (declare-sort tptp.product_prod_int_int 0)
% 5.98/6.33 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 5.98/6.33 (declare-sort tptp.list_list_real 0)
% 5.98/6.33 (declare-sort tptp.list_list_nat 0)
% 5.98/6.33 (declare-sort tptp.list_list_int 0)
% 5.98/6.33 (declare-sort tptp.list_VEBT_VEBT 0)
% 5.98/6.33 (declare-sort tptp.set_list_nat 0)
% 5.98/6.33 (declare-sort tptp.set_list_int 0)
% 5.98/6.33 (declare-sort tptp.product_prod_nat_o 0)
% 5.98/6.33 (declare-sort tptp.product_prod_o_nat 0)
% 5.98/6.33 (declare-sort tptp.product_prod_o_int 0)
% 5.98/6.33 (declare-sort tptp.list_set_nat 0)
% 5.98/6.33 (declare-sort tptp.set_VEBT_VEBT 0)
% 5.98/6.33 (declare-sort tptp.set_set_nat 0)
% 5.98/6.33 (declare-sort tptp.set_Code_integer 0)
% 5.98/6.33 (declare-sort tptp.set_Product_unit 0)
% 5.98/6.33 (declare-sort tptp.list_list_o 0)
% 5.98/6.33 (declare-sort tptp.list_complex 0)
% 5.98/6.33 (declare-sort tptp.set_list_o 0)
% 5.98/6.33 (declare-sort tptp.product_prod_o_o 0)
% 5.98/6.33 (declare-sort tptp.set_complex 0)
% 5.98/6.33 (declare-sort tptp.filter_real 0)
% 5.98/6.33 (declare-sort tptp.option_num 0)
% 5.98/6.33 (declare-sort tptp.filter_nat 0)
% 5.98/6.33 (declare-sort tptp.filter_int 0)
% 5.98/6.33 (declare-sort tptp.set_char 0)
% 5.98/6.33 (declare-sort tptp.list_real 0)
% 5.98/6.33 (declare-sort tptp.set_real 0)
% 5.98/6.33 (declare-sort tptp.list_nat 0)
% 5.98/6.33 (declare-sort tptp.list_int 0)
% 5.98/6.33 (declare-sort tptp.vEBT_VEBT 0)
% 5.98/6.33 (declare-sort tptp.set_rat 0)
% 5.98/6.33 (declare-sort tptp.set_nat 0)
% 5.98/6.33 (declare-sort tptp.set_int 0)
% 5.98/6.33 (declare-sort tptp.code_integer 0)
% 5.98/6.33 (declare-sort tptp.extended_enat 0)
% 5.98/6.33 (declare-sort tptp.list_o 0)
% 5.98/6.33 (declare-sort tptp.complex 0)
% 5.98/6.33 (declare-sort tptp.set_o 0)
% 5.98/6.33 (declare-sort tptp.char 0)
% 5.98/6.33 (declare-sort tptp.real 0)
% 5.98/6.33 (declare-sort tptp.rat 0)
% 5.98/6.33 (declare-sort tptp.num 0)
% 5.98/6.33 (declare-sort tptp.nat 0)
% 5.98/6.33 (declare-sort tptp.int 0)
% 5.98/6.33 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 5.98/6.33 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 5.98/6.33 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 5.98/6.33 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 5.98/6.33 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 5.98/6.33 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 5.98/6.33 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 5.98/6.33 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 5.98/6.33 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 5.98/6.33 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 5.98/6.33 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 5.98/6.33 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 5.98/6.33 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 5.98/6.33 (declare-fun tptp.code_T6385005292777649522of_nat (tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.complete_Inf_Inf_int (tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 5.98/6.33 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 5.98/6.33 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 5.98/6.33 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 5.98/6.33 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 5.98/6.33 (declare-fun tptp.im (tptp.complex) tptp.real)
% 5.98/6.33 (declare-fun tptp.re (tptp.complex) tptp.real)
% 5.98/6.33 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.imaginary_unit () tptp.complex)
% 5.98/6.33 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 5.98/6.33 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 5.98/6.33 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 5.98/6.33 (declare-fun tptp.at_top_int () tptp.filter_int)
% 5.98/6.33 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 5.98/6.33 (declare-fun tptp.at_top_real () tptp.filter_real)
% 5.98/6.33 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 5.98/6.33 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 5.98/6.33 (declare-fun tptp.filterlim_nat_int ((-> tptp.nat tptp.int) tptp.filter_int tptp.filter_nat) Bool)
% 5.98/6.33 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 5.98/6.33 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 5.98/6.33 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 5.98/6.33 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 5.98/6.33 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 5.98/6.33 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.bij_be8532844293280997160at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.bij_be5333170631980326235at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.comp_C2179886998970519596um_nat ((-> tptp.code_integer tptp.num) (-> tptp.nat tptp.code_integer) tptp.nat) tptp.num)
% 5.98/6.33 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 5.98/6.33 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.comp_int_real_real ((-> tptp.int tptp.real) (-> tptp.real tptp.int) tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 5.98/6.33 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 5.98/6.33 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 5.98/6.33 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 5.98/6.33 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 5.98/6.33 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.98/6.33 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.one_one_complex () tptp.complex)
% 5.98/6.33 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.one_one_int () tptp.int)
% 5.98/6.33 (declare-fun tptp.one_one_nat () tptp.nat)
% 5.98/6.33 (declare-fun tptp.one_one_rat () tptp.rat)
% 5.98/6.33 (declare-fun tptp.one_one_real () tptp.real)
% 5.98/6.33 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 5.98/6.33 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.zero_zero_int () tptp.int)
% 5.98/6.33 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 5.98/6.33 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 5.98/6.33 (declare-fun tptp.zero_zero_real () tptp.real)
% 5.98/6.33 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.groups3417619833198082522nteger ((-> Bool tptp.code_integer) tptp.code_integer tptp.list_o) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 5.98/6.33 (declare-fun tptp.groups9119017779487936845_o_nat ((-> Bool tptp.nat) tptp.nat tptp.list_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.groups7488368174851004413at_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.groups1503878375050959669l_real ((-> tptp.real tptp.real) tptp.real tptp.list_real) tptp.real)
% 5.98/6.33 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 5.98/6.33 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 5.98/6.33 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.if_nat_nat_nat (Bool (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 5.98/6.33 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 5.98/6.33 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 5.98/6.33 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 5.98/6.33 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 5.98/6.33 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 5.98/6.33 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 5.98/6.33 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 5.98/6.33 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 5.98/6.33 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 5.98/6.33 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 5.98/6.33 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 5.98/6.33 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.concat_o (tptp.list_list_o) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.concat_int (tptp.list_list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.concat5449216342283422845nteger (tptp.list_l1551831396326329630nteger) tptp.list_P5311841565141990158nteger)
% 5.98/6.33 (declare-fun tptp.concat3620511419746071180nt_int (tptp.list_l5644688499257182253nt_int) tptp.list_P8915022641806594461nt_int)
% 5.98/6.33 (declare-fun tptp.concat1359917873574114197nteger (tptp.list_l7035113777618258358nteger) tptp.list_P7828571989066258726nteger)
% 5.98/6.33 (declare-fun tptp.concat27718206033014914nt_int (tptp.list_l6845168789323398563nt_int) tptp.list_P651320350408439699nt_int)
% 5.98/6.33 (declare-fun tptp.concat4512918505337516154nt_int (tptp.list_l1670014477004246597nt_int) tptp.list_P5707943133018811711nt_int)
% 5.98/6.33 (declare-fun tptp.concat_real (tptp.list_list_real) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.concat_VEBT_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 5.98/6.33 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.foldr_o_int ((-> Bool tptp.int tptp.int) tptp.list_o tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.foldr_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.foldr_real_real ((-> tptp.real tptp.real tptp.real) tptp.list_real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.nil_int () tptp.list_int)
% 5.98/6.33 (declare-fun tptp.nil_nat () tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.map_Co3516991824712006758nteger ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.list_P5311841565141990158nteger) tptp.list_C878401137130745250e_term) tptp.list_l1551831396326329630nteger)
% 5.98/6.33 (declare-fun tptp.map_in2673801078721063236nt_int ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.list_P8915022641806594461nt_int) tptp.list_i8448526496819171953e_term) tptp.list_l5644688499257182253nt_int)
% 5.98/6.33 (declare-fun tptp.map_Pr1383036205076807398nteger ((-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.list_P7828571989066258726nteger) tptp.list_P1316552470764441098e_term) tptp.list_l7035113777618258358nteger)
% 5.98/6.33 (declare-fun tptp.map_Pr6227401909088194244nt_int ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.list_P651320350408439699nt_int) tptp.list_P1743416141875011707e_term) tptp.list_l6845168789323398563nt_int)
% 5.98/6.33 (declare-fun tptp.map_o_o ((-> Bool Bool) tptp.list_o) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.map_o_int ((-> Bool tptp.int) tptp.list_o) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.map_o_nat ((-> Bool tptp.nat) tptp.list_o) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.map_o_real ((-> Bool tptp.real) tptp.list_o) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.map_o_VEBT_VEBT ((-> Bool tptp.vEBT_VEBT) tptp.list_o) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.map_complex_complex ((-> tptp.complex tptp.complex) tptp.list_complex) tptp.list_complex)
% 5.98/6.33 (declare-fun tptp.map_int_o ((-> tptp.int Bool) tptp.list_int) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.map_int_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.map_in7266296235447420877nt_int ((-> tptp.int tptp.list_P5707943133018811711nt_int) tptp.list_int) tptp.list_l1670014477004246597nt_int)
% 5.98/6.33 (declare-fun tptp.map_int_nat ((-> tptp.int tptp.nat) tptp.list_int) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.map_in7157766398909135175nt_int ((-> tptp.int tptp.product_prod_int_int) tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 5.98/6.33 (declare-fun tptp.map_int_real ((-> tptp.int tptp.real) tptp.list_int) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.map_int_VEBT_VEBT ((-> tptp.int tptp.vEBT_VEBT) tptp.list_int) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.map_li7225945977422193158st_nat ((-> tptp.list_nat tptp.list_nat) tptp.list_list_nat) tptp.list_list_nat)
% 5.98/6.33 (declare-fun tptp.map_li576258494306137302st_nat ((-> tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_list_VEBT_VEBT) tptp.list_list_nat)
% 5.98/6.33 (declare-fun tptp.map_li2470829856544091186t_real ((-> tptp.list_VEBT_VEBT tptp.list_real) tptp.list_list_VEBT_VEBT) tptp.list_list_real)
% 5.98/6.33 (declare-fun tptp.map_nat_o ((-> tptp.nat Bool) tptp.list_nat) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.map_nat_int ((-> tptp.nat tptp.int) tptp.list_nat) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.map_nat_real ((-> tptp.nat tptp.real) tptp.list_nat) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.map_nat_VEBT_VEBT ((-> tptp.nat tptp.vEBT_VEBT) tptp.list_nat) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.map_Pr6982716525268357333nteger ((-> tptp.produc8923325533196201883nteger tptp.produc8763457246119570046nteger) tptp.list_P5578671422887162913nteger) tptp.list_P5311841565141990158nteger)
% 5.98/6.33 (declare-fun tptp.map_Pr4561634935768196077nteger ((-> tptp.produc8923325533196201883nteger tptp.produc1908205239877642774nteger) tptp.list_P5578671422887162913nteger) tptp.list_P7828571989066258726nteger)
% 5.98/6.33 (declare-fun tptp.map_Pr1306541819098601986nt_int ((-> tptp.product_prod_int_int tptp.produc7773217078559923341nt_int) tptp.list_P5707943133018811711nt_int) tptp.list_P8915022641806594461nt_int)
% 5.98/6.33 (declare-fun tptp.map_Pr1898935522916328184nt_int ((-> tptp.product_prod_int_int tptp.produc2285326912895808259nt_int) tptp.list_P5707943133018811711nt_int) tptp.list_P651320350408439699nt_int)
% 5.98/6.33 (declare-fun tptp.map_real_real ((-> tptp.real tptp.real) tptp.list_real) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.map_set_nat_set_nat ((-> tptp.set_nat tptp.set_nat) tptp.list_set_nat) tptp.list_set_nat)
% 5.98/6.33 (declare-fun tptp.map_VEBT_VEBT_o ((-> tptp.vEBT_VEBT Bool) tptp.list_VEBT_VEBT) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.map_VEBT_VEBT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.list_VEBT_VEBT) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.map_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.map_VEBT_VEBT_real ((-> tptp.vEBT_VEBT tptp.real) tptp.list_VEBT_VEBT) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 5.98/6.33 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 5.98/6.33 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_list_o2 (tptp.list_list_o) tptp.set_list_o)
% 5.98/6.33 (declare-fun tptp.set_list_int2 (tptp.list_list_int) tptp.set_list_int)
% 5.98/6.33 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 5.98/6.33 (declare-fun tptp.set_list_VEBT_VEBT2 (tptp.list_list_VEBT_VEBT) tptp.set_list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 5.98/6.33 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 5.98/6.33 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 5.98/6.33 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 5.98/6.33 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 5.98/6.33 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 5.98/6.33 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 5.98/6.33 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 5.98/6.33 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 5.98/6.33 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 5.98/6.33 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 5.98/6.33 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.produc4846348955484107138nteger (tptp.list_C878401137130745250e_term tptp.list_P5578671422887162913nteger) tptp.list_P5311841565141990158nteger)
% 5.98/6.33 (declare-fun tptp.produc5707002291657922193nt_int (tptp.list_i8448526496819171953e_term tptp.list_P5707943133018811711nt_int) tptp.list_P8915022641806594461nt_int)
% 5.98/6.33 (declare-fun tptp.produc2929234284598166170nteger (tptp.list_P1316552470764441098e_term tptp.list_P5578671422887162913nteger) tptp.list_P7828571989066258726nteger)
% 5.98/6.33 (declare-fun tptp.produc8640348060098379399nt_int (tptp.list_P1743416141875011707e_term tptp.list_P5707943133018811711nt_int) tptp.list_P651320350408439699nt_int)
% 5.98/6.33 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 5.98/6.33 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 5.98/6.33 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 5.98/6.33 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 5.98/6.33 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 5.98/6.33 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 5.98/6.33 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 5.98/6.33 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 5.98/6.33 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 5.98/6.33 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 5.98/6.33 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 5.98/6.33 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 5.98/6.33 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 5.98/6.33 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 5.98/6.33 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 5.98/6.33 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 5.98/6.33 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.subseqs_o (tptp.list_o) tptp.list_list_o)
% 5.98/6.33 (declare-fun tptp.subseqs_int (tptp.list_int) tptp.list_list_int)
% 5.98/6.33 (declare-fun tptp.subseqs_nat (tptp.list_nat) tptp.list_list_nat)
% 5.98/6.33 (declare-fun tptp.subseqs_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_list_VEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 5.98/6.33 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 5.98/6.33 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s2710708370519433104list_o (tptp.list_list_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s533118279054570080st_int (tptp.list_list_int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s8217280938318005548T_VEBT (tptp.list_list_VEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.inc (tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 5.98/6.33 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.one () tptp.num)
% 5.98/6.33 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 5.98/6.33 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 5.98/6.33 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 5.98/6.33 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 5.98/6.33 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 5.98/6.33 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 5.98/6.33 (declare-fun tptp.none_num () tptp.option_num)
% 5.98/6.33 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 5.98/6.33 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 5.98/6.33 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 5.98/6.33 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 5.98/6.33 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 5.98/6.33 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 5.98/6.33 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 5.98/6.33 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 5.98/6.33 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 5.98/6.33 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 5.98/6.33 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 5.98/6.33 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 5.98/6.33 (declare-fun tptp.top_top_set_list_nat () tptp.set_list_nat)
% 5.98/6.33 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.top_to4669805908274784177at_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.98/6.33 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 5.98/6.33 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 5.98/6.33 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 5.98/6.33 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 5.98/6.33 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 5.98/6.33 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 5.98/6.33 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 5.98/6.33 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 5.98/6.33 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 5.98/6.33 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 5.98/6.33 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 5.98/6.33 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 5.98/6.33 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 5.98/6.33 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 5.98/6.33 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 5.98/6.33 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 5.98/6.33 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 5.98/6.33 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 5.98/6.33 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 5.98/6.33 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 5.98/6.33 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 5.98/6.33 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 5.98/6.33 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 5.98/6.33 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 5.98/6.33 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 5.98/6.33 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 5.98/6.33 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.98/6.33 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.98/6.33 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 5.98/6.33 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 5.98/6.33 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 5.98/6.33 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 5.98/6.33 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 5.98/6.33 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 5.98/6.33 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 5.98/6.33 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 5.98/6.33 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 5.98/6.33 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 5.98/6.33 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 5.98/6.33 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 5.98/6.33 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 5.98/6.33 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 5.98/6.33 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 5.98/6.33 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 5.98/6.33 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 5.98/6.33 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 5.98/6.33 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 5.98/6.33 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 5.98/6.33 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 5.98/6.33 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 5.98/6.33 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 5.98/6.33 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 5.98/6.33 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 5.98/6.33 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 5.98/6.33 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 5.98/6.33 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 5.98/6.33 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 5.98/6.33 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 5.98/6.33 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 5.98/6.33 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 5.98/6.33 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 5.98/6.33 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 5.98/6.33 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 5.98/6.33 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 5.98/6.33 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 5.98/6.33 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 5.98/6.33 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 5.98/6.33 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 5.98/6.33 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 5.98/6.33 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 5.98/6.33 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 5.98/6.33 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 5.98/6.33 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 5.98/6.33 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 5.98/6.33 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 5.98/6.33 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 5.98/6.33 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 5.98/6.33 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 5.98/6.33 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 5.98/6.33 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.pi () tptp.real)
% 5.98/6.33 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 5.98/6.33 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 5.98/6.33 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 5.98/6.33 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 5.98/6.33 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_cnt (tptp.vEBT_VEBT) tptp.real)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_cnt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_space (tptp.vEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_space2 (tptp.vEBT_VEBT) tptp.nat)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_space_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.vEBT_VEBT_space_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 5.98/6.33 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 5.98/6.33 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 5.98/6.33 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 5.98/6.33 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 5.98/6.33 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.98/6.33 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 5.98/6.33 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 5.98/6.33 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 5.98/6.33 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 5.98/6.33 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 5.98/6.33 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 5.98/6.33 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 5.98/6.33 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 5.98/6.33 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 5.98/6.33 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 5.98/6.33 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 5.98/6.33 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 5.98/6.33 (declare-fun tptp.c () tptp.real)
% 5.98/6.33 (declare-fun tptp.deg () tptp.nat)
% 5.98/6.33 (declare-fun tptp.m () tptp.nat)
% 5.98/6.33 (declare-fun tptp.ma () tptp.nat)
% 5.98/6.33 (declare-fun tptp.mi () tptp.nat)
% 5.98/6.33 (declare-fun tptp.na () tptp.nat)
% 5.98/6.33 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 5.98/6.33 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 5.98/6.33 (assert (= tptp.m tptp.na))
% 5.98/6.33 (assert (= tptp.c (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))))
% 5.98/6.33 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 5.98/6.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt tptp.summary)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_1) tptp.m)) tptp.c)))))
% 5.98/6.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.deg) tptp.treeList) tptp.summary))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.plus_plus_nat tptp.na) tptp.na))) (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 _let_1))))))))))
% 5.98/6.33 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 5.98/6.33 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt X)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_1) tptp.na)) tptp.c)))))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) tptp.na))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_2) tptp.one_one_real))) (@ (@ tptp.minus_minus_real _let_2) tptp.c))) tptp.one_one_real)))))
% 5.98/6.33 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X) tptp.na) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt X)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_1) tptp.na)) tptp.c))))))))
% 5.98/6.33 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y)))))))
% 5.98/6.33 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)))))))
% 5.98/6.33 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)))))))
% 5.98/6.33 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y)))))))
% 5.98/6.33 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 5.98/6.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 5.98/6.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 5.98/6.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 5.98/6.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 5.98/6.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 5.98/6.33 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 5.98/6.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 5.98/6.33 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 5.98/6.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 5.98/6.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 5.98/6.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 5.98/6.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 5.98/6.33 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X3 tptp.list_nat)) (@ (@ tptp.member_list_nat X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A2))) A2)))
% 5.98/6.33 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 5.98/6.33 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X4 tptp.list_nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 5.98/6.33 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X4 tptp.set_nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 5.98/6.33 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 5.98/6.33 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 5.98/6.33 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 5.98/6.33 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 5.98/6.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.33 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 5.98/6.33 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.33 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.33 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.33 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.power_power_real _let_2))) (let ((_let_4 (@ _let_3 (@ (@ tptp.plus_plus_nat tptp.na) tptp.na)))) (let ((_let_5 (@ tptp.times_times_real _let_2))) (@ (@ tptp.ord_less_eq_real (@ _let_5 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.c)) (@ _let_3 tptp.na)))) tptp.c)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)))) (@ _let_5 (@ (@ tptp.minus_minus_real _let_4) (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 _let_1)))))))))))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real _let_1))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.deg) tptp.treeList) tptp.summary))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ _let_2 (@ (@ tptp.plus_plus_nat tptp.na) tptp.na))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.c)) (@ _let_2 tptp.na)))) tptp.c)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))))
% 5.98/6.34 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 5.98/6.34 (assert (=> (= tptp.mi tptp.ma) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I) J)) U)) K))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 5.98/6.34 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.34 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 5.98/6.34 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 5.98/6.34 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 5.98/6.34 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.34 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.34 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 5.98/6.34 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 5.98/6.34 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 5.98/6.34 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 5.98/6.34 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X2)) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X2)) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X2)) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X2)) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 5.98/6.34 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y (@ tptp.bit0 X22)))) (not (forall ((X32 tptp.num)) (not (= Y (@ tptp.bit1 X32)))))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 5.98/6.34 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 5.98/6.34 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y)))))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) (let ((_let_4 (@ tptp.bit1 _let_1))) (let ((_let_5 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4)))) (let ((_let_6 (@ tptp.power_power_real _let_2))) (let ((_let_7 (@ tptp.plus_plus_real (@ _let_6 (@ (@ tptp.plus_plus_nat tptp.na) tptp.na))))) (let ((_let_8 (@ tptp.times_times_real _let_2))) (@ (@ tptp.ord_less_eq_real (@ _let_8 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real (@ _let_7 (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.c)) (@ _let_6 tptp.na)))) tptp.c)) _let_3))) (@ _let_8 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real (@ _let_7 (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_4)) _let_5))) tptp.one_one_real))) (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) _let_5))) _let_3))))))))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 5.98/6.34 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y2 tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y2)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 5.98/6.34 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y2 tptp.num)) (not (= X2 (@ tptp.some_num Y2)))) (= X2 tptp.none_num))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((X23 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X23) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X23 Y22))))
% 5.98/6.34 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X23) (@ tptp.some_num Y22)) (= X23 Y22))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 5.98/6.34 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 5.98/6.34 (assert (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))))
% 5.98/6.34 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y2 tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y2 tptp.num)) (= X2 (@ tptp.some_num Y2))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 5.98/6.34 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 5.98/6.34 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 5.98/6.34 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.34 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 5.98/6.34 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 5.98/6.34 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 5.98/6.34 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 5.98/6.34 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.34 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 5.98/6.34 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 5.98/6.34 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 5.98/6.34 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 5.98/6.34 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.34 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 5.98/6.34 (assert (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I2)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.34 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N2)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.34 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.34 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 5.98/6.34 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.34 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.times_times_real X2) X2) tptp.one_one_real) (or (= X2 tptp.one_one_real) (= X2 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.times_times_int X2) X2) tptp.one_one_int) (or (= X2 tptp.one_one_int) (= X2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X2) X2) tptp.one_one_complex) (or (= X2 tptp.one_one_complex) (= X2 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 5.98/6.34 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X2) X2) tptp.one_one_Code_integer) (or (= X2 tptp.one_one_Code_integer) (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X2) X2) tptp.one_one_rat) (or (= X2 tptp.one_one_rat) (= X2 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.34 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 5.98/6.34 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 5.98/6.34 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 5.98/6.34 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 5.98/6.34 (assert (= tptp.minus_minus_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real Y2)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.34 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.34 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.34 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((W tptp.num) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real X2) (@ tptp.uminus_uminus_real _let_1))))))
% 5.98/6.34 (assert (forall ((W tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X2)) (@ (@ tptp.times_times_int X2) (@ tptp.uminus_uminus_int _let_1))))))
% 5.98/6.34 (assert (forall ((W tptp.num) (X2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex X2) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 5.98/6.34 (assert (forall ((W tptp.num) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X2)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 5.98/6.34 (assert (forall ((W tptp.num) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat X2) (@ tptp.uminus_uminus_rat _let_1))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 5.98/6.34 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 5.98/6.34 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 5.98/6.34 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 5.98/6.34 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 5.98/6.34 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 5.98/6.34 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.34 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 5.98/6.34 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 5.98/6.34 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 5.98/6.34 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.98/6.34 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.34 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ (@ tptp.power_power_real X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ (@ tptp.power_power_int X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ (@ tptp.power_power_complex X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ (@ tptp.power_power_rat X2) _let_1)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X2) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X2) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X2) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X2) _let_1))))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((S tptp.set_real)) (=> (exists ((X tptp.real)) (@ (@ tptp.member_real X) S)) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z2)))) (exists ((Y3 tptp.real)) (and (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) S) (@ (@ tptp.ord_less_eq_real X) Y3))) (forall ((Z2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z2))) (@ (@ tptp.ord_less_eq_real Y3) Z2)))))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.34 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_real Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_int Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X2) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus1482373934393186551omplex Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus1351360451143612070nteger Y)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_rat Y)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.34 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (E tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E)) C))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 5.98/6.34 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D)))))
% 5.98/6.34 (assert (forall ((X23 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X23)))))
% 5.98/6.34 (assert (forall ((X23 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X23)))))
% 5.98/6.34 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X23 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X23)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 5.98/6.34 (assert (forall ((Option tptp.option_num) (X23 tptp.num)) (=> (= Option (@ tptp.some_num X23)) (not (= Option tptp.none_num)))))
% 5.98/6.34 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X22 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X22))))))))
% 5.98/6.34 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y (@ tptp.some_num X22))))))))
% 5.98/6.34 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P3 tptp.none_P5556105721700978146at_nat) (exists ((X3 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 5.98/6.34 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_num Bool))) (or (@ P3 tptp.none_num) (exists ((X3 tptp.num)) (@ P3 (@ tptp.some_num X3)))))))
% 5.98/6.34 (assert (= (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P3 tptp.none_P5556105721700978146at_nat) (forall ((X3 tptp.product_prod_nat_nat)) (@ P3 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 5.98/6.34 (assert (= (lambda ((P2 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P2 X6))) (lambda ((P3 (-> tptp.option_num Bool))) (and (@ P3 tptp.none_num) (forall ((X3 tptp.num)) (@ P3 (@ tptp.some_num X3)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X2) Y)))) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X2) Y)))) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X2) Y)))) _let_1))))))
% 5.98/6.34 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X2 (@ tptp.some_num A3)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X2) Y)))) _let_1))))))
% 5.98/6.34 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 5.98/6.34 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real X2) Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ (@ tptp.minus_minus_rat X2) Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y)) (@ (@ tptp.minus_minus_int X2) Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.minus_minus_complex X2) Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) A)) B))))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) A)) B))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) A)) B))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) A)) B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 5.98/6.34 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 5.98/6.34 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 5.98/6.34 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.divide_divide_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X2))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X2)) N) X2)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X2)) N) Y)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 5.98/6.34 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 5.98/6.34 (assert (= tptp.vEBT_VEBT_high (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.34 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex C))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 5.98/6.34 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low X) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X) (@ (@ tptp.ord_less_eq_nat X) tptp.ma)))))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 5.98/6.34 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 5.98/6.34 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 5.98/6.34 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y2) (= X3 Y2)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X2) N3))))))
% 5.98/6.34 (assert (forall ((X tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X))))
% 5.98/6.34 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 5.98/6.34 (assert (forall ((X tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X) X_12))))
% 5.98/6.34 (assert (forall ((X tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_12))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (= tptp.times_times_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A4))))
% 5.98/6.34 (assert (= tptp.times_times_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A4))))
% 5.98/6.34 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A4))))
% 5.98/6.34 (assert (= tptp.times_times_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A4))))
% 5.98/6.34 (assert (= tptp.times_times_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex B3) A4))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.34 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.98/6.34 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.98/6.34 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.98/6.34 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.98/6.34 (assert (= tptp.plus_plus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A4))))
% 5.98/6.34 (assert (= tptp.plus_plus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A4))))
% 5.98/6.34 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A4))))
% 5.98/6.34 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A4))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 5.98/6.34 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (= (@ (@ tptp.minus_minus_complex A) B) (@ (@ tptp.minus_minus_complex C) D)) (= (= A B) (= C D)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 5.98/6.34 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 5.98/6.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 5.98/6.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 5.98/6.34 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 5.98/6.34 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X2 Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y))) (not (= X2 Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y))) (not (= X2 Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X2) (@ tptp.size_size_list_int Y))) (not (= X2 Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y))) (not (= X2 Y)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 5.98/6.34 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.34 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (exists ((C2 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A4) C2))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_complex B) C))))))
% 5.98/6.34 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex C) B) A) (= C (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.minus_minus_complex C) B)) (= (@ (@ tptp.plus_plus_complex A) B) C))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.minus_minus_complex A) B) C) (= A (@ (@ tptp.plus_plus_complex C) B)))))
% 5.98/6.34 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 5.98/6.34 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_complex A2) B) (@ _let_1 (@ (@ tptp.minus_minus_complex A) B)))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 5.98/6.34 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 5.98/6.34 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 5.98/6.34 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 5.98/6.34 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 5.98/6.34 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 5.98/6.34 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N4) (not (= M3 N4))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N4) (= M3 N4)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N 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)))))
% 5.98/6.34 (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)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 5.98/6.34 (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))))
% 5.98/6.34 (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))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 5.98/6.34 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (exists ((K2 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M3) K2))))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (L 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))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (L 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)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (L 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))))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.98/6.34 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 5.98/6.34 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 5.98/6.34 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A4) (@ tptp.uminus_uminus_real B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A4) (@ tptp.uminus_uminus_int B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A4) (@ tptp.uminus1482373934393186551omplex B3)))))
% 5.98/6.34 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.uminus1351360451143612070nteger B3)))))
% 5.98/6.34 (assert (= tptp.minus_minus_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A4) (@ tptp.uminus_uminus_rat B3)))))
% 5.98/6.34 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B4 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 5.98/6.34 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B4 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 5.98/6.34 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B4 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 5.98/6.34 (assert (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 5.98/6.34 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B4 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C 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))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J))))
% 5.98/6.34 (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))))
% 5.98/6.34 (assert (forall ((J tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I) K)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.minus_minus_nat J) I) K) (= J (@ (@ tptp.plus_plus_nat K) I))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L)))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L)))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I) K))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.34 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X3) N4))) (@ (@ tptp.vEBT_VEBT_low X3) N4)))))
% 5.98/6.34 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X2)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X2))))
% 5.98/6.34 (assert (forall ((L tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))))
% 5.98/6.34 (assert (forall ((L tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))))
% 5.98/6.34 (assert (forall ((L tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real _let_1) N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I3)))) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I3)))) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X2 tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I3)))) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X2 Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I3)))) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 5.98/6.34 (assert (forall ((X23 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X23) (@ tptp.suc Y22)) (= X23 Y22))))
% 5.98/6.34 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N)) (= M N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6620942414471956472nteger N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N) tptp.one_one_Code_integer) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (= N tptp.one_one_nat))))
% 5.98/6.34 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 5.98/6.34 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 5.98/6.34 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 5.98/6.34 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 5.98/6.34 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.98/6.34 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W) (@ tptp.semiri4939895301339042750nteger X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 5.98/6.34 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) (@ tptp.suc J))))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 5.98/6.34 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 5.98/6.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N) (@ tptp.semiri4939895301339042750nteger Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 5.98/6.34 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X2)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 5.98/6.34 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 5.98/6.34 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 5.98/6.34 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 5.98/6.34 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y)) (= X2 Y))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 5.98/6.34 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R2 X4) X4)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R2 X4))) (=> (@ _let_1 Y3) (=> (@ (@ R2 Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N3 tptp.nat)) (@ (@ R2 N3) (@ tptp.suc N3))) (@ (@ R2 M) N)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 5.98/6.34 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M4 tptp.nat)) (= M6 (@ tptp.suc M4))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 5.98/6.34 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 5.98/6.34 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I)) (@ tptp.semiri5074537144036343181t_real J)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I)) (@ tptp.semiri4939895301339042750nteger J)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F N))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 5.98/6.34 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.34 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N4)) __flatten_var_0))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 5.98/6.34 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 5.98/6.34 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (exists ((K2 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K2)))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 5.98/6.34 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 5.98/6.34 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 5.98/6.34 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N3))))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N3))))) (not (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N3))))))))))))))))
% 5.98/6.34 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M3)) tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 5.98/6.34 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_real) (B4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B4) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B4) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_set_nat) (B4 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B4) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B4) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B4) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B4)))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))))
% 5.98/6.34 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N4)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M3)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 5.98/6.34 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2)))) tptp.one_one_real)))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 5.98/6.34 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 5.98/6.34 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X2)))))
% 5.98/6.34 (assert (forall ((Y tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X2)) (@ (@ tptp.ord_less_eq_set_int X2) (@ tptp.uminus1532241313380277803et_int Y)))))
% 5.98/6.34 (assert (forall ((Y tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X2) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X2)) Y))))
% 5.98/6.34 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 5.98/6.34 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 5.98/6.34 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 5.98/6.34 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 5.98/6.34 (assert (= (lambda ((Y5 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y5 Z4)) (lambda ((Xs3 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (= (@ (@ tptp.nth_VEBT_VEBT Xs3) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 5.98/6.34 (assert (= (lambda ((Y5 tptp.list_o) (Z4 tptp.list_o)) (= Y5 Z4)) (lambda ((Xs3 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 5.98/6.34 (assert (= (lambda ((Y5 tptp.list_nat) (Z4 tptp.list_nat)) (= Y5 Z4)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 5.98/6.34 (assert (= (lambda ((Y5 tptp.list_int) (Z4 tptp.list_int)) (= Y5 Z4)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.vEBT_VEBT)) (@ (@ P I4) X5)))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs3) I4)))))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 Bool)) (@ (@ P I4) X5)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs3) I4)))))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.nat)) (@ (@ P I4) X5)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs3) I4)))))))))
% 5.98/6.34 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.int)) (@ (@ P I4) X5)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs3) I4)))))))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs Ys)))))
% 5.98/6.34 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 5.98/6.34 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) __flatten_var_0))))
% 5.98/6.34 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A4) tptp.one_one_int)) __flatten_var_0))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N)) (@ tptp.set_complex2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N)) (@ tptp.set_set_nat2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.34 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ P X4))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) X2))))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) X2))))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 5.98/6.34 (assert (= tptp.vEBT_VEBT_low (lambda ((X3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 5.98/6.34 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A4 Bool) (B3 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B3))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary2)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary2) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A22 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X5))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList2) Summary2)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X5)))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList2) Summary2)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary2) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 N4)) (= A22 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))) (exists ((TreeList2 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary2 tptp.vEBT_VEBT) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N4))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList2) Summary2)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 A22)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))
% 5.98/6.34 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 5.98/6.34 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y)) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.34 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.34 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.34 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (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)))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 5.98/6.34 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.34 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.34 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.34 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.34 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.34 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 5.98/6.34 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 5.98/6.34 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.98/6.34 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 5.98/6.34 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.98/6.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 5.98/6.34 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 5.98/6.34 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 5.98/6.34 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 5.98/6.34 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 5.98/6.34 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 5.98/6.34 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 5.98/6.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 5.98/6.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N)) (= tptp.zero_zero_nat N))))
% 5.98/6.34 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 5.98/6.34 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 5.98/6.34 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 5.98/6.34 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 5.98/6.34 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.98/6.34 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.34 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.34 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.34 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.34 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 5.98/6.34 (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))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (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)))))
% 5.98/6.34 (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))))))
% 5.98/6.34 (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))))
% 5.98/6.34 (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))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 5.98/6.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 5.98/6.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 5.98/6.34 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 5.98/6.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 5.98/6.34 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 5.98/6.34 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 5.98/6.35 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.98/6.35 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.35 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.35 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.98/6.35 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 5.98/6.35 (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)))))
% 5.98/6.35 (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))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 5.98/6.35 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 5.98/6.35 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.35 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.98/6.35 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.35 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 5.98/6.35 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 5.98/6.35 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 5.98/6.35 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.35 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.35 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.35 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 5.98/6.35 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 5.98/6.35 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (= (= tptp.zero_zero_complex X2) (= X2 tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X2 (@ tptp.suc N3))))))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 Bool) (B2 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A3) B2)) X4)))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V2)) TreeList3) S3)) X4)))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 5.98/6.35 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B5) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B5) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B5) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B5)) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A5) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A5)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A5 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A5) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A5)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 5.98/6.35 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 5.98/6.35 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 5.98/6.35 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A3 Bool) (B2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (D2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) D2)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) Deg3))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 5.98/6.35 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 5.98/6.35 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 5.98/6.35 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 5.98/6.35 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 5.98/6.35 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 5.98/6.35 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 5.98/6.35 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A4 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A4) B3) tptp.zero_zero_real))))
% 5.98/6.35 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A4) B3) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A4) B3) tptp.zero_zero_int))))
% 5.98/6.35 (assert (= (lambda ((Y5 tptp.complex) (Z4 tptp.complex)) (= Y5 Z4)) (lambda ((A4 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A4) B3) tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 5.98/6.35 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (@ (@ P X4) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X4) Y3) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va))))))))))
% 5.98/6.35 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 5.98/6.35 (assert (forall ((Nat tptp.nat) (X23 tptp.nat)) (=> (= Nat (@ tptp.suc X23)) (not (= Nat tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 5.98/6.35 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((X23 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X23)))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 5.98/6.35 (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)))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 5.98/6.35 (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))))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 5.98/6.35 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D2 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D2)))))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D2 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D2)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P4 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P4) (=> (@ (@ tptp.ord_less_nat M) P4) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P4) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P4))))) (@ P M)))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 5.98/6.35 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N4)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 5.98/6.35 (assert (= tptp.neg_numeral_dbl_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) X3))))
% 5.98/6.35 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat X3) X3))))
% 5.98/6.35 (assert (= tptp.neg_numeral_dbl_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) X3))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X2) Y) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X2) Y) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X2) Y) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 5.98/6.35 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.35 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A4) B3)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A4) B3)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A4) B3)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 5.98/6.35 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.35 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.35 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.35 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 5.98/6.35 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.35 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 5.98/6.35 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ tptp.vEBT_Leaf A) B)) tptp.one_one_real)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K3) (not (@ P I2)))) (@ P K3)))))))
% 5.98/6.35 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M 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))))))
% 5.98/6.35 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)))))))
% 5.98/6.35 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) K))))))
% 5.98/6.35 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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))))))
% 5.98/6.35 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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))))))
% 5.98/6.35 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 5.98/6.35 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.35 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((X23 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X23)) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 5.98/6.35 (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)))))
% 5.98/6.35 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb)) X4)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc)) X4)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X4)))))))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 5.98/6.35 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (exists ((Q3 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q3))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 5.98/6.35 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M3) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M3) N4)) N4)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y)) X2)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y)) X2)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y)) X2)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X2)) X2)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X2)) X2)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X2)) X2)))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.35 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.35 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.35 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 5.98/6.35 (assert (forall ((Y tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.35 (assert (forall ((M tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 5.98/6.35 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M7 tptp.nat)) (=> (@ P X2) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M7))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M4)))))))))))
% 5.98/6.35 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.35 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) K3) (not (@ P I2)))) (@ P (@ tptp.suc K3))))))))
% 5.98/6.35 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 5.98/6.35 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 5.98/6.35 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 5.98/6.35 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 5.98/6.35 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D3 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D3)) (not (@ P D3)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D3 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D3)) (@ P D3)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 5.98/6.35 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 5.98/6.35 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 5.98/6.35 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M4 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K3) M4)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 5.98/6.35 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 5.98/6.35 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 5.98/6.35 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 5.98/6.35 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D))) _let_1))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X2)) Y)))) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X2)) Y)))) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) Z)))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X2) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X2) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X2) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 5.98/6.35 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 5.98/6.35 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.35 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.35 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 5.98/6.35 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 5.98/6.35 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.35 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 5.98/6.35 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N4))))))
% 5.98/6.35 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 5.98/6.35 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N4))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X2) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X2) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 5.98/6.35 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 5.98/6.35 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 5.98/6.35 (assert (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 5.98/6.35 (assert (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R) (=> (@ (@ tptp.ord_less_eq_rat R) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X2) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X2) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X2) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X2) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 5.98/6.35 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.35 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.35 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.35 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.35 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 5.98/6.35 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 5.98/6.35 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 5.98/6.35 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 5.98/6.35 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 5.98/6.35 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ _let_1 M)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ _let_1 N)))))))))
% 5.98/6.35 (assert (forall ((U tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X2) Y)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.35 (assert (forall ((U tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X2) Y)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 5.98/6.35 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X_1))) (not (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))))))))))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 5.98/6.35 (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))))
% 5.98/6.35 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 5.98/6.35 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 5.98/6.35 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 5.98/6.35 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 5.98/6.35 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 5.98/6.35 (assert (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B4) N))))))
% 5.98/6.35 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 5.98/6.35 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 5.98/6.35 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))))
% 5.98/6.35 (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))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((X23 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X23) (@ tptp.bit0 Y22)) (= X23 Y22))))
% 5.98/6.35 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 5.98/6.35 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 5.98/6.35 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 5.98/6.35 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 5.98/6.35 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 5.98/6.35 (assert (forall ((X33 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X33) (@ tptp.bit1 Y32)) (= X33 Y32))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X2 A))))
% 5.98/6.35 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B4) N))))))))
% 5.98/6.35 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 5.98/6.35 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 5.98/6.35 (assert (forall ((P Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 5.98/6.35 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A4) (@ tptp.semiri1314217659103216013at_int B3)))))
% 5.98/6.35 (assert (forall ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 5.98/6.35 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 5.98/6.35 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 5.98/6.35 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_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))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_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)))))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 5.98/6.35 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((M tptp.int) (N 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))))))
% 5.98/6.35 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 5.98/6.35 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.35 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 5.98/6.35 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 5.98/6.35 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 5.98/6.35 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.35 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 5.98/6.35 (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))))
% 5.98/6.35 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 5.98/6.35 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B4) N))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 5.98/6.35 (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)))))
% 5.98/6.35 (assert (forall ((A2 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B4) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (Q5 tptp.int) (R3 tptp.int) (Q2 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 Q5)) R3)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (Q5 tptp.int) (R3 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R3)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B5) Q5)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) 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) R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B5 tptp.int) (Q5 tptp.int) (R3 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 B5) Q5)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R3) B5) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 5.98/6.35 (assert (forall ((B5 tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B5) Q5)) R3)) (=> (@ (@ tptp.ord_less_int R3) B5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ _let_1 Q5)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A5) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B5 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B5))))))))
% 5.98/6.35 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A5) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A5) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B5 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (=> (@ (@ tptp.ord_less_eq_int B5) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B5)) (@ _let_1 B))))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 5.98/6.35 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 5.98/6.35 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 5.98/6.35 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 5.98/6.35 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 5.98/6.35 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 5.98/6.35 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) (@ tptp.suc N)) A))))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (X2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X2) (= A X2) (@ (@ tptp.ord_less_eq_int X2) A))))
% 5.98/6.35 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 5.98/6.35 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N3)) Y))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 5.98/6.35 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X2)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2)))))))
% 5.98/6.35 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 5.98/6.35 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X2)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) Y))))
% 5.98/6.35 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 5.98/6.35 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (= (@ (@ tptp.power_power_real R4) N) A)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real X4) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X4)))))))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))))))
% 5.98/6.35 (assert (forall ((B5 tptp.real) (A5 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B5) A5)) (@ (@ tptp.ord_less_real A5) B5))))
% 5.98/6.35 (assert (forall ((B5 tptp.rat) (A5 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B5) A5)) (@ (@ tptp.ord_less_rat A5) B5))))
% 5.98/6.35 (assert (forall ((B5 tptp.num) (A5 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B5) A5)) (@ (@ tptp.ord_less_num A5) B5))))
% 5.98/6.35 (assert (forall ((B5 tptp.nat) (A5 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B5) A5)) (@ (@ tptp.ord_less_nat A5) B5))))
% 5.98/6.35 (assert (forall ((B5 tptp.int) (A5 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B5) A5)) (@ (@ tptp.ord_less_int A5) B5))))
% 5.98/6.35 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 5.98/6.35 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 5.98/6.35 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.35 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 5.98/6.35 (assert (forall ((X23 tptp.num)) (not (= tptp.one (@ tptp.bit0 X23)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 5.98/6.35 (assert (forall ((X23 tptp.num) (X33 tptp.num)) (not (= (@ tptp.bit0 X23) (@ tptp.bit1 X33)))))
% 5.98/6.35 (assert (forall ((X33 tptp.num)) (not (= tptp.one (@ tptp.bit1 X33)))))
% 5.98/6.35 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I)) (@ _let_1 J)))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 5.98/6.35 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.35 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 5.98/6.35 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z5 tptp.int)) (exists ((N4 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 5.98/6.35 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 5.98/6.35 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.35 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 5.98/6.35 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 5.98/6.35 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ 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)))))))
% 5.98/6.35 (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.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.35 (assert (= tptp.ord_less_eq_int (lambda ((W2 tptp.int) (Z5 tptp.int)) (exists ((N4 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int N4)))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 5.98/6.35 (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))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X2 (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X2) Z)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 5.98/6.35 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 5.98/6.35 (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))))
% 5.98/6.35 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 5.98/6.35 (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))))
% 5.98/6.35 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X2))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 5.98/6.35 (assert (forall ((A2 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B4) N))))))))
% 5.98/6.35 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N)))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X2) Y) (@ P tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 5.98/6.35 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 5.98/6.35 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A4) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))))))))))
% 5.98/6.35 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A4) _let_1))) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 5.98/6.35 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.35 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 5.98/6.35 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 5.98/6.35 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q4))))))
% 5.98/6.35 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))))
% 5.98/6.35 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (not (@ (@ tptp.ord_less_real T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (not (@ (@ tptp.ord_less_rat T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (not (@ (@ tptp.ord_less_num T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (not (@ (@ tptp.ord_less_nat T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (not (@ (@ tptp.ord_less_int T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (@ (@ tptp.ord_less_real T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (@ (@ tptp.ord_less_rat T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (@ (@ tptp.ord_less_num T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (@ (@ tptp.ord_less_nat T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (@ (@ tptp.ord_less_int T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (not (@ (@ tptp.ord_less_real X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (not (@ (@ tptp.ord_less_rat X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (not (@ (@ tptp.ord_less_num X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (not (@ (@ tptp.ord_less_nat X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (not (@ (@ tptp.ord_less_int X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (not (= X T)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (= (or (@ P X) (@ Q X)) (or (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (= (and (@ P X) (@ Q X)) (and (@ P6 X) (@ Q6 X))))))))))
% 5.98/6.35 (assert (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X2 X7) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X2) P) (=> _let_2 P6))))))))
% 5.98/6.35 (assert (forall ((X2 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X2 X7) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X2) P) (and _let_2 P6))))))))
% 5.98/6.35 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 5.98/6.35 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 5.98/6.35 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (not (@ (@ tptp.ord_less_eq_real X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (not (@ (@ tptp.ord_less_eq_rat X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (not (@ (@ tptp.ord_less_eq_num X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (not (@ (@ tptp.ord_less_eq_nat X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (not (@ (@ tptp.ord_less_eq_int X) T)))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X) (@ (@ tptp.ord_less_eq_real T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X) (@ (@ tptp.ord_less_eq_rat T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X) (@ (@ tptp.ord_less_eq_num T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X) (@ (@ tptp.ord_less_eq_nat T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X) (@ (@ tptp.ord_less_eq_int T) X))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (@ (@ tptp.ord_less_eq_real X) T))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (@ (@ tptp.ord_less_eq_rat X) T))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (@ (@ tptp.ord_less_eq_num X) T))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (@ (@ tptp.ord_less_eq_nat X) T))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (@ (@ tptp.ord_less_eq_int X) T))))))
% 5.98/6.35 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real X) Z3) (not (@ (@ tptp.ord_less_eq_real T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X tptp.num)) (=> (@ (@ tptp.ord_less_num X) Z3) (not (@ (@ tptp.ord_less_eq_num T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X)))))))
% 5.98/6.35 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) Z3) (not (@ (@ tptp.ord_less_eq_int T) X)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (forall ((X tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex K4) D4)))) (= (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (=> (forall ((X4 tptp.complex) (K3 tptp.complex)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex K3) D4))))) (forall ((X tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex K4) D4)))) (= (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 5.98/6.35 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P1 X4) (@ P1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ P X4) (@ P1 X4))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 5.98/6.35 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (=> (@ (@ P B2) C3) (=> (@ (@ tptp.ord_less_eq_real A3) B2) (=> (@ (@ tptp.ord_less_eq_real B2) C3) (@ _let_1 C3))))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A3 tptp.real) (B2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A3) X4) (@ (@ tptp.ord_less_eq_real X4) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B2) A3)) D5)) (@ (@ P A3) B2)))))))) (@ (@ P A) B))))))
% 5.98/6.35 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 5.98/6.35 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P X) (@ P (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 5.98/6.35 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X3 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X3) (@ (@ tptp.vEBT_VEBT_membermima T2) X3)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X2) Y))))))
% 5.98/6.35 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X2) Y)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y)))))
% 5.98/6.35 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X2) Y)))))
% 5.98/6.35 (assert (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 5.98/6.35 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 5.98/6.35 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 5.98/6.35 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 5.98/6.35 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 5.98/6.35 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 5.98/6.35 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 5.98/6.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 5.98/6.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 5.98/6.35 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 5.98/6.35 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.35 (assert (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2))))
% 5.98/6.35 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 5.98/6.35 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 5.98/6.35 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 5.98/6.35 (assert (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2))))
% 5.98/6.35 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 5.98/6.35 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 5.98/6.35 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 5.98/6.35 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va3) Vb2)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 5.98/6.35 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 5.98/6.35 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M3) N4)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.unique5026877609467782581ep_nat N4) (@ (@ tptp.unique5055182867167087721od_nat M3) (@ tptp.bit0 N4)))))))
% 5.98/6.35 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M3) N4)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.unique5024387138958732305ep_int N4) (@ (@ tptp.unique5052692396658037445od_int M3) (@ tptp.bit0 N4)))))))
% 5.98/6.35 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N4 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M3) N4)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.unique4921790084139445826nteger N4) (@ (@ tptp.unique3479559517661332726nteger M3) (@ tptp.bit0 N4)))))))
% 5.98/6.35 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X2) Y)))))
% 5.98/6.35 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X2) Y)))))
% 5.98/6.35 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X2) Y)))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 5.98/6.35 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) N) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R)) tptp.one_one_int)))))))))
% 5.98/6.35 (assert (forall ((H tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H)))))))))))))
% 5.98/6.35 (assert (forall ((H tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H))))))))))))
% 5.98/6.35 (assert (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (and (= A A5) (= B B5)))))
% 5.98/6.35 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (and (= A A5) (= B B5)))))
% 5.98/6.35 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B5)) (and (= A A5) (= B B5)))))
% 5.98/6.35 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B5)) (and (= A A5) (= B B5)))))
% 5.98/6.35 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (and (= A A5) (= B B5)))))
% 5.98/6.35 (assert (forall ((X1 tptp.int) (X23 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X23) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 5.98/6.35 (assert (forall ((X1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (X23 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger X1) X23) (@ (@ tptp.produc6137756002093451184nteger Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 5.98/6.35 (assert (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X23 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X23) (@ (@ tptp.produc8603105652947943368nteger Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 5.98/6.35 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X23 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X23) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 5.98/6.35 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X23 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X23) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X23 Y22)))))
% 5.98/6.35 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.98/6.35 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.35 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 5.98/6.35 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R3)) (= R R3))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q5 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R3)) (= Q2 Q5))))))
% 5.98/6.35 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.divide_divide_int K) L) Q2))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.modulo_modulo_int K) L) R))))
% 5.98/6.35 (assert (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 5.98/6.35 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 5.98/6.35 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 5.98/6.35 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 5.98/6.35 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P4 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A3) B2))) (@ P P4))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (P4 tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) B2))) (@ P P4))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P4 tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) B2))) (@ P P4))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P4 tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) B2))) (@ P P4))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P4 tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) B2))) (@ P P4))))
% 5.98/6.35 (assert (forall ((P4 tptp.product_prod_int_int)) (exists ((X4 tptp.int) (Y3 tptp.int)) (= P4 (@ (@ tptp.product_Pair_int_int X4) Y3)))))
% 5.98/6.35 (assert (forall ((P4 tptp.produc8763457246119570046nteger)) (exists ((X4 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P4 (@ (@ tptp.produc6137756002093451184nteger X4) Y3)))))
% 5.98/6.35 (assert (forall ((P4 tptp.produc1908205239877642774nteger)) (exists ((X4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y3 tptp.produc8923325533196201883nteger)) (= P4 (@ (@ tptp.produc8603105652947943368nteger X4) Y3)))))
% 5.98/6.35 (assert (forall ((P4 tptp.produc2285326912895808259nt_int)) (exists ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P4 (@ (@ tptp.produc5700946648718959541nt_int X4) Y3)))))
% 5.98/6.35 (assert (forall ((P4 tptp.produc7773217078559923341nt_int)) (exists ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P4 (@ (@ tptp.produc4305682042979456191nt_int X4) Y3)))))
% 5.98/6.35 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A3) B2)))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc6137756002093451184nteger A3) B2)))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A3) B2)))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A3) B2)))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A3) B2)))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))))
% 5.98/6.35 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.if_int (= R tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R))))))))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (X2 tptp.produc8763457246119570046nteger)) (=> (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (@ P (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3)))) (@ P X2))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X2 tptp.produc1908205239877642774nteger)) (=> (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3)))) (@ P X2))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X2 tptp.produc2285326912895808259nt_int)) (=> (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3)))) (@ P X2))))
% 5.98/6.35 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X2 tptp.produc7773217078559923341nt_int)) (=> (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3)))) (@ P X2))))
% 5.98/6.35 (assert (forall ((Y tptp.produc8763457246119570046nteger)) (not (forall ((A3 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (not (= Y (@ (@ tptp.produc6137756002093451184nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3))))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B2 tptp.code_integer) (C3 tptp.code_integer)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A3) (@ (@ tptp.produc1086072967326762835nteger B2) C3))))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3))))))))
% 5.98/6.35 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A3 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.int) (C3 tptp.int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A3) (@ (@ tptp.product_Pair_int_int B2) C3))))))))
% 5.98/6.35 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_int R) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R) (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 5.98/6.35 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 5.98/6.35 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 5.98/6.35 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 5.98/6.35 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 5.98/6.35 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 5.98/6.35 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5074537144036343181t_real N))))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real X2)) (@ tptp.real_V7735802525324610683m_real X2))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.real_V1022390504157884413omplex X2))))
% 5.98/6.35 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.35 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 5.98/6.35 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 5.98/6.35 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.35 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 5.98/6.35 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 5.98/6.35 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) A)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y)))))
% 5.98/6.35 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 5.98/6.35 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 5.98/6.35 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 5.98/6.35 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (R tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.times_times_real R) S2))))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y))) (@ (@ tptp.times_times_real R) S2))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) E))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) E))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (R tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real R) S2))))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (R tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.plus_plus_real R) S2))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S2))))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S2))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) E))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) E))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y))))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y))))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 5.98/6.35 (assert (forall ((X2 tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y))) E))))
% 5.98/6.35 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y))) E))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.35 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.36 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 5.98/6.36 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 5.98/6.36 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 5.98/6.36 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 5.98/6.36 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ tptp.arsinh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arsinh_real X2)))))
% 5.98/6.36 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X2) Y)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X2) (@ tptp.ln_ln_real Y)) (= X2 Y)))))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.semiri5074537144036343181t_real X2)) N) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.semiri1314217659103216013at_int X2)) N) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.semiri8010041392384452111omplex X2)) N) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat (@ tptp.semiri1316708129612266289at_nat X2)) N) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.semiri4939895301339042750nteger X2)) N) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N))))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 5.98/6.36 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((Z tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N))) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.36 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 5.98/6.36 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 5.98/6.36 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 5.98/6.36 (assert (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) M))))))
% 5.98/6.36 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 5.98/6.36 (assert (forall ((Z tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N))) M))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 5.98/6.36 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) Y)) Y)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X2))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 5.98/6.36 (assert (forall ((R tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 5.98/6.36 (assert (forall ((R tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 5.98/6.36 (assert (forall ((R tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 5.98/6.36 (assert (forall ((R tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 5.98/6.36 (assert (forall ((R tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 5.98/6.36 (assert (= tptp.artanh_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 5.98/6.36 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 5.98/6.36 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R)) (@ (@ tptp.power_power_nat N) R)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (= (@ tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.36 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ tptp.tanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.tanh_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (= (@ tptp.tanh_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.tanh_complex X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.tanh_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X2) (@ tptp.abs_abs_real Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_real Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X2) (@ tptp.abs_abs_int Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_int Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X2) (@ tptp.abs_abs_Code_integer Y)) (or (= X2 Y) (= X2 (@ tptp.uminus1351360451143612070nteger Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X2) (@ tptp.abs_abs_rat Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_rat Y))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 5.98/6.36 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E2))) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E2))) (= X2 tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X2))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 5.98/6.36 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y))))))
% 5.98/6.36 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 5.98/6.36 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_int (lambda ((A4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_Code_integer (lambda ((A4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A4)) A4))))
% 5.98/6.36 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A) R))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A) R))))))
% 5.98/6.36 (assert (= tptp.abs_abs_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A4) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A4)) A4))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D2) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X2 Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) U)) Y))) V)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.produc2285326912895808259nt_int)) (not (forall ((F2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D2 tptp.int) (I3 tptp.int)) (not (= X2 (@ (@ tptp.produc5700946648718959541nt_int F2) (@ (@ tptp.product_Pair_int_int D2) I3))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (D2 tptp.int) (I3 tptp.int)) (not (= X2 (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int D2) I3))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.product_prod_int_int)) (not (forall ((D2 tptp.int) (I3 tptp.int)) (not (= X2 (@ (@ tptp.product_Pair_int_int D2) I3)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y4))) D2) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X2) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X2) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X2) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((Y tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y))))))
% 5.98/6.36 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y))))))
% 5.98/6.36 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) Y))))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (@ (@ P X4) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ P X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ P X4) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ P X4) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))))
% 5.98/6.36 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X23 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X23 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X23)) (@ (@ tptp.plus_plus_nat (@ X2 X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 5.98/6.36 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X2)) Y) (@ (@ tptp.dvd_dvd_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X2)) Y) (@ (@ tptp.dvd_dvd_int X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X2)) Y) (@ (@ tptp.dvd_dvd_complex X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X2)) Y) (@ (@ tptp.dvd_dvd_Code_integer X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X2)) Y) (@ (@ tptp.dvd_dvd_rat X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 5.98/6.36 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 5.98/6.36 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 5.98/6.36 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 5.98/6.36 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 5.98/6.36 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 5.98/6.36 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 5.98/6.36 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 5.98/6.36 (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))))))
% 5.98/6.36 (assert (= (@ tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.arctan X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 5.98/6.36 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 5.98/6.36 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 5.98/6.36 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ _let_1 L)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 5.98/6.36 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 5.98/6.36 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 5.98/6.36 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 5.98/6.36 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X2) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y))))))
% 5.98/6.36 (assert (forall ((P4 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P4) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P4 (@ (@ tptp.times_times_nat X4) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X4) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 5.98/6.36 (assert (forall ((P4 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P4) (@ (@ tptp.times_times_int A) B)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.times_times_int X4) Y3)) (=> (@ (@ tptp.dvd_dvd_int X4) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 5.98/6.36 (assert (forall ((I tptp.int) (D tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_complex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (=> (= A4 tptp.zero_zero_complex) (= B3 tptp.zero_zero_complex)))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_real (lambda ((A4 tptp.real) (B3 tptp.real)) (=> (= A4 tptp.zero_zero_real) (= B3 tptp.zero_zero_real)))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (=> (= A4 tptp.zero_zero_rat) (= B3 tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K3 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K3))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B3 tptp.code_integer) (A4 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A4 (@ (@ tptp.times_3573771949741848930nteger B3) K2))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A4 tptp.real)) (exists ((K2 tptp.real)) (= A4 (@ (@ tptp.times_times_real B3) K2))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (exists ((K2 tptp.rat)) (= A4 (@ (@ tptp.times_times_rat B3) K2))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (exists ((K2 tptp.nat)) (= A4 (@ (@ tptp.times_times_nat B3) K2))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A4 tptp.int)) (exists ((K2 tptp.int)) (= A4 (@ (@ tptp.times_times_int B3) K2))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_complex (lambda ((B3 tptp.complex) (A4 tptp.complex)) (exists ((K2 tptp.complex)) (= A4 (@ (@ tptp.times_times_complex B3) K2))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_complex Y) Z)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y) N)))))
% 5.98/6.36 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 5.98/6.36 (assert (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L) K))))
% 5.98/6.36 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 5.98/6.36 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_int (lambda ((D3 tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D3) (@ tptp.uminus_uminus_int T2)))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_int (lambda ((D3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int D3)) __flatten_var_0))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X2)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.36 (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))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ tptp.arctan (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arctan X2)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M 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))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D2)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X4)) (@ _let_2 Y3)) D2) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X4)) (@ _let_1 Y3)) D2)))))))))
% 5.98/6.36 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L)) R)))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S2))))) (=> (@ (@ tptp.ord_less_real X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S2))))) (=> (@ (@ tptp.ord_less_rat X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S2))))) (=> (@ (@ tptp.ord_less_nat X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S2))))) (=> (@ (@ tptp.ord_less_int X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S2)))) (=> (@ (@ tptp.ord_less_real X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S2)))) (=> (@ (@ tptp.ord_less_rat X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S2)))) (=> (@ (@ tptp.ord_less_nat X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S2)))) (=> (@ (@ tptp.ord_less_int X) Z3) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S2))))) (=> (@ (@ tptp.ord_less_real Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S2))))) (=> (@ (@ tptp.ord_less_rat Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S2))))) (=> (@ (@ tptp.ord_less_nat Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S2))))) (=> (@ (@ tptp.ord_less_int Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X) S2)))) (=> (@ (@ tptp.ord_less_real Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X) S2)))) (=> (@ (@ tptp.ord_less_rat Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X) S2)))) (=> (@ (@ tptp.ord_less_nat Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X) S2)))) (=> (@ (@ tptp.ord_less_int Z3) X) (= _let_1 _let_1)))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B3) A4) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B3) A4) tptp.zero_zero_int))))
% 5.98/6.36 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B3) A4) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y) M))))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y) M))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y) M))))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y) M))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D2))))))))
% 5.98/6.36 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 5.98/6.36 (assert (forall ((M tptp.int) (N 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))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 5.98/6.36 (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)))))))
% 5.98/6.36 (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)))))))
% 5.98/6.36 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (M tptp.int) (T 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)))))))
% 5.98/6.36 (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))))))
% 5.98/6.36 (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)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (D tptp.int) (X2 tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (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))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X3 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X3))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X3) tptp.zero_z3403309356797280102nteger)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X3 tptp.real)) (@ P (@ (@ tptp.times_times_real L) X3))) (exists ((X3 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X3) tptp.zero_zero_real)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X3 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X3))) (exists ((X3 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X3) tptp.zero_zero_rat)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X3 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X3) tptp.zero_zero_nat)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X3 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X3) tptp.zero_zero_int)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X3 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X3))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X3) tptp.zero_zero_complex)) (@ P X3))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 5.98/6.36 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex K4) D4))) T)))))))))
% 5.98/6.36 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 5.98/6.36 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 5.98/6.36 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 5.98/6.36 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex K4) D4))) T))))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 5.98/6.36 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 5.98/6.36 (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)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (M tptp.nat) (N 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))))))
% 5.98/6.36 (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))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))))
% 5.98/6.36 (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)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 5.98/6.36 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 5.98/6.36 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 5.98/6.36 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 5.98/6.36 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B2)))))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B2)))))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2))))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 5.98/6.36 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 5.98/6.36 (assert (= (lambda ((Y5 tptp.code_integer) (Z4 tptp.code_integer)) (= Y5 Z4)) (lambda ((A4 tptp.code_integer) (B3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide6298287555418463151nteger A4) _let_1) (@ (@ tptp.divide6298287555418463151nteger B3) _let_1))))))))
% 5.98/6.36 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_nat A4) _let_1) (@ (@ tptp.divide_divide_nat B3) _let_1))))))))
% 5.98/6.36 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A4) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_int A4) _let_1) (@ (@ tptp.divide_divide_int B3) _let_1))))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X2) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y)) (= X2 Y)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 5.98/6.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 5.98/6.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 5.98/6.36 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N 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)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N 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)))))
% 5.98/6.36 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 5.98/6.36 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.36 (assert (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N) R))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_Code_integer))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D))))))
% 5.98/6.36 (assert (forall ((D tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ P A3) B2) (@ (@ P B2) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B2))))) (@ (@ P A) B))))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 5.98/6.36 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y)))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.36 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 5.98/6.36 (assert (forall ((R tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R))) (=> (not (= R tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 5.98/6.36 (assert (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 5.98/6.36 (assert (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 5.98/6.36 (assert (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 5.98/6.36 (assert (forall ((X33 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X33)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X33)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N4 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A4) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A4) _let_1)))))))
% 5.98/6.36 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A4) _let_1)))))))
% 5.98/6.36 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A4) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A4) _let_1)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 5.98/6.36 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 5.98/6.36 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 5.98/6.36 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 5.98/6.36 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 5.98/6.36 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 5.98/6.36 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 5.98/6.36 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 5.98/6.36 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri3624122377584611663nteger N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1408675320244567234ct_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri5044797733671781792omplex N))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 5.98/6.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 5.98/6.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.98/6.36 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 5.98/6.36 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 5.98/6.36 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 5.98/6.36 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.98/6.36 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 5.98/6.36 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N))))))
% 5.98/6.36 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 5.98/6.36 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 5.98/6.36 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int)))))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 5.98/6.36 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P4))) P4)))
% 5.98/6.36 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P4))) P4)))
% 5.98/6.36 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P4))) P4)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2119862282449309892nteger N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 5.98/6.36 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P4) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P4 Q2))))
% 5.98/6.36 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P4) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P4 Q2))))
% 5.98/6.36 (assert (forall ((P4 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P4) (@ tptp.zero_n356916108424825756nteger Q2)) (= P4 Q2))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 5.98/6.36 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R tptp.int) (S2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R) S2)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L S2)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 5.98/6.36 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (not (or (and P4 (not (@ P tptp.one_one_complex))) (and (not P4) (not (@ P tptp.zero_zero_complex))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (not (or (and P4 (not (@ P tptp.one_one_real))) (and (not P4) (not (@ P tptp.zero_zero_real))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (not (or (and P4 (not (@ P tptp.one_one_rat))) (and (not P4) (not (@ P tptp.zero_zero_rat))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (not (or (and P4 (not (@ P tptp.one_one_nat))) (and (not P4) (not (@ P tptp.zero_zero_nat))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (not (or (and P4 (not (@ P tptp.one_one_int))) (and (not P4) (not (@ P tptp.zero_zero_int))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (not (or (and P4 (not (@ P tptp.one_one_Code_integer))) (and (not P4) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (and (=> P4 (@ P tptp.one_one_complex)) (=> (not P4) (@ P tptp.zero_zero_complex))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (and (=> P4 (@ P tptp.one_one_real)) (=> (not P4) (@ P tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (and (=> P4 (@ P tptp.one_one_rat)) (=> (not P4) (@ P tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (and (=> P4 (@ P tptp.one_one_nat)) (=> (not P4) (@ P tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (and (=> P4 (@ P tptp.one_one_int)) (=> (not P4) (@ P tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (and (=> P4 (@ P tptp.one_one_Code_integer)) (=> (not P4) (@ P tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.36 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 5.98/6.36 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 5.98/6.36 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 5.98/6.36 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 5.98/6.36 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 5.98/6.36 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 5.98/6.36 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 5.98/6.36 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 5.98/6.36 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 5.98/6.36 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R)))) (@ (@ tptp.power_power_nat N) R)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri773545260158071498ct_rat N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N4 tptp.nat) (A4 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.36 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ tptp.modulo_modulo_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.36 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.36 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 5.98/6.36 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.36 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.36 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.nat) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ (@ tptp.times_times_nat _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 5.98/6.36 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.int) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ (@ tptp.times_times_int _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 5.98/6.36 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A3) (@ P A3))) (=> (forall ((A3 tptp.code_integer) (B2 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (@ P A3) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A3) (@ P _let_2)))))) (@ P A)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.36 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M3)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M3)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M3)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M3)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri773545260158071498ct_rat N) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri3624122377584611663nteger N) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri5044797733671781792omplex N) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K))))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.36 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))))
% 5.98/6.36 (assert (forall ((W tptp.real) (Y tptp.real) (X2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 5.98/6.36 (assert (forall ((W tptp.rat) (Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 5.98/6.36 (assert (forall ((W tptp.nat) (Y tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X2))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 5.98/6.36 (assert (forall ((W tptp.int) (Y tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 5.98/6.36 (assert (forall ((W tptp.complex) (Y tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X2))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 5.98/6.36 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 5.98/6.36 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))
% 5.98/6.36 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 5.98/6.36 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N4)) (@ (@ tptp.plus_plus_int K2) _let_1))) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 5.98/6.36 (assert (forall ((X23 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X23)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X23)) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (= tptp.sin_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N4)))))))
% 5.98/6.36 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K2))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K2)))))))))
% 5.98/6.36 (assert (= tptp.cos_coeff (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ tptp.semiri2265585572941072030t_real N4))) tptp.zero_zero_real)))))
% 5.98/6.36 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.98/6.36 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.36 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N4 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.36 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.36 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N4 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.36 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N4 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 5.98/6.36 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 5.98/6.36 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 5.98/6.36 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 5.98/6.36 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X2)) tptp.one_one_complex))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X2)) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X2)) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X2)) tptp.one_one_nat))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X2)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X2))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X2 Xa) Xc))))))))))
% 5.98/6.36 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B3) A4)) Acc) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A4) tptp.one_one_nat)) B3) (@ (@ F3 A4) Acc))))))
% 5.98/6.36 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N4))))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 5.98/6.36 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 5.98/6.36 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))))
% 5.98/6.36 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))))
% 5.98/6.36 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L)))))
% 5.98/6.36 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))))
% 5.98/6.36 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))))
% 5.98/6.36 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X2) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.36 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.sgn_sgn_Code_integer A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.sgn_sgn_rat A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.sgn_sgn_real A)) N))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.sgn_sgn_int A)) N))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 5.98/6.36 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.98/6.36 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2)))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) X2)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real X2) tptp.one_one_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R))) (or (@ _let_1 K) (= R tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R)) K)) (or (@ _let_1 K) (= R tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (R tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((R tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 5.98/6.36 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 5.98/6.36 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N) (and (= N tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X2))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X2))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X2)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.semiri4939895301339042750nteger M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.36 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))))
% 5.98/6.36 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B3) A4))))
% 5.98/6.36 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B3) A4))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))))
% 5.98/6.36 (assert (forall ((M tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N))) (= _let_1 _let_1))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N3)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N3)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X2) tptp.zero_zero_complex) (= X2 tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sgn_sgn_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 5.98/6.36 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 5.98/6.36 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) (@ tptp.sgn_sgn_real Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex X2)) (@ tptp.sgn_sgn_complex Y)))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (not (= (@ tptp.exp_complex X2) tptp.zero_zero_complex))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.exp_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 5.98/6.36 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (= M N))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (= M N))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.36 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X4 tptp.real)) (= (@ tptp.exp_real X4) Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N) (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 5.98/6.36 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N) (and B (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X2) Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) X2))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Y))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Z)))))
% 5.98/6.36 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X2)) (@ tptp.abs_abs_Code_integer X2)) X2)))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) (@ tptp.abs_abs_real X2)) X2)))
% 5.98/6.36 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X2)) (@ tptp.abs_abs_rat X2)) X2)))
% 5.98/6.36 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X2)) (@ tptp.abs_abs_int X2)) X2)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 5.98/6.36 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 5.98/6.36 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K2) (@ tptp.sgn_sgn_Code_integer K2)))))
% 5.98/6.36 (assert (= tptp.abs_abs_real (lambda ((K2 tptp.real)) (@ (@ tptp.times_times_real K2) (@ tptp.sgn_sgn_real K2)))))
% 5.98/6.36 (assert (= tptp.abs_abs_rat (lambda ((K2 tptp.rat)) (@ (@ tptp.times_times_rat K2) (@ tptp.sgn_sgn_rat K2)))))
% 5.98/6.36 (assert (= tptp.abs_abs_int (lambda ((K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ tptp.sgn_sgn_int K2)))))
% 5.98/6.36 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L3 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L3)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 5.98/6.36 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))))))
% 5.98/6.36 (assert (forall ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 5.98/6.36 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 5.98/6.36 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X2) Y) (@ (@ tptp.times_times_real Y) X2)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X2) Y) (@ (@ tptp.times_times_complex Y) X2)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L))))))
% 5.98/6.36 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_se2000444600071755411sk_int N4)))))
% 5.98/6.36 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ tptp.bit_se2002935070580805687sk_nat N4)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se2923211474154528505it_int N) A)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Z)))))
% 5.98/6.36 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))) tptp.one_one_real)))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))) tptp.one_one_complex)))
% 5.98/6.36 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X2) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L)) (@ tptp.sgn_sgn_int L))))))
% 5.98/6.36 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A4) N4)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N4) A4))))
% 5.98/6.36 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A4) N4)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N4) A4))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.36 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.36 (assert (= tptp.sgn_sgn_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_real (= X3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.36 (assert (= tptp.sgn_sgn_int (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_int (= X3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.36 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X3)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 5.98/6.36 (assert (= tptp.sgn_sgn_rat (lambda ((X3 tptp.rat)) (@ (@ (@ tptp.if_rat (= X3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2)))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X4) Y))))))
% 5.98/6.36 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X2)))))
% 5.98/6.36 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X2)))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X2)))) (let ((_let_2 (= X2 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.36 (assert (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))))))
% 5.98/6.36 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M)))))))
% 5.98/6.36 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N4) K2) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N4)))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 5.98/6.36 (assert (forall ((A tptp.int)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N3) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))
% 5.98/6.36 (assert (forall ((A tptp.nat)) (=> (forall ((N3 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N3) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))
% 5.98/6.36 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 5.98/6.36 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X2)))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X2)))))
% 5.98/6.36 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X3)))) (let ((_let_2 (@ tptp.exp_real X3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 5.98/6.36 (assert (= tptp.tanh_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3)))) (let ((_let_2 (@ tptp.exp_complex X3))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 5.98/6.36 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A4) (@ (@ tptp.power_8256067586552552935nteger _let_1) N4))))))))
% 5.98/6.36 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A4) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 5.98/6.36 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A4) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 5.98/6.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 5.98/6.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 5.98/6.36 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 5.98/6.36 (assert (forall ((R tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L)) R)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R)))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N) (= N tptp.zero_zero_nat))))))
% 5.98/6.36 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A32) (=> (=> (= A23 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R4 tptp.int) (Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) R4)) (=> (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R4)))))))))))))
% 5.98/6.36 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A1 K2) (= A22 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L2) (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q4) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A1 K2) (= A22 L2) (= A33 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R5))))))))
% 5.98/6.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 5.98/6.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 5.98/6.36 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K)))))))))
% 5.98/6.36 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))))
% 5.98/6.36 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))))
% 5.98/6.36 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))))
% 5.98/6.36 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A4 tptp.code_integer) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A4) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 5.98/6.36 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A4) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 5.98/6.36 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N4 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A4))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A4) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.36 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.98/6.36 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 5.98/6.36 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real X2)))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 5.98/6.36 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 5.98/6.36 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 5.98/6.36 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K2))))) _let_2)))))))))))
% 5.98/6.36 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K2))))))))))))
% 5.98/6.36 (assert (= tptp.arctan (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X3) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X2) (@ tptp.sqrt Y)) (= X2 Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X2)) (@ _let_1 X2)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 5.98/6.36 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N)) N)))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 5.98/6.36 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 5.98/6.36 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) X2)) (@ tptp.abs_abs_real X2))))
% 5.98/6.36 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 5.98/6.36 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 5.98/6.36 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 5.98/6.36 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 5.98/6.36 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 5.98/6.36 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X2) Y)))))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_real A) X2)))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A) X2)) (@ _let_1 X2))))))))
% 5.98/6.36 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 5.98/6.36 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real A) X2))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A))))))
% 5.98/6.36 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y)))))))))
% 5.98/6.36 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 5.98/6.36 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 5.98/6.36 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) K))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X2)))))
% 5.98/6.37 (assert (not (= tptp.pi tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sqrt X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 5.98/6.37 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 5.98/6.37 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 5.98/6.37 (assert (= tptp.sgn_sgn_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real X3) (@ tptp.abs_abs_real X3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y)))))
% 5.98/6.37 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 5.98/6.37 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P3 (@ tptp.nat2 X3)))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z6)) (= Z Z6)))))))
% 5.98/6.37 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 5.98/6.37 (assert (= tptp.log (lambda ((A4 tptp.real) (X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real A4)))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 5.98/6.37 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 5.98/6.37 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M3) (@ tptp.semiri1314217659103216013at_int N4))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real X2) _let_1) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 5.98/6.37 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 5.98/6.37 (assert (= tptp.sgn_sgn_real (lambda ((A4 tptp.real)) (@ (@ (@ tptp.if_real (= A4 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A4)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B))))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 5.98/6.37 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N4 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N4)) (@ P N4))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z6) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z6)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6))))))
% 5.98/6.37 (assert (= tptp.suc (lambda ((A4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) tptp.one_one_int)))))
% 5.98/6.37 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z6) (=> (@ (@ tptp.ord_less_eq_int Z6) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z6)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z6)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X2) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X2) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y)))))
% 5.98/6.37 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y)))))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y)))))))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X2)))))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 5.98/6.37 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (Z6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z6)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z6)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 5.98/6.37 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X2) Y)))))
% 5.98/6.37 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X2) (= Y tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 5.98/6.37 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X2)))))))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y))))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 5.98/6.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 5.98/6.37 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 5.98/6.37 (assert (= tptp.arsinh_real (lambda ((X3 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X2) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 5.98/6.37 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 5.98/6.37 (assert (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.uminus_uminus_real X2)) (@ tptp.cos_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.cos_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.cos_complex X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.sin_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X2)))))
% 5.98/6.37 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 5.98/6.37 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.37 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 5.98/6.37 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.37 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.37 (assert (= (@ tptp.sin_real tptp.pi) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.sin_real X2))))
% 5.98/6.37 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (let ((_let_2 (@ tptp.cos_real X2))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X2))) (let ((_let_2 (@ tptp.cos_complex X2))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 5.98/6.37 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim7802044766580827645g_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim2889992004027027881ng_rat X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (exists ((R4 tptp.real) (A3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R4))) (and (= X2 (@ _let_1 (@ tptp.cos_real A3))) (= Y (@ _let_1 (@ tptp.sin_real A3))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_int (@ tptp.archim6058952711729229775r_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.archim3151403230148437115or_rat X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_int (@ tptp.archim7802044766580827645g_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.archim2889992004027027881ng_rat X2)))))
% 5.98/6.37 (assert (= tptp.archim7802044766580827645g_real (lambda ((X3 tptp.real)) (@ tptp.uminus_uminus_int (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real X3))))))
% 5.98/6.37 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X3 tptp.rat)) (@ tptp.uminus_uminus_int (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat X3))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.sin_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.sin_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.cos_complex X2) tptp.one_one_complex) (= (@ tptp.sin_complex X2) tptp.zero_zero_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.cos_real X2) tptp.one_one_real) (= (@ tptp.sin_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.sin_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X2)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X2)) (@ tptp.sin_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.sin_complex X2) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X2)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2))) tptp.one_one_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim3151403230148437115or_rat X2))) tptp.one_one_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X2))) (@ tptp.cos_complex X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X2))) (@ tptp.cos_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X2)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X2) Y))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X2)))))
% 5.98/6.37 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) (@ tptp.abs_abs_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.cos_real (@ tptp.arctan X2)) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y)))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R))))))
% 5.98/6.37 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat R) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) (@ tptp.sin_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X2) (@ tptp.cos_real Y)) (= X2 Y)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y)) (@ _let_1 X2))))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X2))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_2)))))))
% 5.98/6.37 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.sin_complex W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 5.98/6.37 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.sin_real W)) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R)))) R))))
% 5.98/6.37 (assert (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R)))) R))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_nat))))
% 5.98/6.37 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X2)))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.pi) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X2)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.pi) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 5.98/6.37 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 5.98/6.37 (assert (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (= Y4 X4))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X2)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.cos_real X4) Y) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ tptp.cos_real Y4) Y)) (= Y4 X4)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X2))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y)) (= X2 Y))))))))))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((W tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (= (@ tptp.cos_complex (@ _let_2 W)) (@ (@ tptp.minus_minus_complex (@ _let_2 (@ (@ tptp.power_power_complex (@ tptp.cos_complex W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))))
% 5.98/6.37 (assert (forall ((W tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (= (@ tptp.cos_real (@ _let_2 W)) (@ (@ tptp.minus_minus_real (@ _let_2 (@ (@ tptp.power_power_real (@ tptp.cos_real W)) (@ tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.cos_real X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X2))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X2) Y))))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.sin_real X4) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ tptp.sin_real Y4) Y)) (= Y4 X4)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X3 tptp.nat)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (or (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N4)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z tptp.real)) (= (= (@ (@ tptp.powr_real W) Z) tptp.zero_zero_real) (= W tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 5.98/6.37 (assert (= (@ tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.tan_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.tan_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.tan_complex X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X2) tptp.zero_zero_real))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) A)) (not (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.37 (assert (= (@ tptp.tan_real tptp.pi) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.tan_real X2))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 5.98/6.37 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X2)) X2)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 5.98/6.37 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 5.98/6.37 (assert (= tptp.zero_zero_complex (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.zero_zero_complex) (and (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X2) A)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) Y))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A) B))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 5.98/6.37 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X2) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X2) (@ _let_1 Y)) (= X2 Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X2) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X2) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) tptp.one_one_real)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X2) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X2) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) A))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X2) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X2))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X2 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X2) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X2)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 5.98/6.37 (assert (= tptp.tan_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X3)) (@ tptp.cos_complex X3)))))
% 5.98/6.37 (assert (= tptp.tan_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X3)) (@ tptp.cos_real X3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) N)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X2) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X2)))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y)))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real X2) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X2))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y)))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X2) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X2))))))
% 5.98/6.37 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) Y)))))))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X2))))))))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X2))))))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 5.98/6.37 (assert (= tptp.powr_real (lambda ((X3 tptp.real) (A4 tptp.real)) (@ (@ (@ tptp.if_real (= X3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A4) (@ tptp.ln_ln_real X3)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X4)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y) (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ tptp.tan_real Y4) Y)) (= Y4 X4)))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X2))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X2))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y))))))
% 5.98/6.37 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X4) Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y) (= (@ tptp.arctan Y) X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X2) Y))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_real X2) Y))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X2) Y))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.plus_plus_real X2) Y))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X2)))))))
% 5.98/6.37 (assert (= tptp.tan_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X3))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 5.98/6.37 (assert (= tptp.tan_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X3))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 5.98/6.37 (assert (= tptp.arcosh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 5.98/6.37 (assert (= tptp.arsinh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.37 (assert (= (@ tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) tptp.zero_zero_complex) (= X2 tptp.zero_zero_real))))
% 5.98/6.37 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X2)) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X2)) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y)) (= (@ tptp.uminus_uminus_real X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y)) (= (@ tptp.uminus_uminus_real X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) (@ tptp.uminus_uminus_real (@ tptp.real_V1803761363581548252l_real Y))) (= X2 (@ tptp.uminus_uminus_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) (@ tptp.uminus1482373934393186551omplex (@ tptp.real_V4546457046886955230omplex Y))) (= X2 (@ tptp.uminus_uminus_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri8010041392384452111omplex N))))
% 5.98/6.37 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.sin_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 5.98/6.37 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real B))))))
% 5.98/6.37 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.complex2 R5) tptp.zero_zero_real))))
% 5.98/6.37 (assert (= tptp.real_V4546457046886955230omplex (lambda ((X3 tptp.real)) (@ (@ tptp.complex2 X3) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (Xa tptp.real)) (= (= (@ (@ tptp.complex2 X2) Y) (@ tptp.real_V4546457046886955230omplex Xa)) (and (= X2 Xa) (= Y tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X2) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X2) R)) (@ (@ tptp.times_times_real Y) R)))))
% 5.98/6.37 (assert (forall ((R tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X2) Y)) (@ (@ tptp.complex2 (@ _let_1 X2)) (@ _let_1 Y))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X2) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X2) R)) Y))))
% 5.98/6.37 (assert (forall ((R tptp.real) (X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X2) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R) X2)) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X2) (@ tptp.arccos Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X2)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X2) (@ tptp.arcsin Y)) (= X2 Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X2))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X2)) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X2) Y))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 5.98/6.37 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 5.98/6.37 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (= (@ tptp.arccos (@ tptp.cos_real X2)) (@ tptp.uminus_uminus_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2))))))
% 5.98/6.37 (assert (= tptp.sin_real (lambda ((X3 tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)))))
% 5.98/6.37 (assert (= tptp.sin_complex (lambda ((X3 tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X3)))))
% 5.98/6.37 (assert (= tptp.cos_real (lambda ((X3 tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)))))
% 5.98/6.37 (assert (= tptp.cos_complex (lambda ((X3 tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X2))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y)))))))
% 5.98/6.37 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y))))))))
% 5.98/6.37 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2)) X2) (exists ((N4 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N4))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2)) X2) (exists ((N4 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N4))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)) X2) (exists ((N4 tptp.int)) (= X2 (@ tptp.ring_1_of_int_rat N4))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)) X2) (exists ((N4 tptp.int)) (= X2 (@ tptp.ring_1_of_int_real N4))))))
% 5.98/6.37 (assert (= (@ tptp.cot_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.cot_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.cot_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.cot_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.cot_complex X2)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.37 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri681578069525770553at_rat N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri5074537144036343181t_real N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri8010041392384452111omplex N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri4939895301339042750nteger N))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (= (@ tptp.cot_real tptp.pi) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z))) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat Z))) (@ tptp.uminus_uminus_int Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_rat _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 _let_1)) (@ tptp.ring_17405671764205052669omplex _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 _let_1)) (@ tptp.ring_18347121197199848620nteger _let_1)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 5.98/6.37 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 Z)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 Z)) (@ tptp.ring_18347121197199848620nteger Z)))))
% 5.98/6.37 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X2))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 5.98/6.37 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X2)))))))
% 5.98/6.37 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 5.98/6.37 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X2)))))))
% 5.98/6.37 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) A))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X2)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2)))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (=> (= X2 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (=> (= X2 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 5.98/6.37 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y4 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X4)))))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) (@ (@ tptp.plus_plus_real R) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) (@ (@ tptp.plus_plus_rat R) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R))) tptp.one_one_real)) R)))
% 5.98/6.37 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R))) tptp.one_one_rat)) R)))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.ring_18347121197199848620nteger X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_int (lambda ((N4 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M3)) tptp.one_one_real)))))
% 5.98/6.37 (assert (= tptp.ord_less_int (lambda ((N4 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N4)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M3)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) tptp.pi))))))
% 5.98/6.37 (assert (= tptp.archim7802044766580827645g_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X3))) (@ (@ (@ tptp.if_int (= X3 (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 5.98/6.37 (assert (= tptp.archim2889992004027027881ng_rat (lambda ((X3 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X3))) (@ (@ (@ tptp.if_int (= X3 (@ tptp.ring_1_of_int_rat _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D))) _let_1))))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) Z))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X2) Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X2) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X2) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.archim7802044766580827645g_real X2) Z))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X2) Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X2) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X2) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I4)))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I4)))))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 5.98/6.37 (assert (= tptp.cot_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X3)) (@ tptp.sin_complex X3)))))
% 5.98/6.37 (assert (= tptp.cot_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X3)) (@ tptp.sin_real X3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 5.98/6.37 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2)))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 5.98/6.37 (assert (forall ((Q2 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P4) Q2)))) Q2)) P4))))
% 5.98/6.37 (assert (forall ((Q2 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P4) Q2)))) Q2)) P4))))
% 5.98/6.37 (assert (forall ((Q2 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P4) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P4) Q2)))) Q2)))))
% 5.98/6.37 (assert (forall ((Q2 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat P4) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P4) Q2)))) Q2)))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 5.98/6.37 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K2))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K2))))))
% 5.98/6.37 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K2))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K2))))))
% 5.98/6.37 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K2))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K2))))))
% 5.98/6.37 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K2))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K2))))))
% 5.98/6.37 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K2))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K2))))))
% 5.98/6.37 (assert (forall ((Q2 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P4) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P4) Q2)))) tptp.one_one_real)) Q2)))))
% 5.98/6.37 (assert (forall ((Q2 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat P4) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P4) Q2)))) tptp.one_one_rat)) Q2)))))
% 5.98/6.37 (assert (forall ((Q2 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P4) Q2)))) tptp.one_one_real)) Q2)) P4))))
% 5.98/6.37 (assert (forall ((Q2 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P4) Q2)))) tptp.one_one_rat)) Q2)) P4))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((N tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X3 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 5.98/6.37 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 5.98/6.37 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 5.98/6.37 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 5.98/6.37 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim8280529875227126926d_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim7778729529865785530nd_rat X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X2)) (@ tptp.archim7802044766580827645g_real X2))))
% 5.98/6.37 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 5.98/6.37 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 5.98/6.37 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X3) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X3) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (= tptp.archim8280529875227126926d_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X3))) (@ tptp.archim7802044766580827645g_real X3)) (@ tptp.archim6058952711729229775r_real X3)))))
% 5.98/6.37 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X3 tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X3))) (@ tptp.archim2889992004027027881ng_rat X3)) (@ tptp.archim3151403230148437115or_rat X3)))))
% 5.98/6.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 5.98/6.37 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 5.98/6.37 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.inverse_inverse_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X2) tptp.one_one_rat) (= X2 tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.sgn_sgn_real A)))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.sgn_sgn_complex A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.sgn_sgn_rat A)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.inverse_inverse_real _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_real B) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_rat B) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ _let_1 A)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ _let_1 A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.inverse_inverse_real A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((Z tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)))
% 5.98/6.37 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 5.98/6.37 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real A) (@ tptp.inverse_inverse_real A)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.inverse_inverse_rat A)) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.inverse_inverse_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 5.98/6.37 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ tptp.inverse_inverse_rat _let_1) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_1)))))
% 5.98/6.37 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 5.98/6.37 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 5.98/6.37 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.real_V7735802525324610683m_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.inverse_inverse_real (@ tptp.real_V1022390504157884413omplex A))))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X2))) (=> (= (@ (@ tptp.times_times_real Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X2) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X2))) (=> (= (@ (@ tptp.times_times_complex Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y))) (let ((_let_2 (@ tptp.times_times_rat X2))) (=> (= (@ (@ tptp.times_times_rat Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= A B))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= A B))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= A B))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N)))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat A)) N) (@ tptp.inverse_inverse_rat (@ (@ tptp.power_power_rat A) N)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ tptp.real_V1803761363581548252l_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.inverse_inverse_real X2)) (@ tptp.invers8013647133539491842omplex (@ tptp.real_V4546457046886955230omplex X2))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 5.98/6.37 (assert (not (= tptp.imaginary_unit tptp.zero_zero_complex)))
% 5.98/6.37 (assert (forall ((A tptp.real)) (not (= (@ tptp.cis A) tptp.zero_zero_complex))))
% 5.98/6.37 (assert (forall ((R tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R) (@ tptp.real_V7735802525324610683m_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X2))) (@ tptp.inverse_inverse_real R))))))
% 5.98/6.37 (assert (forall ((R tptp.real) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R) (@ tptp.real_V1022390504157884413omplex X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X2))) (@ tptp.inverse_inverse_real R))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.inverse_inverse_real A)) (=> (not (= A tptp.zero_zero_real)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ tptp.inverse_inverse_rat A)) (=> (not (= A tptp.zero_zero_rat)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) tptp.zero_zero_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) tptp.zero_zero_rat) (=> (not (= A tptp.zero_zero_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ _let_1 tptp.zero_zero_real) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ _let_1 tptp.zero_zero_rat) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A)))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B)) (@ tptp.invers8013647133539491842omplex A)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A)))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 5.98/6.37 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 5.98/6.37 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 5.98/6.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 5.98/6.37 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 5.98/6.37 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real A4) (@ tptp.inverse_inverse_real B3)))))
% 5.98/6.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex A4) (@ tptp.invers8013647133539491842omplex B3)))))
% 5.98/6.37 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat A4) (@ tptp.inverse_inverse_rat B3)))))
% 5.98/6.37 (assert (= tptp.divide_divide_real (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B3)) A4))))
% 5.98/6.37 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B3)) A4))))
% 5.98/6.37 (assert (= tptp.divide_divide_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B3)) A4))))
% 5.98/6.37 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 5.98/6.37 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 5.98/6.37 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X2)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X2)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X2)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 5.98/6.37 (assert (forall ((Xa tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X2) (@ (@ tptp.times_times_real X2) _let_1)))))
% 5.98/6.37 (assert (forall ((Xa tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ (@ tptp.times_times_complex X2) _let_1)))))
% 5.98/6.37 (assert (forall ((Xa tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ (@ tptp.times_times_rat X2) _let_1)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A))))))
% 5.98/6.37 (assert (forall ((Xa tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X2) (@ (@ tptp.times_times_real X2) _let_1)))))
% 5.98/6.37 (assert (forall ((Xa tptp.int) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ (@ tptp.times_times_complex X2) _let_1)))))
% 5.98/6.37 (assert (forall ((Xa tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ (@ tptp.times_times_rat X2) _let_1)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)) (@ tptp.inverse_inverse_real (@ tptp.exp_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.invers8013647133539491842omplex (@ tptp.exp_complex X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ tptp.inverse_inverse_real (@ _let_1 A))))))
% 5.98/6.37 (assert (= tptp.divide_divide_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ (@ tptp.times_times_real X3) (@ tptp.inverse_inverse_real Y2)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X2)) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X2)) tptp.one_one_rat)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X2))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real B)) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat B)) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X2)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X2)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X2)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X2)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.plus_plus_real A) B))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.plus_plus_complex A) B))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.plus_plus_rat A) B))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_2)) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_2)) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_2)) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) A) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) A) tptp.one_one_rat))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real B) A))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex B) A))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat B) A))) _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real A) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 5.98/6.37 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X2) Y) tptp.imaginary_unit) (and (= X2 tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) B)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X2)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X2)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X2)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X2)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) X2)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 5.98/6.37 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D2) E2) (=> (@ P D2) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 5.98/6.37 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N4)))) (and (not (= N4 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D2 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D2) E2) (=> (@ P D2) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real _let_1) X2) (@ tptp.inverse_inverse_real _let_1))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X2))))))
% 5.98/6.37 (assert (= tptp.archim2898591450579166408c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real X3) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X3))))))
% 5.98/6.37 (assert (= tptp.archimedean_frac_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat X3) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X3))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))) X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N3))) X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X2)) M))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X2)) M))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X2)) M))))))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R))))
% 5.98/6.37 (assert (forall ((R tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 tptp.zero_zero_real) R))))
% 5.98/6.37 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) X2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) X2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X2)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X2) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X2)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X2) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 5.98/6.37 (assert (= tptp.complex2 (lambda ((A4 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (exists ((R4 tptp.real) (A3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R4)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A3))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A3)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X2)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X2)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((R tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R))))
% 5.98/6.37 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (= (@ tptp.sinh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (= (@ tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.sinh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.sinh_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.sinh_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sinh_complex X2)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.cis A)) (@ tptp.cis (@ tptp.uminus_uminus_real A)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sinh_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.37 (assert (= (@ tptp.csqrt tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 5.98/6.37 (assert (= (@ tptp.arg tptp.zero_zero_complex) tptp.zero_zero_real))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ tptp.cis (@ tptp.arg Z)) (@ tptp.sgn_sgn_complex Z)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X2)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X2))))))
% 5.98/6.37 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 5.98/6.37 (assert (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (forall ((Z tptp.complex) (X2 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X2)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arg Z) X2))))))
% 5.98/6.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X2))) (= (@ _let_1 (@ _let_1 Y)) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X2) X2) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)))
% 5.98/6.37 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.37 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.37 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ tptp.cosh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ tptp.cosh_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.cosh_complex X2))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 5.98/6.37 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 5.98/6.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 5.98/6.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 5.98/6.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 5.98/6.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 5.98/6.37 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 5.98/6.37 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.98/6.37 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) tptp.zero_zero_rat) (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (or (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (or (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X2)) (not (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X2)) (not (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X2)))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N)) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.power_power_int A) N)) tptp.ring_1_Ints_int))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N)) tptp.ring_1_Ints_complex))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ tptp.uminus_uminus_real A)) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ tptp.uminus_uminus_int A)) tptp.ring_1_Ints_int))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ tptp.uminus1482373934393186551omplex A)) tptp.ring_1_Ints_complex))))
% 5.98/6.37 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger A)) tptp.ring_11222124179247155820nteger))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ tptp.uminus_uminus_rat A)) tptp.ring_1_Ints_rat))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.uminus_uminus_real X2)) tptp.ring_1_Ints_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.member_int (@ tptp.uminus_uminus_int X2)) tptp.ring_1_Ints_int) (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.member_complex (@ tptp.uminus1482373934393186551omplex X2)) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex X2) tptp.ring_1_Ints_complex))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger X2)) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.member_rat (@ tptp.uminus_uminus_rat X2)) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_real (@ tptp.semiri5074537144036343181t_real N)) tptp.ring_1_Ints_real)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N)) tptp.ring_1_Ints_int)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.ring_1_Ints_complex)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_Code_integer (@ tptp.semiri4939895301339042750nteger N)) tptp.ring_11222124179247155820nteger)))
% 5.98/6.37 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) X2) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X2)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X2))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) N) (not (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int A) B)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.cosh_real X2) tptp.zero_zero_real))))
% 5.98/6.37 (assert (@ (@ tptp.member_complex tptp.zero_zero_complex) tptp.ring_1_Ints_complex))
% 5.98/6.37 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 5.98/6.37 (assert (@ (@ tptp.member_rat tptp.zero_zero_rat) tptp.ring_1_Ints_rat))
% 5.98/6.37 (assert (@ (@ tptp.member_int tptp.zero_zero_int) tptp.ring_1_Ints_int))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat B) C))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int B) C))))))
% 5.98/6.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat B3) A4))))
% 5.98/6.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int B3) A4))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat B))) (let ((_let_2 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int B))) (let ((_let_2 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se6528837805403552850or_nat M) N)) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se6528837805403552850or_nat M) N)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se6528837805403552850or_nat M) N)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real A) B)) tptp.ring_1_Ints_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int A) B)) tptp.ring_1_Ints_int)))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.minus_minus_complex A) B)) tptp.ring_1_Ints_complex)))))
% 5.98/6.37 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 5.98/6.37 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 5.98/6.37 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 5.98/6.37 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.ring_1_Ints_complex)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.ring_1_Ints_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B)) tptp.ring_1_Ints_int)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.times_times_real A) B)) tptp.ring_1_Ints_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.times_times_rat A) B)) tptp.ring_1_Ints_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.times_times_int A) B)) tptp.ring_1_Ints_int)))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.times_times_complex A) B)) tptp.ring_1_Ints_complex)))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N)) tptp.ring_1_Ints_complex)))
% 5.98/6.37 (assert (forall ((N tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N)) tptp.ring_1_Ints_real)))
% 5.98/6.37 (assert (forall ((N tptp.num)) (@ (@ tptp.member_rat (@ tptp.numeral_numeral_rat N)) tptp.ring_1_Ints_rat)))
% 5.98/6.37 (assert (forall ((N tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N)) tptp.ring_1_Ints_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y)) (@ _let_1 X2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (= (= (@ (@ tptp.plus_plus_complex A) A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (= (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (@ (@ tptp.plus_plus_complex (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (= (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) _let_1) (@ (@ tptp.plus_plus_real (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X2) Y)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X2))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 5.98/6.37 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.ring_17405671764205052669omplex A)) (@ tptp.ring_17405671764205052669omplex B))) tptp.ring_1_Ints_complex))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) tptp.ring_1_Ints_rat))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_int (@ (@ tptp.divide_divide_int (@ tptp.ring_1_of_int_int A)) (@ tptp.ring_1_of_int_int B))) tptp.ring_1_Ints_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ tptp.arcosh_real (@ tptp.cosh_real X2)) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X2)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X2)) (@ tptp.sinh_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X2)) (@ tptp.sinh_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X2)) (@ tptp.sinh_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X2)) (@ tptp.sinh_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X2)) (@ tptp.sinh_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X2)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X2)) (@ tptp.sinh_complex Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X2)) (@ tptp.sinh_complex X2)) (@ tptp.exp_complex X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X2)) (@ tptp.sinh_real X2)) (@ tptp.exp_real X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex X2)) (@ tptp.exp_complex X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2)) (@ tptp.exp_real X2))))
% 5.98/6.37 (assert (= tptp.tanh_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X3)) (@ tptp.cosh_complex X3)))))
% 5.98/6.37 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X3)) (@ tptp.cosh_real X3)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_real A) _let_2) (@ (@ tptp.plus_plus_real (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_complex A) _let_2) (@ (@ tptp.plus_plus_complex (@ _let_1 _let_2)) (@ _let_1 K)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ _let_1 tptp.one_one_real)) K))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ _let_1 tptp.one_one_complex)) K))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real K))) (=> (@ (@ tptp.ord_less_eq_real _let_1) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) _let_1)) K)) (@ (@ tptp.gbinomial_real A) K))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real A) _let_3) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real _let_3) A) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real K)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3222712562003087583nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (not (= X2 tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (not (= X2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer) (= X2 tptp.zero_z3403309356797280102nteger)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat) (= X2 tptp.zero_zero_rat)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int) (= X2 tptp.zero_zero_int)))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger) (= (= X2 Y) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) Y))) tptp.one_one_Code_integer))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real) (= (= X2 Y) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y))) tptp.one_one_real))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X2 Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) Y))) tptp.one_one_rat))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X2) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X2 Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Y))) tptp.one_one_int))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X2) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.cosh_real X2)) (@ tptp.sinh_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.cosh_complex X2)) (@ tptp.sinh_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2)) (@ tptp.uminus_uminus_real (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.sinh_complex X2)) (@ tptp.cosh_complex X2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_2)) (@ (@ tptp.gbinomial_real _let_1) _let_2)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.gbinomial_real A) K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_2)) (@ (@ tptp.gbinomial_complex _let_1) _let_2)) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.gbinomial_complex A) K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ (@ tptp.gbinomial_real A) _let_1)) (@ (@ tptp.times_times_real A) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) K))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ (@ tptp.gbinomial_complex A) _let_1)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) K))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X2)))) (let ((_let_2 (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X2)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X2)))) (let ((_let_2 (@ (@ tptp.member_rat X2) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X2)))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X2))) (@ tptp.cosh_complex X2))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X2))) (@ tptp.cosh_real X2))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.gbinomial_real A) K)))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))) (@ (@ tptp.gbinomial_complex A) K)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_real A) tptp.one_one_real))) (= (@ (@ tptp.gbinomial_real _let_2) _let_1) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K)) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.semiri5074537144036343181t_real _let_1))))))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex))) (= (@ (@ tptp.gbinomial_complex _let_2) _let_1) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K)) (@ (@ tptp.divide1717551699836669952omplex _let_2) (@ tptp.semiri8010041392384452111omplex _let_1))))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N))))))
% 5.98/6.37 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K2)) A4)) tptp.one_one_rat)) K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K2)) A4)) tptp.one_one_real)) K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K2)) A4)) tptp.one_one_complex)) K2)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X2) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X2) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X2) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X2) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y))) (let ((_let_2 (@ tptp.tanh_complex X2))) (=> (not (= (@ tptp.cosh_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y))) (let ((_let_2 (@ tptp.tanh_real X2))) (=> (not (= (@ tptp.cosh_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (K tptp.nat)) (= (@ (@ tptp.gbinomial_real (@ tptp.uminus_uminus_real A)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 5.98/6.37 (assert (forall ((A tptp.complex) (K tptp.nat)) (= (@ (@ tptp.gbinomial_complex (@ tptp.uminus1482373934393186551omplex A)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_real A) K) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.37 (assert (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_complex A) K) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 5.98/6.37 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A4)) K2))) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A4)) K2))) (@ tptp.semiri2265585572941072030t_real K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A4)) K2))) (@ tptp.semiri5044797733671781792omplex K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))))
% 5.98/6.37 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))))
% 5.98/6.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 5.98/6.37 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 5.98/6.37 (assert (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 5.98/6.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X2)) _let_1)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X2)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X2)) _let_1)) tptp.one_one_complex)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X2)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X2)) _let_1)) tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X2)) _let_1)) tptp.one_one_complex)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X2)) _let_1)) tptp.one_one_real))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X2)) _let_1)) tptp.one_one_complex))))
% 5.98/6.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.98/6.37 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cosh_real X2) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.cosh_complex X2) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 5.98/6.37 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X2)) _let_2)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X2)) _let_2)))))))
% 5.98/6.37 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) A2) (= A2 B4)))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_real A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_nat A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A2) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B4)) (@ (@ tptp.ord_less_eq_set_int B4) A2))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (not (= A2 B4)) (@ (@ tptp.ord_less_set_int A2) B4)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B4)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) A)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.plus_plus_nat M) N)) A))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat M) (@ (@ tptp.bit_se547839408752420682it_nat N) A)) (@ (@ tptp.bit_se547839408752420682it_nat (@ (@ tptp.plus_plus_nat M) N)) A))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N) L))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (= (@ _let_1 K) (@ _let_1 L))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 5.98/6.37 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 5.98/6.37 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) A) (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) A) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7788150548672797655nteger N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se547839408752420682it_nat N) A)) (or (not (= N tptp.zero_zero_nat)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.pred_numeral L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 5.98/6.37 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 5.98/6.37 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N))))))
% 5.98/6.37 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se7788150548672797655nteger N))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se547839408752420682it_nat N) M)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat N) M)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se547839408752420682it_nat M) N)) (@ (@ tptp.bit_se7788150548672797655nteger M) (@ tptp.semiri4939895301339042750nteger N)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.semiri1314217659103216013at_int N)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X2) Y)))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) A))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat M) N)) A))))))
% 5.98/6.37 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 5.98/6.37 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B4) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (@ (@ tptp.ord_less_eq_set_int B4) A2))))))
% 5.98/6.37 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (= A6 B7))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B4) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (@ _let_1 C5))))))
% 5.98/6.37 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (not (@ (@ tptp.ord_less_eq_set_int B7) A6))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_set_int B4) C5) (@ (@ tptp.ord_less_set_int A2) C5)))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B7) (= A6 B7)))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat) (X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (not (@ (@ tptp.ord_less_eq_set_int B4) A2)))))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int B4) A2))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 5.98/6.37 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X4 tptp.list_nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (@ _let_1 C5))))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B7) (@ (@ tptp.ord_less_eq_set_int B7) A6)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X3 tptp.complex)) (=> (@ P X3) (@ Q X3))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X3 tptp.list_nat)) (=> (@ P X3) (@ Q X3))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X3 tptp.set_nat)) (=> (@ P X3) (@ Q X3))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C5) A2)) A2)))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (= (@ (@ tptp.minus_minus_set_int B4) (@ (@ tptp.minus_minus_set_int C5) A2)) A2)))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) A2)))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) A2)))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (C5 tptp.set_nat) (D4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_set_nat C5) D4))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (C5 tptp.set_int) (D4 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int D4) B4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_set_int C5) D4))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 5.98/6.37 (assert (= tptp.bit_concat_bit (lambda ((N4 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N4) K2)) (@ (@ tptp.bit_se545348938243370406it_int N4) L2)))))
% 5.98/6.37 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A4) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 5.98/6.37 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A4) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_2 (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int (@ _let_2 A)) _let_1))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_2 (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 A)) _let_1))))))
% 5.98/6.37 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)) tptp.zero_zero_int)))))
% 5.98/6.37 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A4) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)) tptp.zero_zero_nat)))))
% 5.98/6.37 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.37 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.times_times_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.37 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ tptp.times_times_int A4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.37 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (A4 tptp.nat)) (@ (@ tptp.times_times_nat A4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.bit_se7788150548672797655nteger N) B2))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.bit_se545348938243370406it_int N) B2))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.bit_se547839408752420682it_nat N) B2))))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y)) _let_1)))))))
% 5.98/6.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.98/6.37 (assert (forall ((Bs tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ (@ tptp.groups3417619833198082522nteger tptp.zero_n356916108424825756nteger) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Bs)) N) (and (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N)))))
% 5.98/6.37 (assert (forall ((Bs tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ (@ tptp.groups9119017779487936845_o_nat tptp.zero_n2687167440665602831ol_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Bs)) N) (and (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N)))))
% 5.98/6.37 (assert (forall ((Bs tptp.list_o) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Bs)) N) (and (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N)))))
% 5.98/6.37 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 5.98/6.37 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 5.98/6.37 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 5.98/6.37 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B4))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B4) _let_1))))
% 5.98/6.37 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B4)) (and (@ _let_1 A2) (not (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (and (@ _let_1 A2) (not (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (and (@ _let_1 A2) (not (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B4)) (and (@ _let_1 A2) (not (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (and (@ _let_1 A2) (not (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_ri7919022796975470100ot_int X2)) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (= (@ tptp.bit_ri7919022796975470100ot_int X2) (@ tptp.bit_ri7919022796975470100ot_int Y)) (= X2 Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X2)) Y) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X2))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int Y)) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.bit_ri7919022796975470100ot_int X2)) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X2)) X2) tptp.zero_zero_int)))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (@ tptp.bit_ri7632146776885996613nteger X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (@ tptp.bit_ri7919022796975470100ot_int X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X2)) X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X2)) X2) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X2) (@ tptp.bit_ri7632146776885996613nteger X2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X2) (@ tptp.bit_ri7919022796975470100ot_int X2)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N)))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ tptp.inc N)))))
% 5.98/6.37 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7632146776885996613nteger A)) (not (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (not (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 5.98/6.37 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B4)) (not (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (not (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (not (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B4)) (not (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (not (@ _let_1 B4))))))
% 5.98/6.37 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B4)) (@ _let_1 A2)))))
% 5.98/6.37 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (@ _let_1 A2)))))
% 5.98/6.37 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (@ _let_1 A2)))))
% 5.98/6.37 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B4)) (@ _let_1 A2)))))
% 5.98/6.37 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ _let_1 A2)))))
% 5.98/6.37 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B4)) (not (=> (@ _let_1 A2) (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B4)) (not (=> (@ _let_1 A2) (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B4)) (not (=> (@ _let_1 A2) (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B4)) (not (=> (@ _let_1 A2) (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B4)) (not (=> (@ _let_1 A2) (@ _let_1 B4)))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B4) (exists ((B2 tptp.real)) (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B4) A2))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B4) (exists ((B2 tptp.complex)) (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B4) A2))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B4) (exists ((B2 tptp.int)) (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A2))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B4) (exists ((B2 tptp.set_nat)) (@ (@ tptp.member_set_nat B2) (@ (@ tptp.minus_2163939370556025621et_nat B4) A2))))))
% 5.98/6.37 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (exists ((B2 tptp.nat)) (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A2))))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.bit_ri7919022796975470100ot_int K)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.ring_1_of_int_int K)))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 A))) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int B))) (= (@ _let_1 A) (@ _let_1 B))))))
% 5.98/6.37 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 5.98/6.37 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A4)) tptp.one_one_Code_integer))))
% 5.98/6.37 (assert (= tptp.uminus_uminus_int (lambda ((A4 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A4)) tptp.one_one_int))))
% 5.98/6.37 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A4 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A4) tptp.one_one_Code_integer)))))
% 5.98/6.37 (assert (= tptp.uminus_uminus_int (lambda ((A4 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A4) tptp.one_one_int)))))
% 5.98/6.37 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A4 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A4)) tptp.one_one_Code_integer))))
% 5.98/6.37 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A4 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A4)) tptp.one_one_int))))
% 5.98/6.37 (assert (forall ((Uu2 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D) (= D tptp.one_one_nat))))
% 5.98/6.37 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K2)) tptp.one_one_int))))
% 5.98/6.37 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B) N3) (@ (@ tptp.bit_se1146084159140164899it_int A) N3))) (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B))))))
% 5.98/6.37 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ (@ tptp.minus_minus_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N)))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))
% 5.98/6.37 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 5.98/6.37 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 5.98/6.37 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 5.98/6.37 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bitM N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bitM N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N))) tptp.zero_zero_int))))
% 5.98/6.37 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat N) M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int M))))))
% 5.98/6.37 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A4) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 5.98/6.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 5.98/6.37 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 5.98/6.37 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 5.98/6.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 5.98/6.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int A)) N) (and (not (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N) tptp.zero_zero_int)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N))))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 5.98/6.37 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 5.98/6.37 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 5.98/6.37 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 5.98/6.37 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X5 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X5 M3)) (@ X5 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X2) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 5.98/6.37 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 5.98/6.37 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 5.98/6.37 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 5.98/6.37 (assert (forall ((Y tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X2) (= (@ (@ tptp.ord_less_eq_set_int X2) Y) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (= (@ (@ tptp.ord_less_eq_rat X2) Y) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (= (@ (@ tptp.ord_less_eq_num X2) Y) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_set_int X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (@ (@ tptp.ord_less_eq_set_int B3) A4)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ tptp.ord_less_eq_rat B3) A4)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ tptp.ord_less_eq_num B3) A4)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ tptp.ord_less_eq_nat B3) A4)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ tptp.ord_less_eq_int B3) A4)))))
% 5.98/6.37 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (@ (@ tptp.ord_less_eq_set_int A4) B3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (@ (@ tptp.ord_less_eq_rat A4) B3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (@ (@ tptp.ord_less_eq_num A4) B3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (@ (@ tptp.ord_less_eq_nat A4) B3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (@ (@ tptp.ord_less_eq_int A4) B3)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (@ (@ tptp.ord_less_eq_set_int Y2) X3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat Y2) X3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (@ (@ tptp.ord_less_eq_num Y2) X3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat Y2) X3)))))
% 5.98/6.37 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int Y2) X3)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_12))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_12))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X2) X_12))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z3) (@ (@ tptp.ord_less_real Z3) Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (exists ((Z3 tptp.rat)) (and (@ (@ tptp.ord_less_rat X2) Z3) (@ (@ tptp.ord_less_rat Z3) Y))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X4) (@ P Y4))) (@ P X4))) (@ P A))))
% 5.98/6.37 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X2)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X2)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.37 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.37 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.37 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 5.98/6.37 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 5.98/6.37 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 5.98/6.37 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 5.98/6.37 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 5.98/6.37 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P2 X6))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P3 N4) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N4) (not (@ P3 M3)))))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ tptp.ord_less_real A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.real)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.rat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ tptp.ord_less_num A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.num)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 5.98/6.37 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B2) (@ (@ P A3) B2))) (=> (forall ((A3 tptp.int)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A3) (@ (@ P A3) B2))) (@ (@ P A) B))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (or (@ (@ tptp.ord_less_real Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (or (@ (@ tptp.ord_less_rat Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (or (@ (@ tptp.ord_less_num Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (or (@ (@ tptp.ord_less_nat Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (or (@ (@ tptp.ord_less_int Y) X2) (= X2 Y)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 5.98/6.37 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_rat X2) Y) (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_num X2) Y) (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_int X2) Y) (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 5.98/6.37 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat)) (not (@ (@ tptp.ord_less_rat X2) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.num)) (not (@ (@ tptp.ord_less_num X2) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) X2) P))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (@ (@ tptp.ord_less_rat Y) X2) P))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X2) Y) (=> (@ (@ tptp.ord_less_num Y) X2) P))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) X2) P))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y) (=> (@ (@ tptp.ord_less_int Y) X2) P))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y) (@ (@ tptp.ord_less_real Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_rat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y) (@ (@ tptp.ord_less_num Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_nat Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y) (@ (@ tptp.ord_less_int Y) X2))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= X2 Y)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= Y X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= Y X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= Y X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= Y X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= Y X2)))))
% 5.98/6.37 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M2)) (@ X8 N6)))) E))))))))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M2)) (@ X8 N6)))) E))))))))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M4)) (@ X8 N3)))) E2)))))))) (@ tptp.topolo6517432010174082258omplex X8))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M10 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M4)) (@ X8 N3)))) E2)))))))) (@ tptp.topolo4055970368930404560y_real X8))))
% 5.98/6.38 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X5 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X5 M3)) (@ X5 N4)))) E3)))))))))))
% 5.98/6.38 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X5 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X5 M3)) (@ X5 N4)))) E3)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y) (or (@ (@ tptp.ord_less_set_int X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_real Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_rat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_num Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_int Y) X2))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X2) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X2) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X2) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X2) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X2) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X2) Z)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X2) Y) (@ (@ tptp.ord_less_eq_set_int X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X2) Y)) (@ (@ tptp.ord_less_num Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (not (= X3 Y2))))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 5.98/6.38 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 5.98/6.38 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 5.98/6.38 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 5.98/6.38 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (@ (@ tptp.ord_less_eq_real A4) B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (not (@ (@ tptp.ord_less_eq_set_int A4) B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (@ (@ tptp.ord_less_eq_rat A4) B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (@ (@ tptp.ord_less_eq_num A4) B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (@ (@ tptp.ord_less_eq_nat A4) B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (@ (@ tptp.ord_less_eq_int A4) B3))))))
% 5.98/6.38 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 5.98/6.38 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A4) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A4 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_int (lambda ((B3 tptp.set_int) (A4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A4 tptp.rat)) (or (@ (@ tptp.ord_less_rat B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A4 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A4 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A4 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A4) (= A4 B3)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W3) (=> (@ (@ tptp.ord_less_real W3) Y) (@ (@ tptp.ord_less_eq_real W3) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) W3) (=> (@ (@ tptp.ord_less_rat W3) Y) (@ (@ tptp.ord_less_eq_rat W3) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.98/6.38 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (=> (forall ((W3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W3) (=> (@ (@ tptp.ord_less_real W3) X2) (@ (@ tptp.ord_less_eq_real Y) W3)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 5.98/6.38 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X2) (=> (forall ((W3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W3) (=> (@ (@ tptp.ord_less_rat W3) X2) (@ (@ tptp.ord_less_eq_rat Y) W3)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (@ (@ tptp.ord_less_eq_real B3) A4))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A4))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (@ (@ tptp.ord_less_eq_rat B3) A4))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (@ (@ tptp.ord_less_eq_num B3) A4))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A4))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (@ (@ tptp.ord_less_eq_int B3) A4))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((A4 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((A4 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((A4 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A4) B3) (not (= A4 B3))))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_real (lambda ((A4 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A4 tptp.set_int) (B3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_rat (lambda ((A4 tptp.rat) (B3 tptp.rat)) (or (@ (@ tptp.ord_less_rat A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_num (lambda ((A4 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_int (lambda ((A4 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A4) B3) (= A4 B3)))))
% 5.98/6.38 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X2)) (@ (@ tptp.ord_less_real X2) Y))))
% 5.98/6.38 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X2)) (@ (@ tptp.ord_less_rat X2) Y))))
% 5.98/6.38 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X2)) (@ (@ tptp.ord_less_num X2) Y))))
% 5.98/6.38 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X2)) (@ (@ tptp.ord_less_nat X2) Y))))
% 5.98/6.38 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X2)) (@ (@ tptp.ord_less_int X2) Y))))
% 5.98/6.38 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y2) (not (@ (@ tptp.ord_less_eq_real Y2) X3))))))
% 5.98/6.38 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y2) (not (@ (@ tptp.ord_less_eq_set_int Y2) X3))))))
% 5.98/6.38 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y2) (not (@ (@ tptp.ord_less_eq_rat Y2) X3))))))
% 5.98/6.38 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y2) (not (@ (@ tptp.ord_less_eq_num Y2) X3))))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y2) (not (@ (@ tptp.ord_less_eq_nat Y2) X3))))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y2) (not (@ (@ tptp.ord_less_eq_int Y2) X3))))))
% 5.98/6.38 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 5.98/6.38 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_eq_rat X4) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.98/6.38 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (@ (@ tptp.ord_less_eq_real Y) X4))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 5.98/6.38 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (@ (@ tptp.ord_less_eq_rat Y) X4))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X2) Y) (= (not (@ (@ tptp.ord_less_set_int X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (= (not (@ (@ tptp.ord_less_num X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (= (not (@ (@ tptp.ord_less_int X2) Y)) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (= (@ (@ tptp.ord_less_eq_real X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X2) Y)) (= (@ (@ tptp.ord_less_eq_set_int X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (= (@ (@ tptp.ord_less_eq_rat X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (= (@ (@ tptp.ord_less_eq_num X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (= (@ (@ tptp.ord_less_eq_int X2) Y) (= X2 Y)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 5.98/6.38 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (not (@ (@ tptp.ord_less_real X2) Y)))))
% 5.98/6.38 (assert (forall ((Y tptp.set_int) (X2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X2) (not (@ (@ tptp.ord_less_set_int X2) Y)))))
% 5.98/6.38 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (not (@ (@ tptp.ord_less_rat X2) Y)))))
% 5.98/6.38 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (not (@ (@ tptp.ord_less_num X2) Y)))))
% 5.98/6.38 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (not (@ (@ tptp.ord_less_nat X2) Y)))))
% 5.98/6.38 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (not (@ (@ tptp.ord_less_int X2) Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv)))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (or (= Xa Mi3) (= Xa Ma3)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) Y) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) Y) (=> (=> (exists ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) Y) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (= Y (not (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (= Y (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s8217280938318005548T_VEBT (@ tptp.subseqs_VEBT_VEBT Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_o)) (= (@ tptp.size_s2710708370519433104list_o (@ tptp.subseqs_o Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_o Xs)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_s3023201423986296836st_nat (@ tptp.subseqs_nat Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_nat Xs)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_s533118279054570080st_int (@ tptp.subseqs_int Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_int Xs)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.re (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5074537144036343181t_real N))))
% 5.98/6.38 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 5.98/6.38 (assert (forall ((Y tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (= (@ tptp.re Y) tptp.zero_zero_real) (= (@ tptp.cos_real (@ tptp.arg Y)) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A6))) (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B7 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X3 tptp.list_nat)) (@ (@ tptp.member_list_nat X3) A6))) (lambda ((X3 tptp.list_nat)) (@ (@ tptp.member_list_nat X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B7)))))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B7 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X3 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B7)))))))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X3 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) A2)))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B7))))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B7))))))
% 5.98/6.38 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A6))) (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) B7))))))
% 5.98/6.38 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B7))))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B7))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 5.98/6.38 (assert (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 5.98/6.38 (assert (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 5.98/6.38 (assert (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 5.98/6.38 (assert (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 5.98/6.38 (assert (= (lambda ((H2 tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 5.98/6.38 (assert (forall ((C tptp.real)) (= (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C)) (@ tptp.times_times_real C))))
% 5.98/6.38 (assert (forall ((C tptp.rat)) (= (lambda ((X3 tptp.rat)) (@ (@ tptp.times_times_rat X3) C)) (@ tptp.times_times_rat C))))
% 5.98/6.38 (assert (forall ((C tptp.nat)) (= (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C)) (@ tptp.times_times_nat C))))
% 5.98/6.38 (assert (forall ((C tptp.int)) (= (lambda ((X3 tptp.int)) (@ (@ tptp.times_times_int X3) C)) (@ tptp.times_times_int C))))
% 5.98/6.38 (assert (forall ((C tptp.complex)) (= (lambda ((X3 tptp.complex)) (@ (@ tptp.times_times_complex X3) C)) (@ tptp.times_times_complex C))))
% 5.98/6.38 (assert (= (lambda ((X3 tptp.real)) X3) (@ tptp.times_times_real tptp.one_one_real)))
% 5.98/6.38 (assert (= (lambda ((X3 tptp.rat)) X3) (@ tptp.times_times_rat tptp.one_one_rat)))
% 5.98/6.38 (assert (= (lambda ((X3 tptp.nat)) X3) (@ tptp.times_times_nat tptp.one_one_nat)))
% 5.98/6.38 (assert (= (lambda ((X3 tptp.int)) X3) (@ tptp.times_times_int tptp.one_one_int)))
% 5.98/6.38 (assert (= (lambda ((X3 tptp.complex)) X3) (@ tptp.times_times_complex tptp.one_one_complex)))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 5.98/6.38 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 5.98/6.38 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 5.98/6.38 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 5.98/6.38 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 5.98/6.38 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 5.98/6.38 (assert (= tptp.times_times_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 5.98/6.38 (assert (= tptp.minus_minus_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 5.98/6.38 (assert (= tptp.divide_divide_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 5.98/6.38 (assert (= tptp.modulo_modulo_nat (lambda ((A4 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A4)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 5.98/6.38 (assert (= (@ tptp.re tptp.imaginary_unit) tptp.zero_zero_real))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X2)) (@ tptp.real_V1022390504157884413omplex X2))))
% 5.98/6.38 (assert (= (@ tptp.re tptp.zero_zero_complex) tptp.zero_zero_real))
% 5.98/6.38 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (= (@ tptp.re (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus_uminus_real (@ tptp.re X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_real (@ tptp.re X2)) (@ tptp.re Y)))))
% 5.98/6.38 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 5.98/6.38 (assert (= tptp.nat_set_decode (lambda ((X3 tptp.nat)) (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat _let_1) N4))))))))))
% 5.98/6.38 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A4 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N4))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A4))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N4)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))
% 5.98/6.38 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A4 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A4))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N4)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))))
% 5.98/6.38 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A4 tptp.rat) (N4 tptp.nat)) (@ (@ (@ tptp.if_rat (= N4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A4) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_rat)))))
% 5.98/6.38 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A4 tptp.real) (N4 tptp.nat)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A4) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_real)))))
% 5.98/6.38 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A4 tptp.int) (N4 tptp.nat)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A4) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_int)))))
% 5.98/6.38 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A4 tptp.complex) (N4 tptp.nat)) (@ (@ (@ tptp.if_complex (= N4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A4) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_complex)))))
% 5.98/6.38 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A4 tptp.code_integer) (N4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N4 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 5.98/6.38 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A4 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A4) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) tptp.one_one_nat)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 5.98/6.38 (assert (= tptp.gbinomial_rat (lambda ((A4 tptp.rat) (K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A4) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K2))))))
% 5.98/6.38 (assert (= tptp.gbinomial_real (lambda ((A4 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A4) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))
% 5.98/6.38 (assert (= tptp.gbinomial_complex (lambda ((A4 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A4) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 5.98/6.38 (assert (forall ((Uy2 tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList) S2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 5.98/6.38 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 5.98/6.38 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc2)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V2)) TreeList3) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V2)) TreeList3) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) Y) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A3) B2)) (= Y (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) Y) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy) (@ tptp.suc V2)) TreeList3) S3))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (not (or (= Xa Mi3) (= Xa Ma3))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))))))))
% 5.98/6.38 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 5.98/6.38 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 5.98/6.38 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 5.98/6.38 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 5.98/6.38 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (D tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.nth_nat Xs) I3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.minus_minus_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs) D)) D)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))
% 5.98/6.38 (assert (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 5.98/6.38 (assert (forall ((D tptp.nat) (Ys tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat D) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Ys) D))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat tptp.plus_plus_nat))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_nat (@ (@ tptp.nth_nat Xs) I3)) (@ (@ tptp.nth_nat Ys) I3)))) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ _let_1 Xs) C)) _let_2)) (@ (@ _let_1 Ys) D)))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri5044797733671781792omplex N)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((Z tptp.int)) (= (@ tptp.im (@ tptp.ring_17405671764205052669omplex Z)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((Z tptp.real)) (= (@ tptp.im (@ tptp.real_V4546457046886955230omplex Z)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) N)) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri8010041392384452111omplex N)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (R tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.re X2)) N)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X2) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X2) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (L tptp.list_real) (K tptp.list_real) (F (-> tptp.real tptp.real tptp.real)) (G (-> tptp.real tptp.real tptp.real))) (=> (= A B) (=> (= L K) (=> (forall ((A3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 L)) (= (@ (@ F X4) A3) (@ (@ G X4) A3)))) (= (@ (@ (@ tptp.foldr_real_real F) L) A) (@ (@ (@ tptp.foldr_real_real G) K) B)))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (L tptp.list_nat) (K tptp.list_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat tptp.nat))) (=> (= A B) (=> (= L K) (=> (forall ((A3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 L)) (= (@ (@ F X4) A3) (@ (@ G X4) A3)))) (= (@ (@ (@ tptp.foldr_nat_nat F) L) A) (@ (@ (@ tptp.foldr_nat_nat G) K) B)))))))
% 5.98/6.38 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 5.98/6.38 (assert (= (@ tptp.im tptp.zero_zero_complex) tptp.zero_zero_real))
% 5.98/6.38 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (= (@ tptp.im (@ tptp.uminus1482373934393186551omplex X2)) (@ tptp.uminus_uminus_real (@ tptp.im X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_real (@ tptp.im X2)) (@ tptp.im Y)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.ring_1_Ints_complex) (and (= (@ tptp.im Z) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= (@ tptp.re Z) (@ tptp.ring_1_of_int_real I4)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.real_V1022390504157884413omplex X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.re Y))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.im Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.re Z))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.re Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.abs_abs_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X2) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X2))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X2) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X2))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.im Y))))))
% 5.98/6.38 (assert (= tptp.uminus1482373934393186551omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real (@ tptp.re X3))) (@ tptp.uminus_uminus_real (@ tptp.im X3))))))
% 5.98/6.38 (assert (= tptp.plus_plus_complex (lambda ((X3 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X3)) (@ tptp.re Y2))) (@ (@ tptp.plus_plus_real (@ tptp.im X3)) (@ tptp.im Y2))))))
% 5.98/6.38 (assert (= tptp.minus_minus_complex (lambda ((X3 tptp.complex) (Y2 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X3)) (@ tptp.re Y2))) (@ (@ tptp.minus_minus_real (@ tptp.im X3)) (@ tptp.im Y2))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 5.98/6.38 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X2))))))
% 5.98/6.38 (assert (= tptp.times_times_complex (lambda ((X3 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.re Y2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X3)))) (let ((_let_3 (@ tptp.im Y2))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X3)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X2))) (@ tptp.im X2))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X2))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 5.98/6.38 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 5.98/6.38 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 5.98/6.38 (assert (= tptp.invers8013647133539491842omplex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X3))) (let ((_let_3 (@ tptp.re X3))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 5.98/6.38 (assert (= tptp.divide1717551699836669952omplex (lambda ((X3 tptp.complex) (Y2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y2))) (let ((_let_3 (@ tptp.re Y2))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X3)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X3)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.38 (assert (= tptp.groups1503878375050959669l_real (lambda ((F3 (-> tptp.real tptp.real)) (A4 tptp.real) (Xs3 tptp.list_real)) (@ (@ (@ tptp.foldr_real_real (lambda ((X3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real (@ F3 X3)) (@ (@ tptp.times_times_real A4) B3)))) Xs3) tptp.zero_zero_real))))
% 5.98/6.38 (assert (= tptp.groups7488368174851004413at_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.nat) (Xs3 tptp.list_nat)) (@ (@ (@ tptp.foldr_nat_nat (lambda ((X3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F3 X3)) (@ (@ tptp.times_times_nat A4) B3)))) Xs3) tptp.zero_zero_nat))))
% 5.98/6.38 (assert (= tptp.groups9116527308978886569_o_int (lambda ((F3 (-> Bool tptp.int)) (A4 tptp.int) (Xs3 tptp.list_o)) (@ (@ (@ tptp.foldr_o_int (lambda ((X3 Bool) (B3 tptp.int)) (@ (@ tptp.plus_plus_int (@ F3 X3)) (@ (@ tptp.times_times_int A4) B3)))) Xs3) tptp.zero_zero_int))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_list_VEBT_VEBT) (N tptp.nat)) (=> (forall ((X4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X4) (@ tptp.set_list_VEBT_VEBT2 Xs)) (= (@ tptp.size_s6755466524823107622T_VEBT X4) N))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs)) N)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_list_o) (N tptp.nat)) (=> (forall ((X4 tptp.list_o)) (=> (@ (@ tptp.member_list_o X4) (@ tptp.set_list_o2 Xs)) (= (@ tptp.size_size_list_o X4) N))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs)) N)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_list_nat) (N tptp.nat)) (=> (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) (@ tptp.set_list_nat2 Xs)) (= (@ tptp.size_size_list_nat X4) N))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_list_int) (N tptp.nat)) (=> (forall ((X4 tptp.list_int)) (=> (@ (@ tptp.member_list_int X4) (@ tptp.set_list_int2 Xs)) (= (@ tptp.size_size_list_int X4) N))) (= (@ tptp.size_size_list_int (@ tptp.concat_int Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s533118279054570080st_int Xs)) N)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_o) (F (-> Bool tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_o_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_nat_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_int_nat F) Xs)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C) D)) (@ (@ tptp.plus_plus_real (@ _let_1 D)) C)))))
% 5.98/6.38 (assert (= (@ tptp.map_nat_nat (lambda ((X3 tptp.nat)) X3)) (lambda ((Xs3 tptp.list_nat)) Xs3)))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (= (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Xs)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X3) (@ G X3)))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (= (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X3) (@ G X3)))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (G (-> tptp.nat tptp.nat))) (= (= (@ (@ tptp.map_nat_nat F) Xs) (@ (@ tptp.map_nat_nat G) Xs)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (= (@ F X3) (@ G X3)))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.38 (assert (forall ((F (-> Bool tptp.vEBT_VEBT)) (Xs tptp.list_o)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_o_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_o Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.vEBT_VEBT)) (Xs tptp.list_nat)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_nat_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_nat Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.int tptp.vEBT_VEBT)) (Xs tptp.list_int)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.map_int_VEBT_VEBT F) Xs)) (@ tptp.size_size_list_int Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_VEBT_VEBT_o F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.38 (assert (forall ((F (-> Bool Bool)) (Xs tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_o_o F) Xs)) (@ tptp.size_size_list_o Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat Bool)) (Xs tptp.list_nat)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_nat_o F) Xs)) (@ tptp.size_size_list_nat Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.int Bool)) (Xs tptp.list_int)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_int_o F) Xs)) (@ tptp.size_size_list_int Xs))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_nat (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_VEBT_VEBT_int F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (F (-> Bool tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_o_VEBT_VEBT F) Xs)) N) (@ F (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (F (-> Bool tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_o_nat F) Xs)) N) (@ F (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (F (-> Bool tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_o_int F) Xs)) N) (@ F (@ (@ tptp.nth_o Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F (-> tptp.nat tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_nat_VEBT_VEBT F) Xs)) N) (@ F (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_nat_int F) Xs)) N) (@ F (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_nat_nat F) Xs)) N) (@ F (@ (@ tptp.nth_nat Xs) N))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N4)))) (@ F tptp.zero_zero_nat))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N4)))) (@ F tptp.zero_zero_nat))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> Bool tptp.real)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_o_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_o Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> Bool tptp.nat)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_o_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_o Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.real)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_nat_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_nat Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_nat_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_nat Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.int tptp.real)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_int_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_int Ys)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (G (-> tptp.int tptp.nat)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_int_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_size_list_int Ys)))))
% 5.98/6.38 (assert (forall ((F (-> Bool tptp.real)) (Xs tptp.list_o) (G (-> tptp.vEBT_VEBT tptp.real)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_o_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Ys)) (= (@ tptp.size_size_list_o Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.38 (assert (forall ((F (-> Bool tptp.nat)) (Xs tptp.list_o) (G (-> tptp.vEBT_VEBT tptp.nat)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_o_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys)) (= (@ tptp.size_size_list_o Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 5.98/6.38 (assert (forall ((Ys tptp.list_real) (F (-> tptp.vEBT_VEBT tptp.real))) (= (exists ((Xs3 tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_real F) Xs3))) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Ys)) (exists ((Y2 tptp.vEBT_VEBT)) (= X3 (@ F Y2))))))))
% 5.98/6.38 (assert (forall ((Ys tptp.list_nat) (F (-> tptp.vEBT_VEBT tptp.nat))) (= (exists ((Xs3 tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_nat F) Xs3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (exists ((Y2 tptp.vEBT_VEBT)) (= X3 (@ F Y2))))))))
% 5.98/6.38 (assert (forall ((Ys tptp.list_nat) (F (-> tptp.nat tptp.nat))) (= (exists ((Xs3 tptp.list_nat)) (= Ys (@ (@ tptp.map_nat_nat F) Xs3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (exists ((Y2 tptp.nat)) (= X3 (@ F Y2))))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= Xs Ys) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Ys))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= Xs Ys) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= Xs Ys) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Ys)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_nat_nat F) Xs) (@ (@ tptp.map_nat_nat G) Ys))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_real_real F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_complex) (F (-> tptp.complex tptp.complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_complex_complex F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_set_nat) (F (-> tptp.set_nat tptp.set_nat))) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_set_nat_set_nat F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_nat_nat F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (= (@ F X4) X4))) (= (@ (@ tptp.map_int_int F) Xs) Xs))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs) (@ (@ tptp.map_VEBT_VEBT_real G) Xs)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= (@ F X4) (@ G X4)))) (= (@ (@ tptp.map_nat_nat F) Xs) (@ (@ tptp.map_nat_nat G) Xs)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Xa tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Fa (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z3 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X2)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real Fa) Xa)) (= X2 Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Xa tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Fa (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z3 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X2)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat Fa) Xa)) (= X2 Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Xa tptp.list_nat) (F (-> tptp.nat tptp.nat)) (Fa (-> tptp.nat tptp.nat))) (=> (forall ((Z3 tptp.nat) (Za tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X2)) (=> (@ (@ tptp.member_nat Za) (@ tptp.set_nat2 Xa)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_nat_nat F) X2) (@ (@ tptp.map_nat_nat Fa) Xa)) (= X2 Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X2)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real G) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X2)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat G) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X2)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_nat F) X2) (@ (@ tptp.map_nat_nat G) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= X2 Ya) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X2) (@ (@ tptp.map_VEBT_VEBT_real G) Ya))))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= X2 Ya) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X2) (@ (@ tptp.map_VEBT_VEBT_nat G) Ya))))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Ya tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= X2 Ya) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_nat F) X2) (@ (@ tptp.map_nat_nat G) Ya))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs tptp.list_list_VEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_real F))) (= (@ _let_1 (@ tptp.concat_VEBT_VEBT Xs)) (@ tptp.concat_real (@ (@ tptp.map_li2470829856544091186t_real _let_1) Xs))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_list_VEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_nat F))) (= (@ _let_1 (@ tptp.concat_VEBT_VEBT Xs)) (@ tptp.concat_nat (@ (@ tptp.map_li576258494306137302st_nat _let_1) Xs))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_list_nat)) (let ((_let_1 (@ tptp.map_nat_nat F))) (= (@ _let_1 (@ tptp.concat_nat Xs)) (@ tptp.concat_nat (@ (@ tptp.map_li7225945977422193158st_nat _let_1) Xs))))))
% 5.98/6.38 (assert (forall ((T tptp.list_nat)) (= (@ (@ tptp.map_nat_nat (lambda ((X3 tptp.nat)) X3)) T) T)))
% 5.98/6.38 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 5.98/6.38 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) tptp.na))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) tptp.treeList)) tptp.zero_zero_real)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real _let_2) tptp.c))))))
% 5.98/6.38 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 5.98/6.38 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 5.98/6.38 (assert (= (@ tptp.suminf_complex (lambda ((N4 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 5.98/6.38 (assert (= (@ tptp.suminf_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 5.98/6.38 (assert (= (@ tptp.suminf_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 5.98/6.38 (assert (= (@ tptp.suminf_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X2) Y) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3)) (not (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary3))) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList3)) tptp.zero_zero_nat)))))))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (C tptp.real) (G (-> tptp.vEBT_VEBT tptp.real)) (D tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real G) Xs)) tptp.zero_zero_real))) D))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (C tptp.real) (G (-> tptp.nat tptp.real)) (D tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_nat_real F) Xs)) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_nat_real G) Xs)) tptp.zero_zero_real))) D))))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.real)) (C tptp.real) (G (-> tptp.int tptp.real)) (D tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ (@ tptp.times_times_real C) (@ G X4))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_int_real F) Xs)) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_int_real G) Xs)) tptp.zero_zero_real))) D))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs tptp.list_VEBT_VEBT) (C tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs)) C)) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real (lambda ((X3 tptp.vEBT_VEBT)) (@ tptp.semiri5074537144036343181t_real (@ F X3)))) Xs)) (@ tptp.semiri5074537144036343181t_real C)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (C tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_nat_nat F) Xs)) C)) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real (lambda ((X3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X3)))) Xs)) (@ tptp.semiri5074537144036343181t_real C)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_s6755466524823107622T_VEBT Xs))) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_o) (F (-> Bool tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_o_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_o Xs))) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_nat Xs))) Bound)) I)))))
% 5.98/6.38 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_real (@ F X4)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_int_real F) Xs)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_int Xs))) Bound)) I)))))
% 5.98/6.38 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_VEBT_space T)) (@ tptp.vEBT_VEBT_space2 T))))
% 5.98/6.38 (assert (= tptp.product_int_int (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (@ tptp.concat4512918505337516154nt_int (@ (@ tptp.map_in7266296235447420877nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.map_in7157766398909135175nt_int (@ tptp.product_Pair_int_int X3)) Ys3))) Xs3)))))
% 5.98/6.38 (assert (= tptp.produc4846348955484107138nteger (lambda ((Xs3 tptp.list_C878401137130745250e_term) (Ys3 tptp.list_P5578671422887162913nteger)) (@ tptp.concat5449216342283422845nteger (@ (@ tptp.map_Co3516991824712006758nteger (lambda ((X3 (-> tptp.code_integer tptp.option6357759511663192854e_term))) (@ (@ tptp.map_Pr6982716525268357333nteger (@ tptp.produc6137756002093451184nteger X3)) Ys3))) Xs3)))))
% 5.98/6.38 (assert (= tptp.produc2929234284598166170nteger (lambda ((Xs3 tptp.list_P1316552470764441098e_term) (Ys3 tptp.list_P5578671422887162913nteger)) (@ tptp.concat1359917873574114197nteger (@ (@ tptp.map_Pr1383036205076807398nteger (lambda ((X3 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term))) (@ (@ tptp.map_Pr4561634935768196077nteger (@ tptp.produc8603105652947943368nteger X3)) Ys3))) Xs3)))))
% 5.98/6.38 (assert (= tptp.produc8640348060098379399nt_int (lambda ((Xs3 tptp.list_P1743416141875011707e_term) (Ys3 tptp.list_P5707943133018811711nt_int)) (@ tptp.concat27718206033014914nt_int (@ (@ tptp.map_Pr6227401909088194244nt_int (lambda ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term))) (@ (@ tptp.map_Pr1898935522916328184nt_int (@ tptp.produc5700946648718959541nt_int X3)) Ys3))) Xs3)))))
% 5.98/6.38 (assert (= tptp.produc5707002291657922193nt_int (lambda ((Xs3 tptp.list_i8448526496819171953e_term) (Ys3 tptp.list_P5707943133018811711nt_int)) (@ tptp.concat3620511419746071180nt_int (@ (@ tptp.map_in2673801078721063236nt_int (lambda ((X3 (-> tptp.int tptp.option6357759511663192854e_term))) (@ (@ tptp.map_Pr1306541819098601986nt_int (@ tptp.produc4305682042979456191nt_int X3)) Ys3))) Xs3)))))
% 5.98/6.38 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList)) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X2) Y) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y tptp.one_one_real))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3)) (not (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary3))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList3)) tptp.zero_zero_real)))))))))))
% 5.98/6.38 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_space (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 5.98/6.38 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_space (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary))) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList)) tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X2) Y) (=> (=> (exists ((A3 Bool) (B2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A3) B2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3)) (not (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary3))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList3)) tptp.zero_zero_nat)))))))))))
% 5.98/6.38 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_space2 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList)) tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X2 _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X2)) I))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (X2 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X2) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X2 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) N)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X2)) N)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X2)) N)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X2)) N)))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.replicate_nat N))) (= (@ (@ tptp.map_nat_nat F) (@ _let_1 X2)) (@ _let_1 (@ F X2))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_real F) (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.replicate_real N) (@ F X2)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_nat F) (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.replicate_nat N) (@ F X2)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.replicate_VEBT_VEBT N))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) (@ _let_1 X2)) (@ _let_1 (@ F X2))))))
% 5.98/6.38 (assert (@ tptp.summable_complex (lambda ((N4 tptp.nat)) tptp.zero_zero_complex)))
% 5.98/6.38 (assert (@ tptp.summable_real (lambda ((N4 tptp.nat)) tptp.zero_zero_real)))
% 5.98/6.38 (assert (@ tptp.summable_nat (lambda ((N4 tptp.nat)) tptp.zero_zero_nat)))
% 5.98/6.38 (assert (@ tptp.summable_int (lambda ((N4 tptp.nat)) tptp.zero_zero_int)))
% 5.98/6.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I)) (@ F R5)) tptp.zero_zero_complex)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I)) (@ F R5)) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I)) (@ F R5)) tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I)) (@ F R5)) tptp.zero_zero_int)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N4) K)))) (@ tptp.summable_real F))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.set_nat) (N tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X2 Y) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I) X2))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X2)) I) X2))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I) X2))))
% 5.98/6.38 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N4)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 5.98/6.38 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N4)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N4)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N4)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 5.98/6.38 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 5.98/6.38 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N4 tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ F N4)))) (@ tptp.summable_complex F))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 5.98/6.38 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_space2 (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (forall ((Va3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va3)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 5.98/6.38 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.sin_real X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 5.98/6.38 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R))))))
% 5.98/6.38 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X2) (and (= X2 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 5.98/6.38 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= X2 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X2 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 5.98/6.38 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.real_V2521375963428798218omplex) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_complex (@ (@ tptp.complex2 X2) tptp.zero_zero_real)) tptp.real_V2521375963428798218omplex)))
% 5.98/6.38 (assert (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N4)))) tptp.one_one_real))
% 5.98/6.38 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) X2))))
% 5.98/6.38 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N4)) (@ F (@ (@ tptp.divide_divide_nat N4) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y))))))
% 5.98/6.38 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.cos_real X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi3) (= Xa Ma3))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va2) Vb))) (=> (= X2 _let_1) (=> (= Y (or (= Xa Mi3) (= Xa Ma3))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X2 _let_2) (=> (= Y (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X2 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList3) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A3) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList3) S3))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa)) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y (and (=> _let_3 A3) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList3) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X2 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))
% 5.98/6.38 (assert (= (@ tptp.diffs_real tptp.cos_coeff) (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N4)))))
% 5.98/6.38 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 5.98/6.38 (assert (forall ((R tptp.real) (X2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R) X2)) (@ (@ tptp.times_times_real R) (@ tptp.re X2)))))
% 5.98/6.38 (assert (forall ((R tptp.real) (X2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R) X2)) (@ (@ tptp.times_times_real R) (@ tptp.im X2)))))
% 5.98/6.38 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.real_V2046097035970521341omplex R) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 5.98/6.38 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X3))) (@ _let_1 (@ tptp.im X3)))))))
% 5.98/6.38 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A4 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A4) (@ (@ tptp.ord_less_eq_real A4) tptp.pi))))))))
% 5.98/6.38 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X2) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3))) (=> (= X2 _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary3))) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList3)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X2) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3))) (=> (= X2 _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary3))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList3)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X2) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) X2) (=> (forall ((A3 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A3) B2))) (=> (= X2 _let_1) (=> (= Y tptp.one_one_real) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList3) Summary3))) (=> (= X2 _let_1) (=> (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary3))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList3)) tptp.zero_zero_real))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 5.98/6.38 (assert (forall ((R tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R) K2)) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R) N))) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R) K2))))) (@ tptp.set_ord_atMost_nat R)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 5.98/6.38 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N4 tptp.nat)) N4)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) tptp.zero_zero_complex))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M3)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 5.98/6.38 (assert (forall ((H tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B8 tptp.real)) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M3)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D2))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.38 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P X) (@ Q X)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D4))))) (forall ((X tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P X) (@ Q X)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T))))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (= (exists ((X5 tptp.int)) (@ P X5)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X3))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) D4)) T))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.plus_plus_int X) D4) T)))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X T) (= (@ (@ tptp.plus_plus_int X) D4) T))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X T)) (not (= (@ (@ tptp.minus_minus_int X) D4) T)))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X T) (= (@ (@ tptp.minus_minus_int X) D4) T))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.plus_plus_int X) D4)))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X) D4)) T))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.minus_minus_int X) D4))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X) D4)) T)))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z2) (= (@ P X4) (@ P6 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) B4) (@ P (@ (@ tptp.plus_plus_int Y2) X3))))))))))))))
% 5.98/6.38 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z2 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X4) (= (@ P X4) (@ P6 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int Y2) A2) (@ P (@ (@ tptp.minus_minus_int Y2) X3))))))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 5.98/6.38 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.38 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.38 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.98/6.38 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N4)) N4))))))
% 5.98/6.38 (assert (= tptp.arctan (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y2))))))))
% 5.98/6.38 (assert (= tptp.arcsin (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y2))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 5.98/6.38 (assert (= (@ tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X2)) (@ tptp.cnj Y)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X2)) (@ tptp.cnj Y)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ tptp.cnj _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.cnj Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.complex2 A))) (= (@ tptp.cnj (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 5.98/6.38 (assert (forall ((T tptp.real)) (= (@ tptp.cnj (@ tptp.cis T)) (@ tptp.cis (@ tptp.uminus_uminus_real T)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X2) (@ tptp.the_real (lambda ((X3 tptp.real)) false))))))
% 5.98/6.38 (assert (= tptp.cnj (lambda ((Z5 tptp.complex)) (@ (@ tptp.complex2 (@ tptp.re Z5)) (@ tptp.uminus_uminus_real (@ tptp.im Z5))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 5.98/6.38 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (= tptp.arccos (lambda ((Y2 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y2)))))))
% 5.98/6.38 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 5.98/6.38 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M3) N4)) (@ (@ tptp.modulo_modulo_nat M3) N4)))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 5.98/6.38 (assert (= tptp.divide1717551699836669952omplex (lambda ((A4 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A4) (@ tptp.cnj B3))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 5.98/6.38 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 5.98/6.38 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real))))))
% 5.98/6.38 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real)))))))
% 5.98/6.38 (assert (= tptp.int_ge_less_than2 (lambda ((D3 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D3) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 5.98/6.38 (assert (= tptp.int_ge_less_than (lambda ((D3 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D3) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 5.98/6.38 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 5.98/6.38 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N4) (@ tptp.suc M3))))))
% 5.98/6.38 (assert (= tptp.set_ord_lessThan_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N4)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 5.98/6.38 (assert (= tptp.set_ord_atMost_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N4))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 5.98/6.38 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J2) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)) (@ (@ P I3) J2)))) (@ (@ P A0) A12)))))
% 5.98/6.38 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 5.98/6.38 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 5.98/6.38 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J3)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 5.98/6.38 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J2))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 5.98/6.38 (assert (= tptp.code_T6385005292777649522of_nat tptp.semiri1314217659103216013at_int))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 5.98/6.38 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 5.98/6.38 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 5.98/6.38 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 5.98/6.38 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 5.98/6.38 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (@ tptp.uminus1351360451143612070nteger L))))
% 5.98/6.38 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 5.98/6.38 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.38 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.38 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 5.98/6.38 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 5.98/6.38 (assert (forall ((X2 tptp.produc8763457246119570046nteger)) (not (forall ((F2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D2 tptp.code_integer) (I3 tptp.code_integer)) (not (= X2 (@ (@ tptp.produc6137756002093451184nteger F2) (@ (@ tptp.produc1086072967326762835nteger D2) I3))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.produc1908205239877642774nteger)) (not (forall ((F2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D2 tptp.code_integer) (I3 tptp.code_integer)) (not (= X2 (@ (@ tptp.produc8603105652947943368nteger F2) (@ (@ tptp.produc1086072967326762835nteger D2) I3))))))))
% 5.98/6.38 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.38 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 5.98/6.38 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 5.98/6.38 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 5.98/6.38 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 5.98/6.38 (assert (= tptp.one_one_int tptp.one_one_int))
% 5.98/6.38 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N))))))
% 5.98/6.38 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 5.98/6.38 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 5.98/6.38 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K2)) K2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int X2)))))
% 5.98/6.38 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.98/6.38 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa) X2)))))
% 5.98/6.38 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 5.98/6.38 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa) X2)))))
% 5.98/6.38 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa) X2)))))
% 5.98/6.38 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 5.98/6.38 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_eq_int Xa) X2))))
% 5.98/6.38 (assert (forall ((Xa tptp.int) (X2 tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa) X2)))))
% 5.98/6.38 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 5.98/6.38 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 5.98/6.38 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 5.98/6.38 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 5.98/6.38 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 5.98/6.38 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.code_int_of_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.semiri1314217659103216013at_int N))))
% 5.98/6.38 (assert (= (@ tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X2) Xa)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger X2)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer X2)))))
% 5.98/6.38 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X2) Xa)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X2) Xa)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa)))))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X2) Xa)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa)))))
% 5.98/6.38 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X3 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa4)))))
% 5.98/6.38 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K2)) (@ tptp.code_int_of_integer L2)))))
% 5.98/6.38 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K2) L2)) (@ (@ tptp.modulo364778990260209775nteger K2) L2)))))
% 5.98/6.38 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 5.98/6.38 (assert (= tptp.code_divmod_abs (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.code_nat_of_integer (@ tptp.semiri4939895301339042750nteger N)) N)))
% 5.98/6.38 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 5.98/6.38 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 5.98/6.38 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 5.98/6.38 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 5.98/6.38 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))))
% 5.98/6.38 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S4)))))) _let_1))))))))))))
% 5.98/6.38 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.98/6.38 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (and (@ _let_1 K) (@ _let_1 L))))))
% 5.98/6.38 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 5.98/6.38 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 5.98/6.38 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)) (@ (@ tptp.plus_plus_int X2) Y))))
% 5.98/6.38 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 5.98/6.38 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 5.98/6.38 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) L2)))))
% 5.98/6.38 (assert (= tptp.bit_concat_bit (lambda ((N4 tptp.nat) (K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N4) K2)) (@ (@ tptp.bit_se545348938243370406it_int N4) L2)))))
% 5.98/6.38 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)) _let_1)))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 5.98/6.38 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 5.98/6.38 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 5.98/6.38 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 5.98/6.38 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 5.98/6.38 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))))))))))))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 5.98/6.38 (assert (= tptp.archim6058952711729229775r_real (lambda ((X3 tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 5.98/6.38 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X2 _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X2 _let_1) (=> (= Xa tptp.one) (=> (= Y tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 5.98/6.38 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.98/6.38 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X3 tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 5.98/6.38 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 5.98/6.38 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 5.98/6.38 (assert (forall ((K tptp.code_integer)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.code_nat_of_integer K)) (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) K))))
% 5.98/6.38 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 5.98/6.38 (assert (= tptp.abs_abs_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A4) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A4)) A4))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y2 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y2) (= X3 Y2)))))
% 5.98/6.38 (assert (= tptp.sgn_sgn_rat (lambda ((A4 tptp.rat)) (@ (@ (@ tptp.if_rat (= A4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.98/6.38 (assert (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R (@ (@ tptp.plus_plus_rat S3) T3)))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M5)))) M)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M5) N)))) M)))))
% 5.98/6.38 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A4)) B3)) (@ tptp.abs_abs_int A4))))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((Q2 tptp.int) (P4 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P4)) (@ tptp.uminus_uminus_int Q2)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X2) Xa)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 5.98/6.38 (assert (forall ((P4 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 5.98/6.38 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.38 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 5.98/6.38 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 5.98/6.38 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) D3)) (@ (@ tptp.times_times_int C2) B3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A4) B3)) (@ (@ tptp.times_times_int C2) D3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((R tptp.rat) (N tptp.int) (D tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int N) D)) (= R (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D))))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A4) D3)) (@ (@ tptp.times_times_int B3) C2))) (@ (@ tptp.times_times_int C2) D3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P4) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B3 tptp.int) (D3 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A4) D3)) (@ (@ tptp.times_times_int B3) C2))) (@ (@ tptp.times_times_int C2) D3))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((R tptp.rat) (P4 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A4)) __flatten_var_0))) (@ tptp.quotient_of P4)))))
% 5.98/6.38 (assert (forall ((R tptp.product_prod_int_int) (P4 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R) (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 5.98/6.38 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P4 tptp.int) (R tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R) S2))) (= (@ (@ tptp.times_times_int P4) S2) (@ (@ tptp.times_times_int R) Q2)))))))
% 5.98/6.38 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P5 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P5)))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A4 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B3 tptp.int) (D3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A4) D3)) (@ (@ tptp.times_times_int C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 5.98/6.38 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K2)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K2) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X2) Xa)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 5.98/6.38 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.bezw X2) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 5.98/6.38 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L)))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 5.98/6.38 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N8) (@ (@ tptp.ord_less_eq_nat X3) M3)))))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N2) (@ (@ tptp.ord_less_nat X4) N))) (@ tptp.finite_finite_nat N2))))
% 5.98/6.38 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N8) (@ (@ tptp.ord_less_nat X3) M3)))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) U)))))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B4) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B4)) (= A2 B4))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D3) M)))))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N2))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N2))))
% 5.98/6.38 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 5.98/6.38 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 5.98/6.38 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K))))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_nat N4) K))))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))))))
% 5.98/6.38 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 5.98/6.38 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D3 tptp.int)) (@ (@ tptp.dvd_dvd_int D3) I)))))))
% 5.98/6.38 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K2))))))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.set_ord_lessThan_nat K3))))))
% 5.98/6.38 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K2))))))
% 5.98/6.38 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M3 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M3) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S)))))))
% 5.98/6.38 (assert (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N6) (@ (@ tptp.member_nat N6) S))))) (not (@ tptp.finite_finite_nat S)))))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N4) (@ (@ tptp.member_nat N4) S)))))))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M3 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N4) (@ (@ tptp.member_nat N4) S)))))))
% 5.98/6.38 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X2) tptp.zero_zero_real)))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X2) (@ _let_1 Y)) (= X2 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X2) Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.inverse_inverse_real (@ _let_1 X2))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X2)) (@ _let_2 (@ _let_1 X2)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N) X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X2)) (@ tptp.sgn_sgn_real X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X2)) (@ (@ tptp.root N) X2)))))))
% 5.98/6.38 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X2))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N2) X2))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X2)) (@ (@ tptp.root N) X2)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X2) (= (@ (@ tptp.root N) X2) Y))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y) N) X2) (= (@ (@ tptp.root N) X2) Y)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N2) X2))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (B tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X2)))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N) X2)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y2 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N)) X2) (@ P Y2))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 5.98/6.38 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 5.98/6.38 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N2))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N2)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N2))))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N2))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) N2))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 5.98/6.38 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N2)) N))))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) S))))
% 5.98/6.38 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) C)))) N)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N) tptp.one_one_complex)))) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 5.98/6.38 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 5.98/6.38 (assert (forall ((Ns tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.nth_nat Ns) I))))))
% 5.98/6.38 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 5.98/6.38 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 5.98/6.38 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 5.98/6.38 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L3)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L3) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))) (@ (@ P K3) L3)))))) (@ (@ P A0) A12)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 5.98/6.38 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.98/6.38 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.98/6.38 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 5.98/6.38 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.98/6.38 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 5.98/6.38 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 5.98/6.38 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K2 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K7) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N4))) (= (@ tptp.finite_card_nat K7) K2))))))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 5.98/6.38 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 5.98/6.38 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 5.98/6.38 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 5.98/6.38 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.38 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L)) (@ (@ tptp.modulo364778990260209775nteger K) L))))
% 5.98/6.38 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 5.98/6.38 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R)))))
% 5.98/6.38 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X2) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X2) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y)))))))))))
% 5.98/6.38 (assert (= tptp.bezw (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X3) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y2 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X3) Y2)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X2) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa))))))))))))))
% 5.98/6.38 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.98/6.38 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P4)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P4)))) tptp.one_one_int))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X2) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa)))))))) (not _let_1)))))))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 5.98/6.38 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))))
% 5.98/6.38 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 5.98/6.38 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X2)) Y) (@ (@ tptp.gcd_gcd_int X2) Y))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.gcd_gcd_int X2))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 5.98/6.38 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 5.98/6.38 (assert (forall ((N tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X2) (@ (@ tptp.gcd_gcd_int _let_1) X2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X2))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int tptp.zero_zero_int) X2) (@ tptp.abs_abs_int X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int X2) tptp.zero_zero_int) (@ tptp.abs_abs_int X2))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X2) Y))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.gcd_gcd_int Y2) (@ (@ tptp.modulo_modulo_int X3) Y2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (exists ((U2 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U2) X2)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X2) Y)))))
% 5.98/6.38 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 5.98/6.38 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X2))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X2)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X2))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 5.98/6.38 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 5.98/6.38 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X2) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X2) Y))))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.gcd_gcd_int L2) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L2))))))))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R4 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R4) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R4 N6)) S))))))))
% 5.98/6.38 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K2) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L2)) S4)))))) _let_1))))))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.gcd_gcd_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.gcd_gcd_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 5.98/6.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X2) tptp.zero_zero_nat) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X2) X2)))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 5.98/6.38 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.gcd_gcd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat M) N)))))
% 5.98/6.38 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ tptp.nat2 (@ (@ tptp.gcd_gcd_int K) (@ tptp.semiri1314217659103216013at_int N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.gcd_gcd_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ (@ tptp.gcd_gcd_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa) Y) (and (=> _let_1 (= Y X2)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X2) Xa)))))))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y2 tptp.zero_zero_nat)) X3) (@ (@ tptp.gcd_gcd_nat Y2) (@ (@ tptp.modulo_modulo_nat X3) Y2))))))
% 5.98/6.38 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X2) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X2) Y))))))
% 5.98/6.38 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y2) (@ (@ tptp.modulo_modulo_nat X3) Y2)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X4))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X4))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L2 tptp.zero_z3403309356797280102nteger)) K2) (@ (@ tptp.gcd_gcd_Code_integer L2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K2)) (@ tptp.abs_abs_Code_integer L2))))))))
% 5.98/6.38 (assert (= tptp.gcd_gcd_int (lambda ((X3 tptp.int) (Y2 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat (@ tptp.nat2 (@ tptp.abs_abs_int X3))) (@ tptp.nat2 (@ tptp.abs_abs_int Y2)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X2) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X2) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X2))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I2) (@ P I2))) (@ P K3)))) (@ P M)))))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X2)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X2) Xa))))) (not _let_1)))))))))
% 5.98/6.38 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 5.98/6.38 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 5.98/6.38 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 5.98/6.38 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X2)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 5.98/6.38 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) M3)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 5.98/6.38 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y2) X3))) (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.ord_less_nat Y2) X3))))
% 5.98/6.38 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N4) (not (= M3 N4))))))
% 5.98/6.38 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.98/6.38 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 5.98/6.38 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 5.98/6.38 (assert (forall ((Xa tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y2))) (let ((_let_2 (@ tptp.times_times_nat X3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))) Xa) X2)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 5.98/6.38 (assert (forall ((Z tptp.int)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X4) Y3))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X2)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X2))))
% 5.98/6.38 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 5.98/6.38 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X3))) X2)))))
% 5.98/6.38 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 5.98/6.38 (assert (forall ((Xa tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U3) Y2)))) __flatten_var_0))) Xa) X2))))
% 5.98/6.38 (assert (forall ((Xa tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U3) Y2)))) __flatten_var_0))) Xa) X2))))
% 5.98/6.38 (assert (forall ((Xa tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) U3)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))) Xa) X2)))))
% 5.98/6.38 (assert (forall ((Xa tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat Y2) U3)))) __flatten_var_0))) Xa) X2)))))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N2) (= (@ tptp.gcd_Gcd_nat N2) tptp.one_one_nat))))
% 5.98/6.38 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y2) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 5.98/6.38 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y2 tptp.nat) (Z5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y2) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 5.98/6.38 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 5.98/6.38 (assert (= tptp.nat2 (lambda ((X3 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X3)))))
% 5.98/6.38 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y2) X3))))))
% 5.98/6.38 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y2))) (let ((_let_2 (@ tptp.times_times_nat X3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))))))
% 5.98/6.38 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat Y2) U3)))) __flatten_var_0))))))
% 5.98/6.38 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y2 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) U3)) (@ (@ tptp.plus_plus_nat Y2) V4)))) __flatten_var_0))))))
% 5.98/6.38 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N4))) M3)))))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (= (@ tptp.nat_prod_encode X2) (@ tptp.nat_prod_encode Y)) (= X2 Y))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 5.98/6.38 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 5.98/6.38 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 5.98/6.38 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 5.98/6.38 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) (@ tptp.suc M3))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 5.98/6.38 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 5.98/6.38 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 5.98/6.38 (assert (= tptp.num_of_nat (@ (@ tptp.comp_C2179886998970519596um_nat tptp.code_num_of_integer) tptp.semiri4939895301339042750nteger)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 5.98/6.38 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M3 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M3)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X2)))))
% 5.98/6.38 (assert (= tptp.sqr (lambda ((X3 tptp.num)) (@ (@ tptp.times_times_num X3) X3))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 5.98/6.38 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 5.98/6.38 (assert (forall ((C tptp.nat) (Y tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat) (N2 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N2) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N2))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I)) (@ tptp.suc J)))))
% 5.98/6.38 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 5.98/6.38 (assert (forall ((N2 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N2)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N2)))))
% 5.98/6.38 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_lessThan_int K2))))))
% 5.98/6.38 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K2))))))
% 5.98/6.38 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.38 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.38 (assert (= tptp.comple4887499456419720421f_real (lambda ((X5 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X5))))))
% 5.98/6.38 (assert (= tptp.complete_Inf_Inf_int (lambda ((X5 tptp.set_int)) (@ tptp.uminus_uminus_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int tptp.uminus_uminus_int) X5))))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.38 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I3))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I4)))) tptp.top_top_set_nat)))))))
% 5.98/6.38 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 5.98/6.38 (assert (= tptp.gcd_Gcd_int (lambda ((K7 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K7))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 5.98/6.38 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 5.98/6.38 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 5.98/6.38 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 5.98/6.38 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 5.98/6.38 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))))
% 5.98/6.38 (assert (@ (@ (@ tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 5.98/6.38 (assert (= (@ (@ tptp.image_2486076414777270412at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 5.98/6.38 (assert (= tptp.root (lambda ((N4 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.if_real (= N4 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y2)) N4)))) X3)))))
% 5.98/6.38 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 5.98/6.38 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 5.98/6.38 (assert (forall ((X1 Bool) (X23 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X23) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 5.98/6.38 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 5.98/6.38 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 5.98/6.38 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 5.98/6.38 (assert (forall ((X1 Bool) (X23 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X23) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 5.98/6.38 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat)) (=> (not (= X2 tptp.nil_nat)) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (not (= X2 (@ (@ tptp.cons_nat X4) Xs2))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X2) Xs)) (and (@ (@ tptp.ord_less_nat I) J) (= I X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs)))))
% 5.98/6.38 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y) (=> (=> (= X2 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X4) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs2)))))))))))))
% 5.98/6.38 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 5.98/6.38 (assert (@ (@ (@ tptp.bij_be8532844293280997160at_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (= (= (@ tptp.nat_list_encode X2) (@ tptp.nat_list_encode Y)) (= X2 Y))))
% 5.98/6.38 (assert (= (@ (@ tptp.image_list_nat_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 5.98/6.38 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X2) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X2) (@ tptp.nat_list_encode Xs)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X4) Xs2))) (=> (= X2 _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 5.98/6.38 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 5.98/6.38 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 5.98/6.38 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 5.98/6.38 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X2) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X2) Xa))) (=> (= (@ (@ tptp.upto X2) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 5.98/6.38 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 5.98/6.38 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 5.98/6.38 (assert (forall ((I tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I) J)) K) _let_1)))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I)) tptp.one_one_int)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 5.98/6.38 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J3)) __flatten_var_0))))
% 5.98/6.38 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J3) tptp.nil_int))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 5.98/6.38 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J3)))))
% 5.98/6.38 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 5.98/6.38 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 5.98/6.38 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X2) Xa))) (=> (= (@ (@ tptp.upto X2) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 5.98/6.38 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ (@ tptp.upto I) J) (@ (@ tptp.cons_int I) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I) tptp.one_one_int)) J))))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 5.98/6.38 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 5.98/6.38 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I))) (=> (@ (@ tptp.ord_less_eq_int I) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 5.98/6.38 (assert (forall ((R tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) tptp.one) (@ tptp.some_num tptp.one))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 5.98/6.38 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M)))))
% 5.98/6.38 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N4) M)))) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N4 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N4) M))))) N))))
% 5.98/6.38 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 5.98/6.38 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 5.98/6.38 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 5.98/6.38 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 5.98/6.38 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 5.98/6.38 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 5.98/6.38 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 5.98/6.38 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M3 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A4 tptp.nat) (X3 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X3))) A4))) (@ (@ tptp.product_Pair_nat_num N4) M3)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z3)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X2)))) (= L tptp.zero_zero_real))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X2) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X2) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (= (@ F X2) (@ F Y)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (= (@ F X2) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X2) H3))) (@ F X2)))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.minus_minus_real X2) H3))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H3))) (@ F X2)))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((H3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H3) (=> (@ (@ tptp.ord_less_real H3) D2) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H3))))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S2))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (Y tptp.real) (X2 tptp.real)) (= (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y) (@ (@ tptp.topolo2177554685111907308n_real (@ tptp.uminus_uminus_real X2)) tptp.top_top_set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ F (@ tptp.uminus_uminus_real X3)))) (@ tptp.uminus_uminus_real Y)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (Y tptp.real)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ F X2) (@ F Y)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X4)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ G X3)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X2)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 5.98/6.38 (assert (forall ((Z tptp.real) (R tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R))) (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) R))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) (@ F X3)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L4 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ F X3) N3))) (@ (@ F4 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X4)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L4) (=> (forall ((N3 tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X4) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L4 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (@ F X3)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A2)))))
% 5.98/6.38 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X4) N4)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R2)) R2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ F N4)) (@ (@ tptp.power_power_real X3) (@ tptp.suc N4))))))) (@ tptp.suminf_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N4)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))) (@ (@ tptp.power_power_real X0) N4))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 5.98/6.38 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 5.98/6.38 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 5.98/6.38 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H) T3) (@ (@ tptp.ord_less_eq_real T3) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real H) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 5.98/6.38 (assert (forall ((H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N)))))))))))
% 5.98/6.38 (assert (forall ((H tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) H) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H) N))))))))))))
% 5.98/6.38 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 5.98/6.38 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (=> (not (= X2 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T3) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T3) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N))))))))))))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real C) T3) (@ (@ tptp.ord_less_real T3) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T3) (@ (@ tptp.ord_less_eq_real T3) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real A) T3) (@ (@ tptp.ord_less_real T3) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T3)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M4 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U3 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U3) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U3) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T4) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T4) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (forall ((X tptp.real)) (=> (and (not (= X C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X))) R4)) (@ (@ tptp.ord_less_real (@ F X)) tptp.zero_zero_real)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (forall ((X tptp.real)) (=> (and (not (= X C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X))) R4)) (not (= (@ F X) tptp.zero_zero_real))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (forall ((X tptp.real)) (=> (and (not (= X C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X))) R4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (@ tptp.root N))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.sqrt)))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (exists ((L5 tptp.real) (M9 tptp.real)) (and (forall ((X tptp.real)) (let ((_let_1 (@ F X))) (=> (and (@ (@ tptp.ord_less_eq_real A) X) (@ (@ tptp.ord_less_eq_real X) B)) (and (@ (@ tptp.ord_less_eq_real L5) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L5) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B) (= (@ F X4) Y4)))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (not (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.archim2898591450579166408c_real))))
% 5.98/6.38 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.ln_ln_real))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X3)) (@ tptp.sin_real X3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (not (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (@ (@ tptp.comp_int_real_real tptp.ring_1_of_int_real) tptp.archim6058952711729229775r_real)))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X2)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 5.98/6.38 (assert (forall ((B tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 5.98/6.38 (assert (forall ((D tptp.real) (X2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X2))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I3))) B4)) (not (forall ((L5 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat))))))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N4)) (@ G N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L3)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 5.98/6.38 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R4 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R4) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.root N4) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 5.98/6.38 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X2) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 5.98/6.38 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N4)))) N4))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 5.98/6.38 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4))))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N4)) (@ A N4)))))))))
% 5.98/6.38 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 5.98/6.38 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L3))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)))) L3)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4))))) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 5.98/6.38 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 5.98/6.38 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C2)))))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 5.98/6.38 (assert (= tptp.real_V975177566351809787t_real (lambda ((X3 tptp.real) (Y2 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y2)))))
% 5.98/6.38 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X3 tptp.complex) (Y2 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y2)))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_bot_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5984915006950818249n_real tptp.zero_zero_real))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 5.98/6.38 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_bot_real) F5))))))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y2)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 5.98/6.38 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 5.98/6.38 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 5.98/6.38 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 5.98/6.38 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 5.98/6.38 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 5.98/6.38 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_top_real) F5))))))
% 5.98/6.38 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_top_real) tptp.at_top_nat))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_top_real) tptp.at_bot_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.uminus_uminus_real) tptp.at_bot_real) tptp.at_top_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) X3))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_top_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 5.98/6.38 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) K)) (@ tptp.exp_real X3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 5.98/6.38 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y2 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) Y2))) Y2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_real)))
% 5.98/6.38 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X4) (exists ((Y4 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 5.98/6.38 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M3 tptp.nat)) (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D3) M3))))) M7)))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D3) N)))) N))))
% 5.98/6.38 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 5.98/6.38 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_infinity_real) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S))))))
% 5.98/6.38 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X5 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X5 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X5)))))
% 5.98/6.38 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N4)) M3))))))))
% 5.98/6.38 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N4) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D3 tptp.int)) (@ (@ tptp.dvd_dvd_int D3) N)))) (@ tptp.abs_abs_int N)))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N4) (@ P N4)))))))
% 5.98/6.38 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X4) (@ P X4))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F5)))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 5.98/6.38 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M) N) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D3))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X3) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real A))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.uminus_uminus_real X3)))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))))
% 5.98/6.38 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 5.98/6.38 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) tptp.at_top_real))))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) tptp.at_top_real) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F5) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_top_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_top_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_1) tptp.at_top_real)))))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 5.98/6.38 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G0 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X3)) (@ G0 X3)))) F5) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F5) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) F5) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F5) _let_1))))))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A)))) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_top_real) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_bot_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) tptp.at_bot_real) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) tptp.at_bot_real) _let_1)))))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 5.98/6.38 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F4 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 5.98/6.38 (assert (@ (@ (@ tptp.filterlim_nat_int tptp.semiri1314217659103216013at_int) tptp.at_top_int) tptp.at_top_nat))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 5.98/6.38 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X5 tptp.real)) (@ P X5)))))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X2) Y) Y)))
% 5.98/6.38 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X2) Y) X2)))
% 5.98/6.38 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 5.98/6.38 (assert (forall ((X2 tptp.produc8923325533196201883nt/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 16192 Alarm clock ( read result; case "$result" in
% 299.35/300.13 unsat)
% 299.35/300.13 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.35/300.13 ;;
% 299.35/300.13 sat)
% 299.35/300.13 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.35/300.13 ;;
% 299.35/300.13 esac; exit 1 )
% 299.35/300.14 Alarm clock
% 299.35/300.14 % cvc5---1.0.5 exiting
% 299.35/300.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------